diff options
158 files changed, 2239 insertions, 1117 deletions
diff --git a/Makefile.in b/Makefile.in index e96173a..5f27eef 100644 --- a/Makefile.in +++ b/Makefile.in @@ -3,7 +3,7 @@ #Tom St Denis #version of library -VERSION=0.35 +VERSION=0.40 VPATH=@srcdir@ srcdir=@srcdir@ @@ -13,6 +13,8 @@ CFLAGS += -I$(srcdir) #CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare +ifndef IGNORE_SPEED + #for speed #CFLAGS += -O3 -funroll-all-loops @@ -26,13 +28,25 @@ CFLAGS += -I$(srcdir) #CFLAGS += -g3 #install as this user -USER=root -GROUP=root - -default: libtommath.a +ifndef INSTALL_GROUP + GROUP=wheel +else + GROUP=$(INSTALL_GROUP) +endif + +ifndef INSTALL_USER + USER=root +else + USER=$(INSTALL_USER) +endif #default files to install -LIBNAME=libtommath.a +ifndef LIBNAME + LIBNAME=libtommath.a +endif + +default: ${LIBNAME} + HEADERS=tommath.h tommath_class.h tommath_superclass.h #LIBPATH-The directory for libtommath to be installed to. @@ -71,9 +85,9 @@ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_ini bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o -libtommath.a: $(OBJECTS) - $(AR) $(ARFLAGS) libtommath.a $(OBJECTS) - $(RANLIB) libtommath.a +$(LIBNAME): $(OBJECTS) + $(AR) $(ARFLAGS) $@ $(OBJECTS) + ranlib $@ #make a profiled library (takes a while!!!) # @@ -95,27 +109,27 @@ profiled_single: ./ltmtest rm -f *.o ltmtest $(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o - $(AR) $(ARFLAGS) libtommath.a mpi.o - ranlib libtommath.a + $(AR) $(ARFLAGS) $(LIBNAME) mpi.o + ranlib $(LIBNAME) -install: libtommath.a +install: $(LIBNAME) install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH) install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH) install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH) install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH) -test: libtommath.a demo/demo.o - $(CC) $(CFLAGS) demo/demo.o libtommath.a -o test +test: $(LIBNAME) demo/demo.o + $(CC) $(CFLAGS) demo/demo.o $(LIBNAME) -o test mtest: test cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest -timing: libtommath.a - $(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest +timing: $(LIBNAME) + $(CC) $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o ltmtest # makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think] docdvi: tommath.src - cd pics ; make + cd pics ; MAKE=${MAKE} ${MAKE} echo "hello" > tommath.ind perl booker.pl latex tommath > /dev/null @@ -132,7 +146,7 @@ poster: poster.tex docs: docdvi dvipdf tommath rm -f tommath.log tommath.aux tommath.dvi tommath.idx tommath.toc tommath.lof tommath.ind tommath.ilg - cd pics ; make clean + cd pics ; MAKE=${MAKE} ${MAKE} clean #LTM user manual mandvi: bn.tex @@ -152,14 +166,21 @@ pretty: clean: rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \ - *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex *.lo *.la + *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la rm -rf .libs - cd etc && make clean - cd pics && make clean + cd etc ; MAKE=${MAKE} ${MAKE} clean + cd pics ; MAKE=${MAKE} ${MAKE} clean + +#zipup the project (take that!) +no_oops: clean + cd .. ; cvs commit + echo Scanning for scratch/dirty files + find . -type f | grep -v CVS | xargs -n 1 bash mess.sh zipup: clean manual poster docs perl gen.pl ; mv mpi.c pre_gen/ ; \ cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \ cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; \ tar -c libtommath-$(VERSION)/* | bzip2 -9vvc > ltm-$(VERSION).tar.bz2 ; \ - zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/* + zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/* ; \ + mv -f ltm* ~ ; rm -rf libtommath-$(VERSION) @@ -1,16 +0,0 @@ -things for book in order of importance... - -- Fix up pseudo-code [only] for combas that are not consistent with source -- Start in chapter 3 [basics] and work up... - - re-write to prose [less abrupt] - - clean up pseudo code [spacing] - - more examples where appropriate and figures - -Goal: - - Get sync done by mid January [roughly 8-12 hours work] - - Finish ch3-6 by end of January [roughly 12-16 hours of work] - - Finish ch7-end by mid Feb [roughly 20-24 hours of work]. - -Goal isn't "first edition" but merely cleaner to read. - - @@ -1,4 +1,4 @@ -\documentclass[b5paper]{book} +\documentclass[synpaper]{book} \usepackage{hyperref} \usepackage{makeidx} \usepackage{amssymb} @@ -49,8 +49,8 @@ \begin{document} \frontmatter \pagestyle{empty} -\title{LibTomMath User Manual \\ v0.35} -\author{Tom St Denis \\ tomstdenis@iahu.ca} +\title{LibTomMath User Manual \\ v0.40} +\author{Tom St Denis \\ tomstdenis@gmail.com} \maketitle This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package. @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ static const struct { @@ -41,3 +41,7 @@ char *mp_error_to_string(int code) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_error.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_fast_mp_invmod.c b/bn_fast_mp_invmod.c index acc8364..1974145 100644 --- a/bn_fast_mp_invmod.c +++ b/bn_fast_mp_invmod.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes the modular inverse via binary extended euclidean algorithm, @@ -142,3 +142,7 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_fast_mp_montgomery_reduce.c b/bn_fast_mp_montgomery_reduce.c index 14f307f..13538c8 100644 --- a/bn_fast_mp_montgomery_reduce.c +++ b/bn_fast_mp_montgomery_reduce.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes xR**-1 == x (mod N) via Montgomery Reduction @@ -166,3 +166,7 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_fast_s_mp_mul_digs.c b/bn_fast_s_mp_mul_digs.c index df3da26..8e2e069 100644 --- a/bn_fast_s_mp_mul_digs.c +++ b/bn_fast_s_mp_mul_digs.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Fast (comba) multiplier @@ -70,6 +70,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) /* execute loop */ for (iz = 0; iz < iy; ++iz) { _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); + } /* store term */ @@ -77,10 +78,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) /* make next carry */ _W = _W >> ((mp_word)DIGIT_BIT); - } - - /* store final carry */ - W[ix] = (mp_digit)(_W & MP_MASK); + } /* setup dest */ olduse = c->used; @@ -103,3 +101,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_digs.c,v $ */ +/* $Revision: 1.7 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_fast_s_mp_mul_high_digs.c b/bn_fast_s_mp_mul_high_digs.c index ee657f9..4778b2f 100644 --- a/bn_fast_s_mp_mul_high_digs.c +++ b/bn_fast_s_mp_mul_high_digs.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* this is a modified version of fast_s_mul_digs that only produces @@ -70,9 +70,6 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) _W = _W >> ((mp_word)DIGIT_BIT); } - /* store final carry */ - W[ix] = (mp_digit)(_W & MP_MASK); - /* setup dest */ olduse = c->used; c->used = pa; @@ -81,7 +78,7 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) register mp_digit *tmpc; tmpc = c->dp + digs; - for (ix = digs; ix <= pa; ix++) { + for (ix = digs; ix < pa; ix++) { /* now extract the previous digit [below the carry] */ *tmpc++ = W[ix]; } @@ -95,3 +92,7 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_high_digs.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/11/14 03:46:25 $ */ diff --git a/bn_fast_s_mp_sqr.c b/bn_fast_s_mp_sqr.c index 66a2942..bb5974c 100644 --- a/bn_fast_s_mp_sqr.c +++ b/bn_fast_s_mp_sqr.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* the jist of squaring... @@ -108,3 +108,7 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_sqr.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_2expt.c b/bn_mp_2expt.c index 45a6818..9e5f32e 100644 --- a/bn_mp_2expt.c +++ b/bn_mp_2expt.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes a = 2**b @@ -42,3 +42,7 @@ mp_2expt (mp_int * a, int b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_2expt.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_abs.c b/bn_mp_abs.c index 34f810f..9643c5e 100644 --- a/bn_mp_abs.c +++ b/bn_mp_abs.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* b = |a| @@ -37,3 +37,7 @@ mp_abs (mp_int * a, mp_int * b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_abs.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_add.c b/bn_mp_add.c index 554b7f7..a90eef6 100644 --- a/bn_mp_add.c +++ b/bn_mp_add.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* high level addition (handles signs) */ @@ -47,3 +47,7 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_add.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_add_d.c b/bn_mp_add_d.c index bdd0280..5af5aa9 100644 --- a/bn_mp_add_d.c +++ b/bn_mp_add_d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* single digit addition */ @@ -40,6 +40,9 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c) /* fix sign */ a->sign = c->sign = MP_NEG; + /* clamp */ + mp_clamp(c); + return res; } @@ -103,3 +106,7 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_add_d.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_addmod.c b/bn_mp_addmod.c index 13eb33f..d3b3ac4 100644 --- a/bn_mp_addmod.c +++ b/bn_mp_addmod.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* d = a + b (mod c) */ @@ -35,3 +35,7 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_addmod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_and.c b/bn_mp_and.c index 61dc386..9a2c0ee 100644 --- a/bn_mp_and.c +++ b/bn_mp_and.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* AND two ints together */ @@ -51,3 +51,7 @@ mp_and (mp_int * a, mp_int * b, mp_int * c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_and.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_clamp.c b/bn_mp_clamp.c index c172611..da4e1ef 100644 --- a/bn_mp_clamp.c +++ b/bn_mp_clamp.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* trim unused digits @@ -38,3 +38,7 @@ mp_clamp (mp_int * a) } } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_clamp.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_clear.c b/bn_mp_clear.c index 1dc053b..000bd06 100644 --- a/bn_mp_clear.c +++ b/bn_mp_clear.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* clear one (frees) */ @@ -41,3 +41,7 @@ mp_clear (mp_int * a) } } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_clear.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_clear_multi.c b/bn_mp_clear_multi.c index 24cbe73..e1859be 100644 --- a/bn_mp_clear_multi.c +++ b/bn_mp_clear_multi.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ #include <stdarg.h> @@ -28,3 +28,7 @@ void mp_clear_multi(mp_int *mp, ...) va_end(args); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_clear_multi.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_cmp.c b/bn_mp_cmp.c index 583b5f8..f4e2af7 100644 --- a/bn_mp_cmp.c +++ b/bn_mp_cmp.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* compare two ints (signed)*/ @@ -37,3 +37,7 @@ mp_cmp (mp_int * a, mp_int * b) } } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_cmp.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_cmp_d.c b/bn_mp_cmp_d.c index 882b1c9..20a19bc 100644 --- a/bn_mp_cmp_d.c +++ b/bn_mp_cmp_d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* compare a digit */ @@ -38,3 +38,7 @@ int mp_cmp_d(mp_int * a, mp_digit b) } } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_cmp_mag.c b/bn_mp_cmp_mag.c index a0f351c..5dc7a3f 100644 --- a/bn_mp_cmp_mag.c +++ b/bn_mp_cmp_mag.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* compare maginitude of two ints (unsigned) */ @@ -49,3 +49,7 @@ int mp_cmp_mag (mp_int * a, mp_int * b) return MP_EQ; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_mag.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_cnt_lsb.c b/bn_mp_cnt_lsb.c index 571f03f..017b990 100644 --- a/bn_mp_cnt_lsb.c +++ b/bn_mp_cnt_lsb.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ static const int lnz[16] = { @@ -47,3 +47,7 @@ int mp_cnt_lsb(mp_int *a) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_cnt_lsb.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_copy.c b/bn_mp_copy.c index 183ec9b..d820397 100644 --- a/bn_mp_copy.c +++ b/bn_mp_copy.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* copy, b = a */ @@ -62,3 +62,7 @@ mp_copy (mp_int * a, mp_int * b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_copy.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_count_bits.c b/bn_mp_count_bits.c index f3f85ac..ff4db22 100644 --- a/bn_mp_count_bits.c +++ b/bn_mp_count_bits.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* returns the number of bits in an int */ @@ -39,3 +39,7 @@ mp_count_bits (mp_int * a) return r; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_count_bits.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_div.c b/bn_mp_div.c index 6b2b8f0..8bd1029 100644 --- a/bn_mp_div.c +++ b/bn_mp_div.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ #ifdef BN_MP_DIV_SMALL @@ -286,3 +286,7 @@ LBL_Q:mp_clear (&q); #endif #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_div.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_div_2.c b/bn_mp_div_2.c index 5777997..0035e56 100644 --- a/bn_mp_div_2.c +++ b/bn_mp_div_2.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* b = a/2 */ @@ -62,3 +62,7 @@ int mp_div_2(mp_int * a, mp_int * b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_div_2.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_div_2d.c b/bn_mp_div_2d.c index cf103f2..6c18d80 100644 --- a/bn_mp_div_2d.c +++ b/bn_mp_div_2d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ @@ -91,3 +91,7 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_div_2d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_div_3.c b/bn_mp_div_3.c index 7cbafc1..c6090f4 100644 --- a/bn_mp_div_3.c +++ b/bn_mp_div_3.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* divide by three (based on routine from MPI and the GMP manual) */ @@ -73,3 +73,7 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_div_3.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_div_d.c b/bn_mp_div_d.c index 9b58aa6..771aa6a 100644 --- a/bn_mp_div_d.c +++ b/bn_mp_div_d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ static int s_is_power_of_two(mp_digit b, int *p) @@ -104,3 +104,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_div_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_dr_is_modulus.c b/bn_mp_dr_is_modulus.c index 5ef78a3..e9223f3 100644 --- a/bn_mp_dr_is_modulus.c +++ b/bn_mp_dr_is_modulus.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines if a number is a valid DR modulus */ @@ -37,3 +37,7 @@ int mp_dr_is_modulus(mp_int *a) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_dr_is_modulus.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_dr_reduce.c b/bn_mp_dr_reduce.c index 9bb7ad7..d2ef18f 100644 --- a/bn_mp_dr_reduce.c +++ b/bn_mp_dr_reduce.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reduce "x" in place modulo "n" using the Diminished Radix algorithm. @@ -88,3 +88,7 @@ top: return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_dr_reduce.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_dr_setup.c b/bn_mp_dr_setup.c index 029d310..3e82c9b 100644 --- a/bn_mp_dr_setup.c +++ b/bn_mp_dr_setup.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines the setup value */ @@ -26,3 +26,7 @@ void mp_dr_setup(mp_int *a, mp_digit *d) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_dr_setup.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_exch.c b/bn_mp_exch.c index 0ef485a..81a42ac 100644 --- a/bn_mp_exch.c +++ b/bn_mp_exch.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* swap the elements of two integers, for cases where you can't simply swap the @@ -28,3 +28,7 @@ mp_exch (mp_int * a, mp_int * b) *b = t; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_exch.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_expt_d.c b/bn_mp_expt_d.c index fdb8bd9..656cf68 100644 --- a/bn_mp_expt_d.c +++ b/bn_mp_expt_d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* calculate c = a**b using a square-multiply algorithm */ @@ -51,3 +51,7 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_expt_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_exptmod.c b/bn_mp_exptmod.c index 7c4e2f8..d72ab20 100644 --- a/bn_mp_exptmod.c +++ b/bn_mp_exptmod.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ @@ -66,7 +66,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) } /* modified diminished radix reduction */ -#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) +#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C) if (mp_reduce_is_2k_l(P) == MP_YES) { return s_mp_exptmod(G, X, P, Y, 1); } @@ -106,3 +106,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_exptmod_fast.c b/bn_mp_exptmod_fast.c index 82be9ac..32f8f16 100644 --- a/bn_mp_exptmod_fast.c +++ b/bn_mp_exptmod_fast.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 @@ -315,3 +315,7 @@ LBL_M: } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod_fast.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_exteuclid.c b/bn_mp_exteuclid.c index c4ebab4..25ccba9 100644 --- a/bn_mp_exteuclid.c +++ b/bn_mp_exteuclid.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Extended euclidean algorithm of (a, b) produces @@ -76,3 +76,7 @@ _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL return err; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_exteuclid.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_fread.c b/bn_mp_fread.c index 293df3f..c3bd08d 100644 --- a/bn_mp_fread.c +++ b/bn_mp_fread.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* read a bigint from a file stream in ASCII */ @@ -61,3 +61,7 @@ int mp_fread(mp_int *a, int radix, FILE *stream) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_fread.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_fwrite.c b/bn_mp_fwrite.c index 8fa3129..006f923 100644 --- a/bn_mp_fwrite.c +++ b/bn_mp_fwrite.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ int mp_fwrite(mp_int *a, int radix, FILE *stream) @@ -46,3 +46,7 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_fwrite.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_gcd.c b/bn_mp_gcd.c index 6265df1..23f6b02 100644 --- a/bn_mp_gcd.c +++ b/bn_mp_gcd.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Greatest Common Divisor using the binary method */ @@ -22,21 +22,13 @@ int mp_gcd (mp_int * a, mp_int * b, mp_int * c) int k, u_lsb, v_lsb, res; /* either zero than gcd is the largest */ - if (mp_iszero (a) == 1 && mp_iszero (b) == 0) { + if (mp_iszero (a) == MP_YES) { return mp_abs (b, c); } - if (mp_iszero (a) == 0 && mp_iszero (b) == 1) { + if (mp_iszero (b) == MP_YES) { return mp_abs (a, c); } - /* optimized. At this point if a == 0 then - * b must equal zero too - */ - if (mp_iszero (a) == 1) { - mp_zero(c); - return MP_OKAY; - } - /* get copies of a and b we can modify */ if ((res = mp_init_copy (&u, a)) != MP_OKAY) { return res; @@ -107,3 +99,7 @@ LBL_U:mp_clear (&v); return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_gcd.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_get_int.c b/bn_mp_get_int.c index 034467b..7948d46 100644 --- a/bn_mp_get_int.c +++ b/bn_mp_get_int.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* get the lower 32-bits of an mp_int */ @@ -39,3 +39,7 @@ unsigned long mp_get_int(mp_int * a) return res & 0xFFFFFFFFUL; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_get_int.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_grow.c b/bn_mp_grow.c index 12a78a8..2d50058 100644 --- a/bn_mp_grow.c +++ b/bn_mp_grow.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* grow as required */ @@ -51,3 +51,7 @@ int mp_grow (mp_int * a, int size) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_grow.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_init.c b/bn_mp_init.c index 9d70554..565ea47 100644 --- a/bn_mp_init.c +++ b/bn_mp_init.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* init a new mp_int */ @@ -40,3 +40,7 @@ int mp_init (mp_int * a) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_init.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_init_copy.c b/bn_mp_init_copy.c index b1b0fa2..8e7329c 100644 --- a/bn_mp_init_copy.c +++ b/bn_mp_init_copy.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* creates "a" then copies b into it */ @@ -26,3 +26,7 @@ int mp_init_copy (mp_int * a, mp_int * b) return mp_copy (b, a); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_init_copy.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_init_multi.c b/bn_mp_init_multi.c index 8cb123a..d592f43 100644 --- a/bn_mp_init_multi.c +++ b/bn_mp_init_multi.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ #include <stdarg.h> @@ -53,3 +53,7 @@ int mp_init_multi(mp_int *mp, ...) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_init_multi.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_init_set.c b/bn_mp_init_set.c index 0251e61..a7ee8f7 100644 --- a/bn_mp_init_set.c +++ b/bn_mp_init_set.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* initialize and set a digit */ @@ -26,3 +26,7 @@ int mp_init_set (mp_int * a, mp_digit b) return err; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_init_set.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_init_set_int.c b/bn_mp_init_set_int.c index f59fd19..7c9dd46 100644 --- a/bn_mp_init_set_int.c +++ b/bn_mp_init_set_int.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* initialize and set a digit */ @@ -25,3 +25,7 @@ int mp_init_set_int (mp_int * a, unsigned long b) return mp_set_int(a, b); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_init_set_int.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_init_size.c b/bn_mp_init_size.c index 845ce2c..4aebd1f 100644 --- a/bn_mp_init_size.c +++ b/bn_mp_init_size.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* init an mp_init for a given size */ @@ -42,3 +42,7 @@ int mp_init_size (mp_int * a, int size) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_init_size.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_invmod.c b/bn_mp_invmod.c index 46118ad..3f5791f 100644 --- a/bn_mp_invmod.c +++ b/bn_mp_invmod.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* hac 14.61, pp608 */ @@ -37,3 +37,7 @@ int mp_invmod (mp_int * a, mp_int * b, mp_int * c) return MP_VAL; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_invmod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_invmod_slow.c b/bn_mp_invmod_slow.c index c048655..a4e4fbc 100644 --- a/bn_mp_invmod_slow.c +++ b/bn_mp_invmod_slow.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* hac 14.61, pp608 */ @@ -169,3 +169,7 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_invmod_slow.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_is_square.c b/bn_mp_is_square.c index 969d237..a235d97 100644 --- a/bn_mp_is_square.c +++ b/bn_mp_is_square.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Check if remainders are possible squares - fast exclude non-squares */ @@ -103,3 +103,7 @@ ERR:mp_clear(&t); return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_is_square.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_jacobi.c b/bn_mp_jacobi.c index 74cbbf3..2e88fd4 100644 --- a/bn_mp_jacobi.c +++ b/bn_mp_jacobi.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes the jacobi c = (a | n) (or Legendre if n is prime) @@ -99,3 +99,7 @@ LBL_A1:mp_clear (&a1); return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_jacobi.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_karatsuba_mul.c b/bn_mp_karatsuba_mul.c index daa78c7..35dc9a4 100644 --- a/bn_mp_karatsuba_mul.c +++ b/bn_mp_karatsuba_mul.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* c = |a| * |b| using Karatsuba Multiplication using @@ -26,12 +26,12 @@ * b = b1 * B**n + b0 * * Then, a * b => - a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0 + a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 * * Note that a1b1 and a0b0 are used twice and only need to be * computed once. So in total three half size (half # of * digit) multiplications are performed, a0b0, a1b1 and - * (a1-b1)(a0-b0) + * (a1+b1)(a0+b0) * * Note that a multiplication of half the digits requires * 1/4th the number of single precision multiplications so in @@ -122,19 +122,19 @@ int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c) if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) goto X1Y1; /* x1y1 = x1*y1 */ - /* now calc x1-x0 and y1-y0 */ - if (mp_sub (&x1, &x0, &t1) != MP_OKAY) + /* now calc x1+x0 and y1+y0 */ + if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = x1 - x0 */ - if (mp_sub (&y1, &y0, &x0) != MP_OKAY) + if (s_mp_add (&y1, &y0, &x0) != MP_OKAY) goto X1Y1; /* t2 = y1 - y0 */ if (mp_mul (&t1, &x0, &t1) != MP_OKAY) - goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */ + goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ /* add x0y0 */ if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) goto X1Y1; /* t2 = x0y0 + x1y1 */ - if (mp_sub (&x0, &t1, &t1) != MP_OKAY) - goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */ + if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY) + goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) @@ -161,3 +161,7 @@ ERR: return err; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_mul.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_karatsuba_sqr.c b/bn_mp_karatsuba_sqr.c index 315ceab..6d8ad6e 100644 --- a/bn_mp_karatsuba_sqr.c +++ b/bn_mp_karatsuba_sqr.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Karatsuba squaring, computes b = a*a using three @@ -80,8 +80,8 @@ int mp_karatsuba_sqr (mp_int * a, mp_int * b) if (mp_sqr (&x1, &x1x1) != MP_OKAY) goto X1X1; /* x1x1 = x1*x1 */ - /* now calc (x1-x0)**2 */ - if (mp_sub (&x1, &x0, &t1) != MP_OKAY) + /* now calc (x1+x0)**2 */ + if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) goto X1X1; /* t1 = x1 - x0 */ if (mp_sqr (&t1, &t1) != MP_OKAY) goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ @@ -89,8 +89,8 @@ int mp_karatsuba_sqr (mp_int * a, mp_int * b) /* add x0y0 */ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) goto X1X1; /* t2 = x0x0 + x1x1 */ - if (mp_sub (&t2, &t1, &t1) != MP_OKAY) - goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */ + if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY) + goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) @@ -115,3 +115,7 @@ ERR: return err; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_sqr.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_lcm.c b/bn_mp_lcm.c index 8e3a759..48b2b63 100644 --- a/bn_mp_lcm.c +++ b/bn_mp_lcm.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes least common multiple as |a*b|/(a, b) */ @@ -54,3 +54,7 @@ LBL_T: return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_lcm.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_lshd.c b/bn_mp_lshd.c index 398b648..ca9b853 100644 --- a/bn_mp_lshd.c +++ b/bn_mp_lshd.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shift left a certain amount of digits */ @@ -61,3 +61,7 @@ int mp_lshd (mp_int * a, int b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_lshd.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_mod.c b/bn_mp_mod.c index 75779bb..be1f36d 100644 --- a/bn_mp_mod.c +++ b/bn_mp_mod.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* c = a mod b, 0 <= c < b */ @@ -42,3 +42,7 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c) return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_mod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_mod_2d.c b/bn_mp_mod_2d.c index 589e4ba..461b1b2 100644 --- a/bn_mp_mod_2d.c +++ b/bn_mp_mod_2d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* calc a value mod 2**b */ @@ -49,3 +49,7 @@ mp_mod_2d (mp_int * a, int b, mp_int * c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_mod_2d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_mod_d.c b/bn_mp_mod_d.c index 8a2ad24..8bc499b 100644 --- a/bn_mp_mod_d.c +++ b/bn_mp_mod_d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ int @@ -21,3 +21,7 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) return mp_div_d(a, b, NULL, c); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_mod_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_montgomery_calc_normalization.c b/bn_mp_montgomery_calc_normalization.c index e2efc34..91eb5fe 100644 --- a/bn_mp_montgomery_calc_normalization.c +++ b/bn_mp_montgomery_calc_normalization.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* @@ -53,3 +53,7 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_montgomery_reduce.c b/bn_mp_montgomery_reduce.c index 3095fa7..a121d2a 100644 --- a/bn_mp_montgomery_reduce.c +++ b/bn_mp_montgomery_reduce.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes xR**-1 == x (mod N) via Montgomery Reduction */ @@ -112,3 +112,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_reduce.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_montgomery_setup.c b/bn_mp_montgomery_setup.c index 9dfc087..0dc800e 100644 --- a/bn_mp_montgomery_setup.c +++ b/bn_mp_montgomery_setup.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* setups the montgomery reduction stuff */ @@ -48,8 +48,12 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho) #endif /* rho = -1/m mod b */ - *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; + *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/12/04 21:34:03 $ */ diff --git a/bn_mp_mul.c b/bn_mp_mul.c index f9cfa09..f941a1a 100644 --- a/bn_mp_mul.c +++ b/bn_mp_mul.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* high level multiplication (handles sign) */ @@ -60,3 +60,7 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c) return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_mul.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_mul_2.c b/bn_mp_mul_2.c index 6936681..0d27a9d 100644 --- a/bn_mp_mul_2.c +++ b/bn_mp_mul_2.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* b = a*2 */ @@ -76,3 +76,7 @@ int mp_mul_2(mp_int * a, mp_int * b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_mul_2d.c b/bn_mp_mul_2d.c index 04cb8dd..d803bf4 100644 --- a/bn_mp_mul_2d.c +++ b/bn_mp_mul_2d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shift left by a certain bit count */ @@ -79,3 +79,7 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_mul_d.c b/bn_mp_mul_d.c index 9e11eef..a6324aa 100644 --- a/bn_mp_mul_d.c +++ b/bn_mp_mul_d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* multiply by a digit */ @@ -73,3 +73,7 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_mul_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_mulmod.c b/bn_mp_mulmod.c index d34e90a..46818b6 100644 --- a/bn_mp_mulmod.c +++ b/bn_mp_mulmod.c @@ -12,12 +12,11 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* d = a * b (mod c) */ -int -mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) +int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) { int res; mp_int t; @@ -35,3 +34,7 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_mulmod.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_n_root.c b/bn_mp_n_root.c index 7b11aa2..c154016 100644 --- a/bn_mp_n_root.c +++ b/bn_mp_n_root.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* find the n'th root of an integer @@ -126,3 +126,7 @@ LBL_T1:mp_clear (&t1); return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_n_root.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_neg.c b/bn_mp_neg.c index 159cd74..0db9b40 100644 --- a/bn_mp_neg.c +++ b/bn_mp_neg.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* b = -a */ @@ -34,3 +34,7 @@ int mp_neg (mp_int * a, mp_int * b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_neg.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* OR two ints together */ @@ -44,3 +44,7 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_or.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_prime_fermat.c b/bn_mp_prime_fermat.c index fd74dbe..1869867 100644 --- a/bn_mp_prime_fermat.c +++ b/bn_mp_prime_fermat.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* performs one Fermat test. @@ -56,3 +56,7 @@ LBL_T:mp_clear (&t); return err; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_fermat.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_prime_is_divisible.c b/bn_mp_prime_is_divisible.c index f85fe7c..d065451 100644 --- a/bn_mp_prime_is_divisible.c +++ b/bn_mp_prime_is_divisible.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines if an integers is divisible by one @@ -44,3 +44,7 @@ int mp_prime_is_divisible (mp_int * a, int *result) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_divisible.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_prime_is_prime.c b/bn_mp_prime_is_prime.c index 188053a..d93d46a 100644 --- a/bn_mp_prime_is_prime.c +++ b/bn_mp_prime_is_prime.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* performs a variable number of rounds of Miller-Rabin @@ -77,3 +77,7 @@ LBL_B:mp_clear (&b); return err; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_prime.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_prime_miller_rabin.c b/bn_mp_prime_miller_rabin.c index 758a2c3..9bd6ba1 100644 --- a/bn_mp_prime_miller_rabin.c +++ b/bn_mp_prime_miller_rabin.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Miller-Rabin test of "a" to the base of "b" as described in @@ -97,3 +97,7 @@ LBL_N1:mp_clear (&n1); return err; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_miller_rabin.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_prime_next_prime.c b/bn_mp_prime_next_prime.c index 24f93c4..a2da345 100644 --- a/bn_mp_prime_next_prime.c +++ b/bn_mp_prime_next_prime.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* finds the next prime after the number "a" using "t" trials @@ -164,3 +164,7 @@ LBL_ERR: } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_next_prime.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_prime_rabin_miller_trials.c b/bn_mp_prime_rabin_miller_trials.c index d1d0867..140b254 100644 --- a/bn_mp_prime_rabin_miller_trials.c +++ b/bn_mp_prime_rabin_miller_trials.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ @@ -46,3 +46,7 @@ int mp_prime_rabin_miller_trials(int size) #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_rabin_miller_trials.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_prime_random_ex.c b/bn_mp_prime_random_ex.c index 78c0583..cde7a38 100644 --- a/bn_mp_prime_random_ex.c +++ b/bn_mp_prime_random_ex.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* makes a truly random prime of a given size (bits), @@ -62,10 +62,8 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback maskOR_msb = 0; maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; if (flags & LTM_PRIME_2MSB_ON) { - maskOR_msb |= 1 << ((size - 2) & 7); - } else if (flags & LTM_PRIME_2MSB_OFF) { - maskAND &= ~(1 << ((size - 2) & 7)); - } + maskOR_msb |= 0x80 >> ((9 - size) & 7); + } /* get the maskOR_lsb */ maskOR_lsb = 1; @@ -121,3 +119,7 @@ error: #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_random_ex.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_radix_size.c b/bn_mp_radix_size.c index 3d423ba..c9e8822 100644 --- a/bn_mp_radix_size.c +++ b/bn_mp_radix_size.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* returns size of ASCII reprensentation */ @@ -36,7 +36,7 @@ int mp_radix_size (mp_int * a, int radix, int *size) } if (mp_iszero(a) == MP_YES) { - *size = 2; + *size = 2; return MP_OKAY; } @@ -72,3 +72,7 @@ int mp_radix_size (mp_int * a, int radix, int *size) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_radix_size.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_radix_smap.c b/bn_mp_radix_smap.c index bc7517d..58c3a5e 100644 --- a/bn_mp_radix_smap.c +++ b/bn_mp_radix_smap.c @@ -12,9 +12,13 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* chars used in radix conversions */ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_radix_smap.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_rand.c b/bn_mp_rand.c index 0dc7019..6c8f3b3 100644 --- a/bn_mp_rand.c +++ b/bn_mp_rand.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* makes a pseudo-random int of a given size */ @@ -49,3 +49,7 @@ mp_rand (mp_int * a, int digits) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_rand.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_read_radix.c b/bn_mp_read_radix.c index 1ec3937..d2119c1 100644 --- a/bn_mp_read_radix.c +++ b/bn_mp_read_radix.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* read a string [ASCII] in a given radix */ @@ -21,6 +21,9 @@ int mp_read_radix (mp_int * a, const char *str, int radix) int y, res, neg; char ch; + /* zero the digit bignum */ + mp_zero(a); + /* make sure the radix is ok */ if (radix < 2 || radix > 64) { return MP_VAL; @@ -76,3 +79,7 @@ int mp_read_radix (mp_int * a, const char *str, int radix) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_read_radix.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_read_signed_bin.c b/bn_mp_read_signed_bin.c index 814d6c1..e3df3c3 100644 --- a/bn_mp_read_signed_bin.c +++ b/bn_mp_read_signed_bin.c @@ -12,12 +12,11 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* read signed bin, big endian, first byte is 0==positive or 1==negative */ -int -mp_read_signed_bin (mp_int * a, unsigned char *b, int c) +int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c) { int res; @@ -36,3 +35,7 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_read_signed_bin.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_read_unsigned_bin.c b/bn_mp_read_unsigned_bin.c index 946457d..0c471ed 100644 --- a/bn_mp_read_unsigned_bin.c +++ b/bn_mp_read_unsigned_bin.c @@ -12,12 +12,11 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reads a unsigned char array, assumes the msb is stored first [big endian] */ -int -mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) +int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c) { int res; @@ -50,3 +49,7 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_read_unsigned_bin.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_reduce.c b/bn_mp_reduce.c index d746445..3f7284a 100644 --- a/bn_mp_reduce.c +++ b/bn_mp_reduce.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reduces x mod m, assumes 0 < x < m**2, mu is @@ -94,3 +94,7 @@ CLEANUP: return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_reduce_2k.c b/bn_mp_reduce_2k.c index 28c3a00..5810696 100644 --- a/bn_mp_reduce_2k.c +++ b/bn_mp_reduce_2k.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reduces a modulo n where n is of the form 2**p - d */ @@ -55,3 +55,7 @@ ERR: } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_reduce_2k_l.c b/bn_mp_reduce_2k_l.c index 1d7e1f0..53b435f 100644 --- a/bn_mp_reduce_2k_l.c +++ b/bn_mp_reduce_2k_l.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reduces a modulo n where n is of the form 2**p - d @@ -56,3 +56,7 @@ ERR: } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_l.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_reduce_2k_setup.c b/bn_mp_reduce_2k_setup.c index 585e1b7..07de0ec 100644 --- a/bn_mp_reduce_2k_setup.c +++ b/bn_mp_reduce_2k_setup.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines the setup value */ @@ -41,3 +41,7 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_reduce_2k_setup_l.c b/bn_mp_reduce_2k_setup_l.c index 810a456..05f0385 100644 --- a/bn_mp_reduce_2k_setup_l.c +++ b/bn_mp_reduce_2k_setup_l.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines the setup value */ @@ -38,3 +38,7 @@ ERR: return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup_l.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_reduce_is_2k.c b/bn_mp_reduce_is_2k.c index 0fb8384..0897b0a 100644 --- a/bn_mp_reduce_is_2k.c +++ b/bn_mp_reduce_is_2k.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines if mp_reduce_2k can be used */ @@ -46,3 +46,7 @@ int mp_reduce_is_2k(mp_int *a) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_reduce_is_2k_l.c b/bn_mp_reduce_is_2k_l.c index ceba0ed..c4b42c9 100644 --- a/bn_mp_reduce_is_2k_l.c +++ b/bn_mp_reduce_is_2k_l.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines if reduce_2k_l can be used */ @@ -38,3 +38,7 @@ int mp_reduce_is_2k_l(mp_int *a) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k_l.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_reduce_setup.c b/bn_mp_reduce_setup.c index 99f158a..5085af0 100644 --- a/bn_mp_reduce_setup.c +++ b/bn_mp_reduce_setup.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* pre-calculate the value required for Barrett reduction @@ -28,3 +28,7 @@ int mp_reduce_setup (mp_int * a, mp_int * b) return mp_div (a, b, a, NULL); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_setup.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_rshd.c b/bn_mp_rshd.c index 913dda6..534bd4d 100644 --- a/bn_mp_rshd.c +++ b/bn_mp_rshd.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shift right a certain amount of digits */ @@ -66,3 +66,7 @@ void mp_rshd (mp_int * a, int b) a->used -= b; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_rshd.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_set.c b/bn_mp_set.c index 078fd5f..a1ebadb 100644 --- a/bn_mp_set.c +++ b/bn_mp_set.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* set to a digit */ @@ -23,3 +23,7 @@ void mp_set (mp_int * a, mp_digit b) a->used = (a->dp[0] != 0) ? 1 : 0; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_set.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_set_int.c b/bn_mp_set_int.c index bd47136..35e844f 100644 --- a/bn_mp_set_int.c +++ b/bn_mp_set_int.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* set a 32-bit const */ @@ -42,3 +42,7 @@ int mp_set_int (mp_int * a, unsigned long b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_set_int.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_shrink.c b/bn_mp_shrink.c index b31f9d2..e676068 100644 --- a/bn_mp_shrink.c +++ b/bn_mp_shrink.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shrink a bignum */ @@ -29,3 +29,7 @@ int mp_shrink (mp_int * a) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_shrink.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_signed_bin_size.c b/bn_mp_signed_bin_size.c index 30048cb..8df0b78 100644 --- a/bn_mp_signed_bin_size.c +++ b/bn_mp_signed_bin_size.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* get the size for an signed equivalent */ @@ -21,3 +21,7 @@ int mp_signed_bin_size (mp_int * a) return 1 + mp_unsigned_bin_size (a); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_signed_bin_size.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_sqr.c b/bn_mp_sqr.c index b1fdb57..bff8a7d 100644 --- a/bn_mp_sqr.c +++ b/bn_mp_sqr.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes b = a*a */ @@ -52,3 +52,7 @@ if (a->used >= KARATSUBA_SQR_CUTOFF) { return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_sqr.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_sqrmod.c b/bn_mp_sqrmod.c index 1923be4..38cbc92 100644 --- a/bn_mp_sqrmod.c +++ b/bn_mp_sqrmod.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* c = a * a (mod b) */ @@ -35,3 +35,7 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c) return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_sqrmod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_sqrt.c b/bn_mp_sqrt.c index 76cec87..4449625 100644 --- a/bn_mp_sqrt.c +++ b/bn_mp_sqrt.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* this function is less generic than mp_n_root, simpler and faster */ @@ -75,3 +75,7 @@ E2: mp_clear(&t1); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_sqrt.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_sub.c b/bn_mp_sub.c index 97495f4..a69d032 100644 --- a/bn_mp_sub.c +++ b/bn_mp_sub.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* high level subtraction (handles signs) */ @@ -53,3 +53,7 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_sub.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_sub_d.c b/bn_mp_sub_d.c index 4923dde..ee77a5a 100644 --- a/bn_mp_sub_d.c +++ b/bn_mp_sub_d.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* single digit subtraction */ @@ -36,6 +36,10 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c) a->sign = MP_ZPOS; res = mp_add_d(a, b, c); a->sign = c->sign = MP_NEG; + + /* clamp */ + mp_clamp(c); + return res; } @@ -83,3 +87,7 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_sub_d.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_submod.c b/bn_mp_submod.c index b999c85..bd24f25 100644 --- a/bn_mp_submod.c +++ b/bn_mp_submod.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* d = a - b (mod c) */ @@ -36,3 +36,7 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) return res; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_submod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_to_signed_bin.c b/bn_mp_to_signed_bin.c index b0a597e..9125d07 100644 --- a/bn_mp_to_signed_bin.c +++ b/bn_mp_to_signed_bin.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* store in signed [big endian] format */ @@ -27,3 +27,7 @@ int mp_to_signed_bin (mp_int * a, unsigned char *b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_to_signed_bin_n.c b/bn_mp_to_signed_bin_n.c index 0f765ee..4e9d217 100644 --- a/bn_mp_to_signed_bin_n.c +++ b/bn_mp_to_signed_bin_n.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* store in signed [big endian] format */ @@ -25,3 +25,7 @@ int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) return mp_to_signed_bin(a, b); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin_n.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_to_unsigned_bin.c b/bn_mp_to_unsigned_bin.c index 000967e..b25935d 100644 --- a/bn_mp_to_unsigned_bin.c +++ b/bn_mp_to_unsigned_bin.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* store in unsigned [big endian] format */ @@ -42,3 +42,7 @@ int mp_to_unsigned_bin (mp_int * a, unsigned char *b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_to_unsigned_bin_n.c b/bn_mp_to_unsigned_bin_n.c index d0256b4..4abf4e1 100644 --- a/bn_mp_to_unsigned_bin_n.c +++ b/bn_mp_to_unsigned_bin_n.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* store in unsigned [big endian] format */ @@ -25,3 +25,7 @@ int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) return mp_to_unsigned_bin(a, b); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin_n.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_toom_mul.c b/bn_mp_toom_mul.c index 125331b..fa29078 100644 --- a/bn_mp_toom_mul.c +++ b/bn_mp_toom_mul.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* multiplication using the Toom-Cook 3-way algorithm @@ -278,3 +278,7 @@ ERR: } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_toom_mul.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_toom_sqr.c b/bn_mp_toom_sqr.c index 8c46fea..093181a 100644 --- a/bn_mp_toom_sqr.c +++ b/bn_mp_toom_sqr.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* squaring using Toom-Cook 3-way algorithm */ @@ -220,3 +220,7 @@ ERR: } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_toom_sqr.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_toradix.c b/bn_mp_toradix.c index a206d5e..c500832 100644 --- a/bn_mp_toradix.c +++ b/bn_mp_toradix.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* stores a bignum as a ASCII string in a given radix (2..64) */ @@ -69,3 +69,7 @@ int mp_toradix (mp_int * a, char *str, int radix) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_toradix.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_toradix_n.c b/bn_mp_toradix_n.c index 7d43558..7c0f3bc 100644 --- a/bn_mp_toradix_n.c +++ b/bn_mp_toradix_n.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* stores a bignum as a ASCII string in a given radix (2..64) @@ -27,12 +27,12 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) char *_s = str; /* check range of the maxlen, radix */ - if (maxlen < 3 || radix < 2 || radix > 64) { + if (maxlen < 2 || radix < 2 || radix > 64) { return MP_VAL; } /* quick out if its zero */ - if (mp_iszero(a) == 1) { + if (mp_iszero(a) == MP_YES) { *str++ = '0'; *str = '\0'; return MP_OKAY; @@ -57,21 +57,20 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) digs = 0; while (mp_iszero (&t) == 0) { + if (--maxlen < 1) { + /* no more room */ + break; + } if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { mp_clear (&t); return res; } *str++ = mp_s_rmap[d]; ++digs; - - if (--maxlen == 1) { - /* no more room */ - break; - } } /* reverse the digits of the string. In this case _s points - * to the first digit [exluding the sign] of the number] + * to the first digit [exluding the sign] of the number */ bn_reverse ((unsigned char *)_s, digs); @@ -83,3 +82,7 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_toradix_n.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_unsigned_bin_size.c b/bn_mp_unsigned_bin_size.c index 091f406..00d6aa0 100644 --- a/bn_mp_unsigned_bin_size.c +++ b/bn_mp_unsigned_bin_size.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* get the size for an unsigned equivalent */ @@ -22,3 +22,7 @@ int mp_unsigned_bin_size (mp_int * a) return (size / 8 + ((size & 7) != 0 ? 1 : 0)); } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_unsigned_bin_size.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_xor.c b/bn_mp_xor.c index de7e62c..508c1a0 100644 --- a/bn_mp_xor.c +++ b/bn_mp_xor.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* XOR two ints together */ @@ -45,3 +45,7 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_xor.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_mp_zero.c b/bn_mp_zero.c index c8d8907..d8fd536 100644 --- a/bn_mp_zero.c +++ b/bn_mp_zero.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* set to zero */ @@ -30,3 +30,7 @@ void mp_zero (mp_int * a) } } #endif + +/* $Source: /cvs/libtom/libtommath/bn_mp_zero.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_prime_tab.c b/bn_prime_tab.c index 14306c2..522d428 100644 --- a/bn_prime_tab.c +++ b/bn_prime_tab.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ const mp_digit ltm_prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, @@ -55,3 +55,7 @@ const mp_digit ltm_prime_tab[] = { #endif }; #endif + +/* $Source: /cvs/libtom/libtommath/bn_prime_tab.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_reverse.c b/bn_reverse.c index 851a6e8..ed19627 100644 --- a/bn_reverse.c +++ b/bn_reverse.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reverse an array, used for radix code */ @@ -33,3 +33,7 @@ bn_reverse (unsigned char *s, int len) } } #endif + +/* $Source: /cvs/libtom/libtommath/bn_reverse.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_s_mp_add.c b/bn_s_mp_add.c index 2b378ae..5d17f12 100644 --- a/bn_s_mp_add.c +++ b/bn_s_mp_add.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* low level addition, based on HAC pp.594, Algorithm 14.7 */ @@ -103,3 +103,7 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_s_mp_add.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_s_mp_exptmod.c b/bn_s_mp_exptmod.c index 597e877..189197c 100644 --- a/bn_s_mp_exptmod.c +++ b/bn_s_mp_exptmod.c @@ -12,9 +12,8 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ - #ifdef MP_LOW_MEM #define TAB_SIZE 32 #else @@ -247,3 +246,7 @@ LBL_M: return err; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_s_mp_exptmod.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_s_mp_mul_digs.c b/bn_s_mp_mul_digs.c index b40ae2e..7d55b81 100644 --- a/bn_s_mp_mul_digs.c +++ b/bn_s_mp_mul_digs.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* multiplies |a| * |b| and only computes upto digs digits of result @@ -84,3 +84,7 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_digs.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_s_mp_mul_high_digs.c b/bn_s_mp_mul_high_digs.c index a060248..1c0aae4 100644 --- a/bn_s_mp_mul_high_digs.c +++ b/bn_s_mp_mul_high_digs.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* multiplies |a| * |b| and does not compute the lower digs digits @@ -75,3 +75,7 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_high_digs.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_s_mp_sqr.c b/bn_s_mp_sqr.c index 9cdb563..b0063bc 100644 --- a/bn_s_mp_sqr.c +++ b/bn_s_mp_sqr.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ @@ -78,3 +78,7 @@ int s_mp_sqr (mp_int * a, mp_int * b) return MP_OKAY; } #endif + +/* $Source: /cvs/libtom/libtommath/bn_s_mp_sqr.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/bn_s_mp_sub.c b/bn_s_mp_sub.c index 5b7aef9..f5949f5 100644 --- a/bn_s_mp_sub.c +++ b/bn_s_mp_sub.c @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ @@ -83,3 +83,7 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c) } #endif + +/* $Source: /cvs/libtom/libtommath/bn_s_mp_sub.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ @@ -12,7 +12,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Known optimal configurations @@ -20,13 +20,17 @@ CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) - AMD Athlon64 /GCC v3.4.4 / 74/ 124/LTM 0.34 + AMD Athlon64 /GCC v3.4.4 / 80/ 120/LTM 0.35 */ -int KARATSUBA_MUL_CUTOFF = 74, /* Min. number of digits before Karatsuba multiplication is used. */ - KARATSUBA_SQR_CUTOFF = 124, /* Min. number of digits before Karatsuba squaring is used. */ +int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */ + KARATSUBA_SQR_CUTOFF = 120, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400; #endif + +/* $Source: /cvs/libtom/libtommath/bncore.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ @@ -82,13 +82,16 @@ while (<IN>) { # scan till next end of comment, e.g. skip license while (<SRC>) { $text[$line++] = $_; - last if ($_ =~ /math\.libtomcrypt\.org/); + last if ($_ =~ /math\.libtomcrypt\.com/); } <SRC>; } $inline = 0; while (<SRC>) { + next if ($_ =~ /\$Source/); + next if ($_ =~ /\$Revision/); + next if ($_ =~ /\$Date/); $text[$line++] = $_; ++$inline; chomp($_); @@ -218,7 +221,7 @@ while (<IN>) { $str = "chapter eight"; } elsif ($a == 9) { $str = "chapter nine"; - } elsif ($a == 2) { + } elsif ($a == 10) { $str = "chapter ten"; } } else { diff --git a/changes.txt b/changes.txt index 99e40c1..aaaf69f 100644 --- a/changes.txt +++ b/changes.txt @@ -1,3 +1,36 @@ +December 24th, 2006 +v0.40 -- Updated makefile to properly support LIBNAME + -- Fixed bug in fast_s_mp_mul_high_digs() which overflowed (line 83), thanks Valgrind! + +April 4th, 2006 +v0.39 -- Jim Wigginton pointed out my Montgomery examples in figures 6.4 and 6.6 were off by one, k should be 9 not 8 + -- Bruce Guenter suggested I use --tag=CC for libtool builds where the compiler may think it's C++. + -- "mm" from sci.crypt pointed out that my mp_gcd was sub-optimal (I also updated and corrected the book) + -- updated some of the @@ tags in tommath.src to reflect source changes. + -- updated email and url info in all source files + +Jan 26th, 2006 +v0.38 -- broken makefile.shared fixed + -- removed some carry stores that were not required [updated text] + +November 18th, 2005 +v0.37 -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs. Fixed. + -- [rinick@gmail.com] reported the makefile.bcc was messed up. Fixed. + -- [Kevin Kenny] reported some issues with mp_toradix_n(). Now it doesn't require a min of 3 chars of output. + -- Made the make command renamable. Wee + +August 1st, 2005 +v0.36 -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed. + -- [Peter LaDow] found a typo in the XREALLOC macro + -- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input + -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags] + -- Kevin Kenny pointed out a stray // + -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code] + -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use + unsigned operations in the routine. + -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix) + -- Updated makefiles to be way more flexible + March 12th, 2005 v0.35 -- Stupid XOR function missing line again... oops. -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt] diff --git a/demo/demo.c b/demo/demo.c index 0a6115a..bb5eb44 100644 --- a/demo/demo.c +++ b/demo/demo.c @@ -389,8 +389,8 @@ printf("compare no compare!\n"); exit(EXIT_FAILURE); } sub_d_n = 0; /* force KARA and TOOM to enable despite cutoffs */ - KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 110; - TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 150; + KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8; + TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16; for (;;) { /* randomly clear and re-init one variable, this has the affect of triming the alloc space */ @@ -734,3 +734,7 @@ printf("compare no compare!\n"); exit(EXIT_FAILURE); } } return 0; } + +/* $Source: /cvs/libtom/libtommath/demo/demo.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2005/06/24 11:32:07 $ */ diff --git a/demo/timing.c b/demo/timing.c index bb3be52..d4660a9 100644 --- a/demo/timing.c +++ b/demo/timing.c @@ -313,3 +313,7 @@ int main(void) return 0; } + +/* $Source: /cvs/libtom/libtommath/demo/timing.c,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/etc/2kprime.c b/etc/2kprime.c index d48b83e..c09818f 100644 --- a/etc/2kprime.c +++ b/etc/2kprime.c @@ -78,3 +78,7 @@ int main(void) + +/* $Source: /cvs/libtom/libtommath/etc/2kprime.c,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/etc/drprime.c b/etc/drprime.c index 0ab8ea6..e413985 100644 --- a/etc/drprime.c +++ b/etc/drprime.c @@ -58,3 +58,7 @@ int main(void) return 0; } + +/* $Source: /cvs/libtom/libtommath/etc/drprime.c,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/etc/drprimes.txt b/etc/drprimes.txt index 2c887ea..7c97f67 100644 --- a/etc/drprimes.txt +++ b/etc/drprimes.txt @@ -1,6 +1,9 @@ -280-bit prime: -p == 1942668892225729070919461906823518906642406839052139521251812409738904285204940164839 +300-bit prime: +p == 2037035976334486086268445688409378161051468393665936250636140449354381298610415201576637819 -532-bit prime: -p == 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368691747 +540-bit prime: +p == 3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206810991770626477344739 + +780-bit prime: +p == 6359114106063703798370219984742410466332205126109989319225557147754704702203399726411277962562135973685197744935448875852478791860694279747355800678568677946181447581781401213133886609947027230004277244697462656003655947791725966271167 diff --git a/etc/makefile.icc b/etc/makefile.icc index 0a50728..8a1ffff 100644 --- a/etc/makefile.icc +++ b/etc/makefile.icc @@ -16,7 +16,7 @@ CFLAGS += -I../ # B - Blend of P4 and PM [mobile] # # Default to just generic max opts -CFLAGS += -O3 -xN -ip +CFLAGS += -O3 -xP -ip # default lib name (requires install with root) # LIBNAME=-ltommath diff --git a/etc/mersenne.c b/etc/mersenne.c index 1cd5b50..6a6497a 100644 --- a/etc/mersenne.c +++ b/etc/mersenne.c @@ -1,6 +1,6 @@ /* Finds Mersenne primes using the Lucas-Lehmer test * - * Tom St Denis, tomstdenis@iahu.ca + * Tom St Denis, tomstdenis@gmail.com */ #include <time.h> #include <tommath.h> @@ -138,3 +138,7 @@ main (void) } return 0; } + +/* $Source: /cvs/libtom/libtommath/etc/mersenne.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:47 $ */ @@ -44,3 +44,7 @@ int main(void) + +/* $Source: /cvs/libtom/libtommath/etc/mont.c,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/etc/pprime.c b/etc/pprime.c index 26e0d84..317e2a0 100644 --- a/etc/pprime.c +++ b/etc/pprime.c @@ -1,8 +1,8 @@ /* Generates provable primes * - * See http://iahu.ca:8080/papers/pp.pdf for more info. + * See http://gmail.com:8080/papers/pp.pdf for more info. * - * Tom St Denis, tomstdenis@iahu.ca, http://tom.iahu.ca + * Tom St Denis, tomstdenis@gmail.com, http://tom.gmail.com */ #include <time.h> #include "tommath.h" @@ -394,3 +394,7 @@ main (void) return 0; } + +/* $Source: /cvs/libtom/libtommath/etc/pprime.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:47 $ */ @@ -1,6 +1,6 @@ /* Tune the Karatsuba parameters * - * Tom St Denis, tomstdenis@iahu.ca + * Tom St Denis, tomstdenis@gmail.com */ #include <tommath.h> #include <time.h> @@ -136,3 +136,7 @@ main (void) return 0; } + +/* $Source: /cvs/libtom/libtommath/etc/tune.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:47 $ */ diff --git a/logs/expt.log b/logs/expt.log index 920ba55..70932ab 100644 --- a/logs/expt.log +++ b/logs/expt.log @@ -1,7 +1,7 @@ -513 1489160 -769 3688476 -1025 8162061 -2049 49260015 -2561 89579052 -3073 148797060 -4097 324449263 +513 1435869 +769 3544970 +1025 7791638 +2049 46902238 +2561 85334899 +3073 141451412 +4097 308770310 diff --git a/logs/expt_2k.log b/logs/expt_2k.log index 56b50db..97d325f 100644 --- a/logs/expt_2k.log +++ b/logs/expt_2k.log @@ -1,5 +1,5 @@ -607 2272809 -1279 9557382 -2203 36250309 -3217 87666486 -4253 174168369 +607 2109225 +1279 10148314 +2203 34126877 +3217 82716424 +4253 161569606 diff --git a/logs/expt_2kl.log b/logs/expt_2kl.log index b2eb8c2..d9ad4be 100644 --- a/logs/expt_2kl.log +++ b/logs/expt_2kl.log @@ -1,4 +1,4 @@ -1024 6954080 -2048 35993987 -4096 176068521 -521 1683720 +1024 7705271 +2048 34286851 +4096 165207491 +521 1618631 diff --git a/logs/expt_dr.log b/logs/expt_dr.log index eb93fc9..c6bbe07 100644 --- a/logs/expt_dr.log +++ b/logs/expt_dr.log @@ -1,7 +1,7 @@ -532 1989592 -784 3898697 -1036 6519700 -1540 15676650 -2072 33128187 -3080 82963362 -4116 168358337 +532 1928550 +784 3763908 +1036 7564221 +1540 16566059 +2072 32283784 +3080 79851565 +4116 157843530 diff --git a/logs/index.html b/logs/index.html index 19fe403..4b68c25 100644 --- a/logs/index.html +++ b/logs/index.html @@ -21,4 +21,7 @@ <hr> </body> -</html>
\ No newline at end of file +</html> +/* $Source: /cvs/libtom/libtommath/logs/index.html,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/logs/sqr.old b/logs/sqr.old deleted file mode 100644 index 3c85882..0000000 --- a/logs/sqr.old +++ /dev/null @@ -1,17 +0,0 @@ -896 382617 -1344 207161 -1792 131522 -2240 90775 -2688 66652 -3136 50955 -3584 11678 -4032 9342 -4480 7684 -4928 6382 -5376 5399 -5824 4545 -6272 3994 -6720 3490 -7168 3075 -7616 2733 -8064 2428 diff --git a/makefile.bcc b/makefile.bcc index 647c69a..67743d9 100644 --- a/makefile.bcc +++ b/makefile.bcc @@ -39,6 +39,6 @@ TARGET = libtommath.lib $(TARGET): $(OBJECTS) -.c.objbjbjbj: +.c.obj: $(CC) $(CFLAGS) $< $(LIB) $(TARGET) -+$@ diff --git a/makefile.cygwin_dll b/makefile.cygwin_dll index 85b10c7..85a9b20 100644 --- a/makefile.cygwin_dll +++ b/makefile.cygwin_dll @@ -49,3 +49,7 @@ windll: $(OBJECTS) test: $(OBJECTS) windll gcc $(CFLAGS) demo/demo.c libtommath.dll.a -Wl,--enable-auto-import -o test -s cd mtest ; $(CC) -O3 -fomit-frame-pointer -funroll-loops mtest.c -o mtest -s + +/* $Source: /cvs/libtom/libtommath/makefile.cygwin_dll,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:45 $ */ diff --git a/makefile.icc b/makefile.icc index e764253..cf70ab0 100644 --- a/makefile.icc +++ b/makefile.icc @@ -19,7 +19,7 @@ CFLAGS += -I./ # B - Blend of P4 and PM [mobile] # # Default to just generic max opts -CFLAGS += -O3 -xN +CFLAGS += -O3 -xP -ip #install as this user USER=root diff --git a/makefile.msvc b/makefile.msvc index dbbf9f3..5edebec 100644 --- a/makefile.msvc +++ b/makefile.msvc @@ -2,7 +2,7 @@ # #Tom St Denis -CFLAGS = /I. /Ox /DWIN32 /W4 +CFLAGS = /I. /Ox /DWIN32 /W3 /Fo$@ default: library @@ -34,5 +34,7 @@ bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \ bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \ bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj +HEADERS=tommath.h tommath_class.h tommath_superclass.h + library: $(OBJECTS) lib /out:tommath.lib $(OBJECTS) diff --git a/makefile.shared b/makefile.shared index 7c35881..e230fb8 100644 --- a/makefile.shared +++ b/makefile.shared @@ -1,11 +1,14 @@ #Makefile for GCC # #Tom St Denis -VERSION=0:35 +VERSION=0:40 + +CC = libtool --mode=compile --tag=CC gcc -CC = libtool --mode=compile gcc CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare +ifndef IGNORE_SPEED + #for speed CFLAGS += -O3 -funroll-loops @@ -15,14 +18,30 @@ CFLAGS += -O3 -funroll-loops #x86 optimizations [should be valid for any GCC install though] CFLAGS += -fomit-frame-pointer +endif + #install as this user -USER=root -GROUP=root +ifndef INSTALL_GROUP + GROUP=wheel +else + GROUP=$(INSTALL_GROUP) +endif + +ifndef INSTALL_USER + USER=root +else + USER=$(INSTALL_USER) +endif default: libtommath.la #default files to install -LIBNAME=libtommath.la +ifndef LIBNAME + LIBNAME=libtommath.la +endif +ifndef LIBNAME_S + LIBNAME_S=libtommath.a +endif HEADERS=tommath.h tommath_class.h tommath_superclass.h #LIBPATH-The directory for libtommath to be installed to. @@ -61,20 +80,23 @@ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_ini bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o +objs: $(OBJECTS) + +$(LIBNAME): $(OBJECTS) + libtool --mode=link gcc *.lo -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION) -libtommath.la: $(OBJECTS) - libtool --mode=link gcc *.lo -o libtommath.la -rpath $(LIBPATH) -version-info $(VERSION) - libtool --mode=link gcc *.o -o libtommath.a - libtool --mode=install install -c libtommath.la $(LIBPATH)/libtommath.la +install: $(LIBNAME) + install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH) + libtool --mode=install install -c $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME) install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH) install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH) -test: libtommath.a demo/demo.o +test: $(LIBNAME) demo/demo.o gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o - libtool --mode=link gcc -o test demo/demo.o libtommath.la + libtool --mode=link gcc -o test demo/demo.o $(LIBNAME_S) mtest: test - cd mtest ; gcc $(CFLAGS) mtest.c -o mtest -s + cd mtest ; gcc $(CFLAGS) mtest.c -o mtest -timing: libtommath.la - gcc $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s +timing: $(LIBNAME) + gcc $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME_S) -o ltmtest @@ -0,0 +1,4 @@ +#!/bin/bash +if cvs log $1 >/dev/null 2>/dev/null; then exit 0; else echo "$1 shouldn't be here" ; exit 1; fi + + diff --git a/mtest/logtab.h b/mtest/logtab.h index 68462bd..bbefaef 100644 --- a/mtest/logtab.h +++ b/mtest/logtab.h @@ -18,3 +18,7 @@ const float s_logv_2[] = { 0.166666667 }; + +/* $Source: /cvs/libtom/libtommath/mtest/logtab.h,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/mtest/mpi-config.h b/mtest/mpi-config.h index 1baf2c2..6049c25 100644 --- a/mtest/mpi-config.h +++ b/mtest/mpi-config.h @@ -1,5 +1,5 @@ /* Default configuration for MPI library */ -/* $Id: mpi-config.h,v 1.8 2000/07/11 04:28:14 sting Exp sting $ */ +/* $Id: mpi-config.h,v 1.2 2005/05/05 14:38:47 tom Exp $ */ #ifndef MPI_CONFIG_H_ #define MPI_CONFIG_H_ @@ -84,3 +84,7 @@ /* crc==3287762869, version==2, Sat Feb 02 06:43:53 2002 */ + +/* $Source: /cvs/libtom/libtommath/mtest/mpi-config.h,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/mtest/mpi-types.h b/mtest/mpi-types.h index e097188..026de58 100644 --- a/mtest/mpi-types.h +++ b/mtest/mpi-types.h @@ -14,3 +14,7 @@ typedef int mp_err; #define DIGIT_FMT "%04X" #define RADIX (MP_DIGIT_MAX+1) + +/* $Source: /cvs/libtom/libtommath/mtest/mpi-types.h,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/mtest/mpi.c b/mtest/mpi.c index f7688f3..7c712dd 100644 --- a/mtest/mpi.c +++ b/mtest/mpi.c @@ -6,7 +6,7 @@ Arbitrary precision integer arithmetic library - $Id: mpi.c,v 1.22 2001/09/14 15:11:20 sting Exp sting $ + $Id: mpi.c,v 1.2 2005/05/05 14:38:47 tom Exp $ */ #include "mpi.h" @@ -3979,3 +3979,7 @@ int s_mp_outlen(int bits, int r) /*------------------------------------------------------------------------*/ /* HERE THERE BE DRAGONS */ /* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */ + +/* $Source: /cvs/libtom/libtommath/mtest/mpi.c,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/mtest/mpi.h b/mtest/mpi.h index f7a3d14..66ae873 100644 --- a/mtest/mpi.h +++ b/mtest/mpi.h @@ -6,7 +6,7 @@ Arbitrary precision integer arithmetic library - $Id: mpi.h,v 1.15 2001/09/17 14:16:22 sting Exp $ + $Id: mpi.h,v 1.2 2005/05/05 14:38:47 tom Exp $ */ #ifndef _H_MPI_ @@ -225,3 +225,7 @@ int mp_char2value(char ch, int r); const char *mp_strerror(mp_err ec); #endif /* end _H_MPI_ */ + +/* $Source: /cvs/libtom/libtommath/mtest/mpi.h,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/mtest/mtest.c b/mtest/mtest.c index d46f456..bdfe612 100644 --- a/mtest/mtest.c +++ b/mtest/mtest.c @@ -302,3 +302,7 @@ int main(void) fclose(rng); return 0; } + +/* $Source: /cvs/libtom/libtommath/mtest/mtest.c,v $ */ +/* $Revision: 1.2 $ */ +/* $Date: 2005/05/05 14:38:47 $ */ diff --git a/pre_gen/mpi.c b/pre_gen/mpi.c index 8ec8a10..f651138 100644 --- a/pre_gen/mpi.c +++ b/pre_gen/mpi.c @@ -13,7 +13,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ static const struct { @@ -43,6 +43,10 @@ char *mp_error_to_string(int code) #endif +/* $Source: /cvs/libtom/libtommath/bn_error.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_error.c */ /* Start: bn_fast_mp_invmod.c */ @@ -60,7 +64,7 @@ char *mp_error_to_string(int code) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes the modular inverse via binary extended euclidean algorithm, @@ -191,6 +195,10 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); } #endif +/* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_fast_mp_invmod.c */ /* Start: bn_fast_mp_montgomery_reduce.c */ @@ -208,7 +216,7 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes xR**-1 == x (mod N) via Montgomery Reduction @@ -363,6 +371,10 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) } #endif +/* $Source: /cvs/libtom/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_fast_mp_montgomery_reduce.c */ /* Start: bn_fast_s_mp_mul_digs.c */ @@ -380,7 +392,7 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Fast (comba) multiplier @@ -438,6 +450,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) /* execute loop */ for (iz = 0; iz < iy; ++iz) { _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); + } /* store term */ @@ -445,10 +458,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) /* make next carry */ _W = _W >> ((mp_word)DIGIT_BIT); - } - - /* store final carry */ - W[ix] = (mp_digit)(_W & MP_MASK); + } /* setup dest */ olduse = c->used; @@ -472,6 +482,10 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) } #endif +/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_digs.c,v $ */ +/* $Revision: 1.7 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_fast_s_mp_mul_digs.c */ /* Start: bn_fast_s_mp_mul_high_digs.c */ @@ -489,7 +503,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* this is a modified version of fast_s_mul_digs that only produces @@ -547,9 +561,6 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) _W = _W >> ((mp_word)DIGIT_BIT); } - /* store final carry */ - W[ix] = (mp_digit)(_W & MP_MASK); - /* setup dest */ olduse = c->used; c->used = pa; @@ -558,7 +569,7 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) register mp_digit *tmpc; tmpc = c->dp + digs; - for (ix = digs; ix <= pa; ix++) { + for (ix = digs; ix < pa; ix++) { /* now extract the previous digit [below the carry] */ *tmpc++ = W[ix]; } @@ -573,6 +584,10 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) } #endif +/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_high_digs.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/11/14 03:46:25 $ */ + /* End: bn_fast_s_mp_mul_high_digs.c */ /* Start: bn_fast_s_mp_sqr.c */ @@ -590,7 +605,7 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* the jist of squaring... @@ -687,6 +702,10 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_sqr.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_fast_s_mp_sqr.c */ /* Start: bn_mp_2expt.c */ @@ -704,7 +723,7 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes a = 2**b @@ -735,6 +754,10 @@ mp_2expt (mp_int * a, int b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_2expt.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_2expt.c */ /* Start: bn_mp_abs.c */ @@ -752,7 +775,7 @@ mp_2expt (mp_int * a, int b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* b = |a| @@ -778,6 +801,10 @@ mp_abs (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_abs.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_abs.c */ /* Start: bn_mp_add.c */ @@ -795,7 +822,7 @@ mp_abs (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* high level addition (handles signs) */ @@ -831,6 +858,10 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_add.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_add.c */ /* Start: bn_mp_add_d.c */ @@ -848,7 +879,7 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* single digit addition */ @@ -876,6 +907,9 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c) /* fix sign */ a->sign = c->sign = MP_NEG; + /* clamp */ + mp_clamp(c); + return res; } @@ -940,6 +974,10 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_add_d.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_add_d.c */ /* Start: bn_mp_addmod.c */ @@ -957,7 +995,7 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* d = a + b (mod c) */ @@ -981,6 +1019,10 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_addmod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_addmod.c */ /* Start: bn_mp_and.c */ @@ -998,7 +1040,7 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* AND two ints together */ @@ -1038,6 +1080,10 @@ mp_and (mp_int * a, mp_int * b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_and.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_and.c */ /* Start: bn_mp_clamp.c */ @@ -1055,7 +1101,7 @@ mp_and (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* trim unused digits @@ -1082,6 +1128,10 @@ mp_clamp (mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_clamp.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_clamp.c */ /* Start: bn_mp_clear.c */ @@ -1099,7 +1149,7 @@ mp_clamp (mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* clear one (frees) */ @@ -1126,6 +1176,10 @@ mp_clear (mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_clear.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_clear.c */ /* Start: bn_mp_clear_multi.c */ @@ -1143,7 +1197,7 @@ mp_clear (mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ #include <stdarg.h> @@ -1160,6 +1214,10 @@ void mp_clear_multi(mp_int *mp, ...) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_clear_multi.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_clear_multi.c */ /* Start: bn_mp_cmp.c */ @@ -1177,7 +1235,7 @@ void mp_clear_multi(mp_int *mp, ...) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* compare two ints (signed)*/ @@ -1203,6 +1261,10 @@ mp_cmp (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_cmp.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_cmp.c */ /* Start: bn_mp_cmp_d.c */ @@ -1220,7 +1282,7 @@ mp_cmp (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* compare a digit */ @@ -1247,6 +1309,10 @@ int mp_cmp_d(mp_int * a, mp_digit b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_cmp_d.c */ /* Start: bn_mp_cmp_mag.c */ @@ -1264,7 +1330,7 @@ int mp_cmp_d(mp_int * a, mp_digit b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* compare maginitude of two ints (unsigned) */ @@ -1302,6 +1368,10 @@ int mp_cmp_mag (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_mag.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_cmp_mag.c */ /* Start: bn_mp_cnt_lsb.c */ @@ -1319,7 +1389,7 @@ int mp_cmp_mag (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ static const int lnz[16] = { @@ -1355,6 +1425,10 @@ int mp_cnt_lsb(mp_int *a) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_cnt_lsb.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_cnt_lsb.c */ /* Start: bn_mp_copy.c */ @@ -1372,7 +1446,7 @@ int mp_cnt_lsb(mp_int *a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* copy, b = a */ @@ -1423,6 +1497,10 @@ mp_copy (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_copy.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_copy.c */ /* Start: bn_mp_count_bits.c */ @@ -1440,7 +1518,7 @@ mp_copy (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* returns the number of bits in an int */ @@ -1468,6 +1546,10 @@ mp_count_bits (mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_count_bits.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_count_bits.c */ /* Start: bn_mp_div.c */ @@ -1485,7 +1567,7 @@ mp_count_bits (mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ #ifdef BN_MP_DIV_SMALL @@ -1760,6 +1842,10 @@ LBL_Q:mp_clear (&q); #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_div.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_div.c */ /* Start: bn_mp_div_2.c */ @@ -1777,7 +1863,7 @@ LBL_Q:mp_clear (&q); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* b = a/2 */ @@ -1828,6 +1914,10 @@ int mp_div_2(mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_div_2.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_div_2.c */ /* Start: bn_mp_div_2d.c */ @@ -1845,7 +1935,7 @@ int mp_div_2(mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ @@ -1925,6 +2015,10 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_div_2d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_div_2d.c */ /* Start: bn_mp_div_3.c */ @@ -1942,7 +2036,7 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* divide by three (based on routine from MPI and the GMP manual) */ @@ -2004,6 +2098,10 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_div_3.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_div_3.c */ /* Start: bn_mp_div_d.c */ @@ -2021,7 +2119,7 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ static int s_is_power_of_two(mp_digit b, int *p) @@ -2114,6 +2212,10 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_div_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_div_d.c */ /* Start: bn_mp_dr_is_modulus.c */ @@ -2131,7 +2233,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines if a number is a valid DR modulus */ @@ -2157,6 +2259,10 @@ int mp_dr_is_modulus(mp_int *a) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_dr_is_modulus.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_dr_is_modulus.c */ /* Start: bn_mp_dr_reduce.c */ @@ -2174,7 +2280,7 @@ int mp_dr_is_modulus(mp_int *a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reduce "x" in place modulo "n" using the Diminished Radix algorithm. @@ -2251,6 +2357,10 @@ top: } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_dr_reduce.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_dr_reduce.c */ /* Start: bn_mp_dr_setup.c */ @@ -2268,7 +2378,7 @@ top: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines the setup value */ @@ -2283,6 +2393,10 @@ void mp_dr_setup(mp_int *a, mp_digit *d) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_dr_setup.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_dr_setup.c */ /* Start: bn_mp_exch.c */ @@ -2300,7 +2414,7 @@ void mp_dr_setup(mp_int *a, mp_digit *d) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* swap the elements of two integers, for cases where you can't simply swap the @@ -2317,6 +2431,10 @@ mp_exch (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_exch.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_exch.c */ /* Start: bn_mp_expt_d.c */ @@ -2334,7 +2452,7 @@ mp_exch (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* calculate c = a**b using a square-multiply algorithm */ @@ -2374,6 +2492,10 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_expt_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_expt_d.c */ /* Start: bn_mp_exptmod.c */ @@ -2391,7 +2513,7 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ @@ -2445,7 +2567,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) } /* modified diminished radix reduction */ -#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) +#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C) if (mp_reduce_is_2k_l(P) == MP_YES) { return s_mp_exptmod(G, X, P, Y, 1); } @@ -2486,6 +2608,10 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_exptmod.c */ /* Start: bn_mp_exptmod_fast.c */ @@ -2503,7 +2629,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 @@ -2807,6 +2933,10 @@ LBL_M: #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod_fast.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_exptmod_fast.c */ /* Start: bn_mp_exteuclid.c */ @@ -2824,7 +2954,7 @@ LBL_M: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Extended euclidean algorithm of (a, b) produces @@ -2889,6 +3019,10 @@ _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_exteuclid.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_exteuclid.c */ /* Start: bn_mp_fread.c */ @@ -2906,7 +3040,7 @@ _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* read a bigint from a file stream in ASCII */ @@ -2956,6 +3090,10 @@ int mp_fread(mp_int *a, int radix, FILE *stream) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_fread.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_fread.c */ /* Start: bn_mp_fwrite.c */ @@ -2973,7 +3111,7 @@ int mp_fread(mp_int *a, int radix, FILE *stream) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ int mp_fwrite(mp_int *a, int radix, FILE *stream) @@ -3008,6 +3146,10 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_fwrite.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_fwrite.c */ /* Start: bn_mp_gcd.c */ @@ -3025,7 +3167,7 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Greatest Common Divisor using the binary method */ @@ -3035,21 +3177,13 @@ int mp_gcd (mp_int * a, mp_int * b, mp_int * c) int k, u_lsb, v_lsb, res; /* either zero than gcd is the largest */ - if (mp_iszero (a) == 1 && mp_iszero (b) == 0) { + if (mp_iszero (a) == MP_YES) { return mp_abs (b, c); } - if (mp_iszero (a) == 0 && mp_iszero (b) == 1) { + if (mp_iszero (b) == MP_YES) { return mp_abs (a, c); } - /* optimized. At this point if a == 0 then - * b must equal zero too - */ - if (mp_iszero (a) == 1) { - mp_zero(c); - return MP_OKAY; - } - /* get copies of a and b we can modify */ if ((res = mp_init_copy (&u, a)) != MP_OKAY) { return res; @@ -3121,6 +3255,10 @@ LBL_U:mp_clear (&v); } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_gcd.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_gcd.c */ /* Start: bn_mp_get_int.c */ @@ -3138,7 +3276,7 @@ LBL_U:mp_clear (&v); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* get the lower 32-bits of an mp_int */ @@ -3166,6 +3304,10 @@ unsigned long mp_get_int(mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_get_int.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_get_int.c */ /* Start: bn_mp_grow.c */ @@ -3183,7 +3325,7 @@ unsigned long mp_get_int(mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* grow as required */ @@ -3223,6 +3365,10 @@ int mp_grow (mp_int * a, int size) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_grow.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_grow.c */ /* Start: bn_mp_init.c */ @@ -3240,7 +3386,7 @@ int mp_grow (mp_int * a, int size) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* init a new mp_int */ @@ -3269,6 +3415,10 @@ int mp_init (mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_init.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_init.c */ /* Start: bn_mp_init_copy.c */ @@ -3286,7 +3436,7 @@ int mp_init (mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* creates "a" then copies b into it */ @@ -3301,6 +3451,10 @@ int mp_init_copy (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_init_copy.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_init_copy.c */ /* Start: bn_mp_init_multi.c */ @@ -3318,7 +3472,7 @@ int mp_init_copy (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ #include <stdarg.h> @@ -3360,6 +3514,10 @@ int mp_init_multi(mp_int *mp, ...) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_init_multi.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_init_multi.c */ /* Start: bn_mp_init_set.c */ @@ -3377,7 +3535,7 @@ int mp_init_multi(mp_int *mp, ...) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* initialize and set a digit */ @@ -3392,6 +3550,10 @@ int mp_init_set (mp_int * a, mp_digit b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_init_set.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_init_set.c */ /* Start: bn_mp_init_set_int.c */ @@ -3409,7 +3571,7 @@ int mp_init_set (mp_int * a, mp_digit b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* initialize and set a digit */ @@ -3423,6 +3585,10 @@ int mp_init_set_int (mp_int * a, unsigned long b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_init_set_int.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_init_set_int.c */ /* Start: bn_mp_init_size.c */ @@ -3440,7 +3606,7 @@ int mp_init_set_int (mp_int * a, unsigned long b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* init an mp_init for a given size */ @@ -3471,6 +3637,10 @@ int mp_init_size (mp_int * a, int size) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_init_size.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_init_size.c */ /* Start: bn_mp_invmod.c */ @@ -3488,7 +3658,7 @@ int mp_init_size (mp_int * a, int size) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* hac 14.61, pp608 */ @@ -3514,6 +3684,10 @@ int mp_invmod (mp_int * a, mp_int * b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_invmod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_invmod.c */ /* Start: bn_mp_invmod_slow.c */ @@ -3531,7 +3705,7 @@ int mp_invmod (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* hac 14.61, pp608 */ @@ -3689,6 +3863,10 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_invmod_slow.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_invmod_slow.c */ /* Start: bn_mp_is_square.c */ @@ -3706,7 +3884,7 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Check if remainders are possible squares - fast exclude non-squares */ @@ -3798,6 +3976,10 @@ ERR:mp_clear(&t); } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_is_square.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_is_square.c */ /* Start: bn_mp_jacobi.c */ @@ -3815,7 +3997,7 @@ ERR:mp_clear(&t); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes the jacobi c = (a | n) (or Legendre if n is prime) @@ -3903,6 +4085,10 @@ LBL_A1:mp_clear (&a1); } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_jacobi.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_jacobi.c */ /* Start: bn_mp_karatsuba_mul.c */ @@ -3920,7 +4106,7 @@ LBL_A1:mp_clear (&a1); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* c = |a| * |b| using Karatsuba Multiplication using @@ -3934,12 +4120,12 @@ LBL_A1:mp_clear (&a1); * b = b1 * B**n + b0 * * Then, a * b => - a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0 + a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 * * Note that a1b1 and a0b0 are used twice and only need to be * computed once. So in total three half size (half # of * digit) multiplications are performed, a0b0, a1b1 and - * (a1-b1)(a0-b0) + * (a1+b1)(a0+b0) * * Note that a multiplication of half the digits requires * 1/4th the number of single precision multiplications so in @@ -4030,19 +4216,19 @@ int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c) if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) goto X1Y1; /* x1y1 = x1*y1 */ - /* now calc x1-x0 and y1-y0 */ - if (mp_sub (&x1, &x0, &t1) != MP_OKAY) + /* now calc x1+x0 and y1+y0 */ + if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = x1 - x0 */ - if (mp_sub (&y1, &y0, &x0) != MP_OKAY) + if (s_mp_add (&y1, &y0, &x0) != MP_OKAY) goto X1Y1; /* t2 = y1 - y0 */ if (mp_mul (&t1, &x0, &t1) != MP_OKAY) - goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */ + goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ /* add x0y0 */ if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) goto X1Y1; /* t2 = x0y0 + x1y1 */ - if (mp_sub (&x0, &t1, &t1) != MP_OKAY) - goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */ + if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY) + goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) @@ -4070,6 +4256,10 @@ ERR: } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_mul.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_karatsuba_mul.c */ /* Start: bn_mp_karatsuba_sqr.c */ @@ -4087,7 +4277,7 @@ ERR: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Karatsuba squaring, computes b = a*a using three @@ -4155,8 +4345,8 @@ int mp_karatsuba_sqr (mp_int * a, mp_int * b) if (mp_sqr (&x1, &x1x1) != MP_OKAY) goto X1X1; /* x1x1 = x1*x1 */ - /* now calc (x1-x0)**2 */ - if (mp_sub (&x1, &x0, &t1) != MP_OKAY) + /* now calc (x1+x0)**2 */ + if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) goto X1X1; /* t1 = x1 - x0 */ if (mp_sqr (&t1, &t1) != MP_OKAY) goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ @@ -4164,8 +4354,8 @@ int mp_karatsuba_sqr (mp_int * a, mp_int * b) /* add x0y0 */ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) goto X1X1; /* t2 = x0x0 + x1x1 */ - if (mp_sub (&t2, &t1, &t1) != MP_OKAY) - goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */ + if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY) + goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ /* shift by B */ if (mp_lshd (&t1, B) != MP_OKAY) @@ -4191,6 +4381,10 @@ ERR: } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_sqr.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_karatsuba_sqr.c */ /* Start: bn_mp_lcm.c */ @@ -4208,7 +4402,7 @@ ERR: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes least common multiple as |a*b|/(a, b) */ @@ -4251,6 +4445,10 @@ LBL_T: } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_lcm.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_lcm.c */ /* Start: bn_mp_lshd.c */ @@ -4268,7 +4466,7 @@ LBL_T: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shift left a certain amount of digits */ @@ -4318,6 +4516,10 @@ int mp_lshd (mp_int * a, int b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_lshd.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_lshd.c */ /* Start: bn_mp_mod.c */ @@ -4335,7 +4537,7 @@ int mp_lshd (mp_int * a, int b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* c = a mod b, 0 <= c < b */ @@ -4366,6 +4568,10 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_mod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_mod.c */ /* Start: bn_mp_mod_2d.c */ @@ -4383,7 +4589,7 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* calc a value mod 2**b */ @@ -4421,6 +4627,10 @@ mp_mod_2d (mp_int * a, int b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_mod_2d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_mod_2d.c */ /* Start: bn_mp_mod_d.c */ @@ -4438,7 +4648,7 @@ mp_mod_2d (mp_int * a, int b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ int @@ -4448,6 +4658,10 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_mod_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_mod_d.c */ /* Start: bn_mp_montgomery_calc_normalization.c */ @@ -4465,7 +4679,7 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* @@ -4507,6 +4721,10 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_montgomery_calc_normalization.c */ /* Start: bn_mp_montgomery_reduce.c */ @@ -4524,7 +4742,7 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes xR**-1 == x (mod N) via Montgomery Reduction */ @@ -4625,6 +4843,10 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_reduce.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_montgomery_reduce.c */ /* Start: bn_mp_montgomery_setup.c */ @@ -4642,7 +4864,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* setups the montgomery reduction stuff */ @@ -4678,12 +4900,16 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho) #endif /* rho = -1/m mod b */ - *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; + *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; return MP_OKAY; } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/12/04 21:34:03 $ */ + /* End: bn_mp_montgomery_setup.c */ /* Start: bn_mp_mul.c */ @@ -4701,7 +4927,7 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* high level multiplication (handles sign) */ @@ -4750,6 +4976,10 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_mul.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_mul.c */ /* Start: bn_mp_mul_2.c */ @@ -4767,7 +4997,7 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* b = a*2 */ @@ -4832,6 +5062,10 @@ int mp_mul_2(mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_mul_2.c */ /* Start: bn_mp_mul_2d.c */ @@ -4849,7 +5083,7 @@ int mp_mul_2(mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shift left by a certain bit count */ @@ -4917,6 +5151,10 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_mul_2d.c */ /* Start: bn_mp_mul_d.c */ @@ -4934,7 +5172,7 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* multiply by a digit */ @@ -4996,6 +5234,10 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_mul_d.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_mul_d.c */ /* Start: bn_mp_mulmod.c */ @@ -5013,12 +5255,11 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* d = a * b (mod c) */ -int -mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) +int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) { int res; mp_int t; @@ -5037,6 +5278,10 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_mulmod.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_mulmod.c */ /* Start: bn_mp_n_root.c */ @@ -5054,7 +5299,7 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* find the n'th root of an integer @@ -5169,6 +5414,10 @@ LBL_T1:mp_clear (&t1); } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_n_root.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_n_root.c */ /* Start: bn_mp_neg.c */ @@ -5186,7 +5435,7 @@ LBL_T1:mp_clear (&t1); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* b = -a */ @@ -5209,6 +5458,10 @@ int mp_neg (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_neg.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_neg.c */ /* Start: bn_mp_or.c */ @@ -5226,7 +5479,7 @@ int mp_neg (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* OR two ints together */ @@ -5259,6 +5512,10 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_or.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_or.c */ /* Start: bn_mp_prime_fermat.c */ @@ -5276,7 +5533,7 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* performs one Fermat test. @@ -5321,6 +5578,10 @@ LBL_T:mp_clear (&t); } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_fermat.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_prime_fermat.c */ /* Start: bn_mp_prime_is_divisible.c */ @@ -5338,7 +5599,7 @@ LBL_T:mp_clear (&t); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines if an integers is divisible by one @@ -5371,6 +5632,10 @@ int mp_prime_is_divisible (mp_int * a, int *result) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_divisible.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_prime_is_divisible.c */ /* Start: bn_mp_prime_is_prime.c */ @@ -5388,7 +5653,7 @@ int mp_prime_is_divisible (mp_int * a, int *result) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* performs a variable number of rounds of Miller-Rabin @@ -5454,6 +5719,10 @@ LBL_B:mp_clear (&b); } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_prime.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_prime_is_prime.c */ /* Start: bn_mp_prime_miller_rabin.c */ @@ -5471,7 +5740,7 @@ LBL_B:mp_clear (&b); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Miller-Rabin test of "a" to the base of "b" as described in @@ -5557,6 +5826,10 @@ LBL_N1:mp_clear (&n1); } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_miller_rabin.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_prime_miller_rabin.c */ /* Start: bn_mp_prime_next_prime.c */ @@ -5574,7 +5847,7 @@ LBL_N1:mp_clear (&n1); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* finds the next prime after the number "a" using "t" trials @@ -5727,6 +6000,10 @@ LBL_ERR: #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_next_prime.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_prime_next_prime.c */ /* Start: bn_mp_prime_rabin_miller_trials.c */ @@ -5744,7 +6021,7 @@ LBL_ERR: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ @@ -5779,6 +6056,10 @@ int mp_prime_rabin_miller_trials(int size) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_rabin_miller_trials.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_prime_rabin_miller_trials.c */ /* Start: bn_mp_prime_random_ex.c */ @@ -5796,7 +6077,7 @@ int mp_prime_rabin_miller_trials(int size) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* makes a truly random prime of a given size (bits), @@ -5846,10 +6127,8 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback maskOR_msb = 0; maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; if (flags & LTM_PRIME_2MSB_ON) { - maskOR_msb |= 1 << ((size - 2) & 7); - } else if (flags & LTM_PRIME_2MSB_OFF) { - maskAND &= ~(1 << ((size - 2) & 7)); - } + maskOR_msb |= 0x80 >> ((9 - size) & 7); + } /* get the maskOR_lsb */ maskOR_lsb = 1; @@ -5906,6 +6185,10 @@ error: #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_prime_random_ex.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_prime_random_ex.c */ /* Start: bn_mp_radix_size.c */ @@ -5923,7 +6206,7 @@ error: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* returns size of ASCII reprensentation */ @@ -5947,7 +6230,7 @@ int mp_radix_size (mp_int * a, int radix, int *size) } if (mp_iszero(a) == MP_YES) { - *size = 2; + *size = 2; return MP_OKAY; } @@ -5984,6 +6267,10 @@ int mp_radix_size (mp_int * a, int radix, int *size) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_radix_size.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_radix_size.c */ /* Start: bn_mp_radix_smap.c */ @@ -6001,13 +6288,17 @@ int mp_radix_size (mp_int * a, int radix, int *size) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* chars used in radix conversions */ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_radix_smap.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_radix_smap.c */ /* Start: bn_mp_rand.c */ @@ -6025,7 +6316,7 @@ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrs * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* makes a pseudo-random int of a given size */ @@ -6063,6 +6354,10 @@ mp_rand (mp_int * a, int digits) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_rand.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_rand.c */ /* Start: bn_mp_read_radix.c */ @@ -6080,7 +6375,7 @@ mp_rand (mp_int * a, int digits) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* read a string [ASCII] in a given radix */ @@ -6089,6 +6384,9 @@ int mp_read_radix (mp_int * a, const char *str, int radix) int y, res, neg; char ch; + /* zero the digit bignum */ + mp_zero(a); + /* make sure the radix is ok */ if (radix < 2 || radix > 64) { return MP_VAL; @@ -6145,6 +6443,10 @@ int mp_read_radix (mp_int * a, const char *str, int radix) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_read_radix.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_read_radix.c */ /* Start: bn_mp_read_signed_bin.c */ @@ -6162,12 +6464,11 @@ int mp_read_radix (mp_int * a, const char *str, int radix) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* read signed bin, big endian, first byte is 0==positive or 1==negative */ -int -mp_read_signed_bin (mp_int * a, unsigned char *b, int c) +int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c) { int res; @@ -6187,6 +6488,10 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_read_signed_bin.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_read_signed_bin.c */ /* Start: bn_mp_read_unsigned_bin.c */ @@ -6204,12 +6509,11 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reads a unsigned char array, assumes the msb is stored first [big endian] */ -int -mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) +int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c) { int res; @@ -6243,6 +6547,10 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_read_unsigned_bin.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_read_unsigned_bin.c */ /* Start: bn_mp_reduce.c */ @@ -6260,7 +6568,7 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reduces x mod m, assumes 0 < x < m**2, mu is @@ -6343,6 +6651,10 @@ CLEANUP: } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_reduce.c */ /* Start: bn_mp_reduce_2k.c */ @@ -6360,7 +6672,7 @@ CLEANUP: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reduces a modulo n where n is of the form 2**p - d */ @@ -6404,6 +6716,10 @@ ERR: #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_reduce_2k.c */ /* Start: bn_mp_reduce_2k_l.c */ @@ -6421,7 +6737,7 @@ ERR: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reduces a modulo n where n is of the form 2**p - d @@ -6466,6 +6782,10 @@ ERR: #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_l.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_reduce_2k_l.c */ /* Start: bn_mp_reduce_2k_setup.c */ @@ -6483,7 +6803,7 @@ ERR: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines the setup value */ @@ -6513,6 +6833,10 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_reduce_2k_setup.c */ /* Start: bn_mp_reduce_2k_setup_l.c */ @@ -6530,7 +6854,7 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines the setup value */ @@ -6557,6 +6881,10 @@ ERR: } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup_l.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_reduce_2k_setup_l.c */ /* Start: bn_mp_reduce_is_2k.c */ @@ -6574,7 +6902,7 @@ ERR: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines if mp_reduce_2k can be used */ @@ -6609,6 +6937,10 @@ int mp_reduce_is_2k(mp_int *a) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_reduce_is_2k.c */ /* Start: bn_mp_reduce_is_2k_l.c */ @@ -6626,7 +6958,7 @@ int mp_reduce_is_2k(mp_int *a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* determines if reduce_2k_l can be used */ @@ -6653,6 +6985,10 @@ int mp_reduce_is_2k_l(mp_int *a) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k_l.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_reduce_is_2k_l.c */ /* Start: bn_mp_reduce_setup.c */ @@ -6670,7 +7006,7 @@ int mp_reduce_is_2k_l(mp_int *a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* pre-calculate the value required for Barrett reduction @@ -6687,6 +7023,10 @@ int mp_reduce_setup (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_setup.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_reduce_setup.c */ /* Start: bn_mp_rshd.c */ @@ -6704,7 +7044,7 @@ int mp_reduce_setup (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shift right a certain amount of digits */ @@ -6759,6 +7099,10 @@ void mp_rshd (mp_int * a, int b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_rshd.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_rshd.c */ /* Start: bn_mp_set.c */ @@ -6776,7 +7120,7 @@ void mp_rshd (mp_int * a, int b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* set to a digit */ @@ -6788,6 +7132,10 @@ void mp_set (mp_int * a, mp_digit b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_set.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_set.c */ /* Start: bn_mp_set_int.c */ @@ -6805,7 +7153,7 @@ void mp_set (mp_int * a, mp_digit b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* set a 32-bit const */ @@ -6836,6 +7184,10 @@ int mp_set_int (mp_int * a, unsigned long b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_set_int.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_set_int.c */ /* Start: bn_mp_shrink.c */ @@ -6853,7 +7205,7 @@ int mp_set_int (mp_int * a, unsigned long b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* shrink a bignum */ @@ -6871,6 +7223,10 @@ int mp_shrink (mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_shrink.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_shrink.c */ /* Start: bn_mp_signed_bin_size.c */ @@ -6888,7 +7244,7 @@ int mp_shrink (mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* get the size for an signed equivalent */ @@ -6898,6 +7254,10 @@ int mp_signed_bin_size (mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_signed_bin_size.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_signed_bin_size.c */ /* Start: bn_mp_sqr.c */ @@ -6915,7 +7275,7 @@ int mp_signed_bin_size (mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* computes b = a*a */ @@ -6956,6 +7316,10 @@ if (a->used >= KARATSUBA_SQR_CUTOFF) { } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_sqr.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_sqr.c */ /* Start: bn_mp_sqrmod.c */ @@ -6973,7 +7337,7 @@ if (a->used >= KARATSUBA_SQR_CUTOFF) { * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* c = a * a (mod b) */ @@ -6997,6 +7361,10 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_sqrmod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_sqrmod.c */ /* Start: bn_mp_sqrt.c */ @@ -7014,7 +7382,7 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* this function is less generic than mp_n_root, simpler and faster */ @@ -7078,6 +7446,10 @@ E2: mp_clear(&t1); #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_sqrt.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_sqrt.c */ /* Start: bn_mp_sub.c */ @@ -7095,7 +7467,7 @@ E2: mp_clear(&t1); * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* high level subtraction (handles signs) */ @@ -7137,6 +7509,10 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_sub.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_sub.c */ /* Start: bn_mp_sub_d.c */ @@ -7154,7 +7530,7 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* single digit subtraction */ @@ -7178,6 +7554,10 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c) a->sign = MP_ZPOS; res = mp_add_d(a, b, c); a->sign = c->sign = MP_NEG; + + /* clamp */ + mp_clamp(c); + return res; } @@ -7226,6 +7606,10 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_sub_d.c,v $ */ +/* $Revision: 1.5 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_sub_d.c */ /* Start: bn_mp_submod.c */ @@ -7243,7 +7627,7 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* d = a - b (mod c) */ @@ -7268,6 +7652,10 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_submod.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_submod.c */ /* Start: bn_mp_to_signed_bin.c */ @@ -7285,7 +7673,7 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* store in signed [big endian] format */ @@ -7301,6 +7689,10 @@ int mp_to_signed_bin (mp_int * a, unsigned char *b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_to_signed_bin.c */ /* Start: bn_mp_to_signed_bin_n.c */ @@ -7318,7 +7710,7 @@ int mp_to_signed_bin (mp_int * a, unsigned char *b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* store in signed [big endian] format */ @@ -7332,6 +7724,10 @@ int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin_n.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_to_signed_bin_n.c */ /* Start: bn_mp_to_unsigned_bin.c */ @@ -7349,7 +7745,7 @@ int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* store in unsigned [big endian] format */ @@ -7380,6 +7776,10 @@ int mp_to_unsigned_bin (mp_int * a, unsigned char *b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_to_unsigned_bin.c */ /* Start: bn_mp_to_unsigned_bin_n.c */ @@ -7397,7 +7797,7 @@ int mp_to_unsigned_bin (mp_int * a, unsigned char *b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* store in unsigned [big endian] format */ @@ -7411,6 +7811,10 @@ int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin_n.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_to_unsigned_bin_n.c */ /* Start: bn_mp_toom_mul.c */ @@ -7428,7 +7832,7 @@ int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* multiplication using the Toom-Cook 3-way algorithm @@ -7695,6 +8099,10 @@ ERR: #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_toom_mul.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_toom_mul.c */ /* Start: bn_mp_toom_sqr.c */ @@ -7712,7 +8120,7 @@ ERR: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* squaring using Toom-Cook 3-way algorithm */ @@ -7921,6 +8329,10 @@ ERR: #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_toom_sqr.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_toom_sqr.c */ /* Start: bn_mp_toradix.c */ @@ -7938,7 +8350,7 @@ ERR: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* stores a bignum as a ASCII string in a given radix (2..64) */ @@ -7996,6 +8408,10 @@ int mp_toradix (mp_int * a, char *str, int radix) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_toradix.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_toradix.c */ /* Start: bn_mp_toradix_n.c */ @@ -8013,7 +8429,7 @@ int mp_toradix (mp_int * a, char *str, int radix) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* stores a bignum as a ASCII string in a given radix (2..64) @@ -8028,12 +8444,12 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) char *_s = str; /* check range of the maxlen, radix */ - if (maxlen < 3 || radix < 2 || radix > 64) { + if (maxlen < 2 || radix < 2 || radix > 64) { return MP_VAL; } /* quick out if its zero */ - if (mp_iszero(a) == 1) { + if (mp_iszero(a) == MP_YES) { *str++ = '0'; *str = '\0'; return MP_OKAY; @@ -8058,21 +8474,20 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) digs = 0; while (mp_iszero (&t) == 0) { + if (--maxlen < 1) { + /* no more room */ + break; + } if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { mp_clear (&t); return res; } *str++ = mp_s_rmap[d]; ++digs; - - if (--maxlen == 1) { - /* no more room */ - break; - } } /* reverse the digits of the string. In this case _s points - * to the first digit [exluding the sign] of the number] + * to the first digit [exluding the sign] of the number */ bn_reverse ((unsigned char *)_s, digs); @@ -8085,6 +8500,10 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_toradix_n.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_toradix_n.c */ /* Start: bn_mp_unsigned_bin_size.c */ @@ -8102,7 +8521,7 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* get the size for an unsigned equivalent */ @@ -8113,6 +8532,10 @@ int mp_unsigned_bin_size (mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_unsigned_bin_size.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_unsigned_bin_size.c */ /* Start: bn_mp_xor.c */ @@ -8130,7 +8553,7 @@ int mp_unsigned_bin_size (mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* XOR two ints together */ @@ -8164,6 +8587,10 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_xor.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_xor.c */ /* Start: bn_mp_zero.c */ @@ -8181,7 +8608,7 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* set to zero */ @@ -8200,6 +8627,10 @@ void mp_zero (mp_int * a) } #endif +/* $Source: /cvs/libtom/libtommath/bn_mp_zero.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_mp_zero.c */ /* Start: bn_prime_tab.c */ @@ -8217,7 +8648,7 @@ void mp_zero (mp_int * a) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ const mp_digit ltm_prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, @@ -8261,6 +8692,10 @@ const mp_digit ltm_prime_tab[] = { }; #endif +/* $Source: /cvs/libtom/libtommath/bn_prime_tab.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_prime_tab.c */ /* Start: bn_reverse.c */ @@ -8278,7 +8713,7 @@ const mp_digit ltm_prime_tab[] = { * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* reverse an array, used for radix code */ @@ -8300,6 +8735,10 @@ bn_reverse (unsigned char *s, int len) } #endif +/* $Source: /cvs/libtom/libtommath/bn_reverse.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_reverse.c */ /* Start: bn_s_mp_add.c */ @@ -8317,7 +8756,7 @@ bn_reverse (unsigned char *s, int len) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* low level addition, based on HAC pp.594, Algorithm 14.7 */ @@ -8409,6 +8848,10 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c) } #endif +/* $Source: /cvs/libtom/libtommath/bn_s_mp_add.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_s_mp_add.c */ /* Start: bn_s_mp_exptmod.c */ @@ -8426,9 +8869,8 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ - #ifdef MP_LOW_MEM #define TAB_SIZE 32 #else @@ -8662,6 +9104,10 @@ LBL_M: } #endif +/* $Source: /cvs/libtom/libtommath/bn_s_mp_exptmod.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_s_mp_exptmod.c */ /* Start: bn_s_mp_mul_digs.c */ @@ -8679,7 +9125,7 @@ LBL_M: * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* multiplies |a| * |b| and only computes upto digs digits of result @@ -8752,6 +9198,10 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) } #endif +/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_digs.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_s_mp_mul_digs.c */ /* Start: bn_s_mp_mul_high_digs.c */ @@ -8769,7 +9219,7 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* multiplies |a| * |b| and does not compute the lower digs digits @@ -8833,6 +9283,10 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) } #endif +/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_high_digs.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_s_mp_mul_high_digs.c */ /* Start: bn_s_mp_sqr.c */ @@ -8850,7 +9304,7 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ @@ -8917,6 +9371,10 @@ int s_mp_sqr (mp_int * a, mp_int * b) } #endif +/* $Source: /cvs/libtom/libtommath/bn_s_mp_sqr.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_s_mp_sqr.c */ /* Start: bn_s_mp_sub.c */ @@ -8934,7 +9392,7 @@ int s_mp_sqr (mp_int * a, mp_int * b) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ @@ -9006,6 +9464,10 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c) #endif +/* $Source: /cvs/libtom/libtommath/bn_s_mp_sub.c,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bn_s_mp_sub.c */ /* Start: bncore.c */ @@ -9023,7 +9485,7 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c) * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ /* Known optimal configurations @@ -9031,17 +9493,21 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c) CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) - AMD Athlon64 /GCC v3.4.4 / 74/ 124/LTM 0.34 + AMD Athlon64 /GCC v3.4.4 / 80/ 120/LTM 0.35 */ -int KARATSUBA_MUL_CUTOFF = 74, /* Min. number of digits before Karatsuba multiplication is used. */ - KARATSUBA_SQR_CUTOFF = 124, /* Min. number of digits before Karatsuba squaring is used. */ +int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */ + KARATSUBA_SQR_CUTOFF = 120, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400; #endif +/* $Source: /cvs/libtom/libtommath/bncore.c,v $ */ +/* $Revision: 1.4 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ + /* End: bncore.c */ @@ -10,7 +10,7 @@ * The library is free for all purposes without any express * guarantee it works. * - * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org + * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com */ #ifndef BN_H_ #define BN_H_ @@ -23,10 +23,13 @@ #include "tommath_class.h" -#undef MIN -#define MIN(x,y) ((x)<(y)?(x):(y)) -#undef MAX -#define MAX(x,y) ((x)>(y)?(x):(y)) +#ifndef MIN + #define MIN(x,y) ((x)<(y)?(x):(y)) +#endif + +#ifndef MAX + #define MAX(x,y) ((x)>(y)?(x):(y)) +#endif #ifdef __cplusplus extern "C" { @@ -112,7 +115,7 @@ extern "C" { #else /* prototypes for our heap functions */ extern void *XMALLOC(size_t n); - extern void *REALLOC(void *p, size_t n); + extern void *XREALLOC(void *p, size_t n); extern void *XCALLOC(size_t n, size_t s); extern void XFREE(void *p); #endif @@ -147,7 +150,6 @@ extern "C" { /* Primality generation flags */ #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ -#define LTM_PRIME_2MSB_OFF 0x0004 /* force 2nd MSB to 0 */ #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ typedef int mp_err; @@ -164,7 +166,7 @@ extern int KARATSUBA_MUL_CUTOFF, /* default precision */ #ifndef MP_PREC #ifndef MP_LOW_MEM - #define MP_PREC 64 /* default digits of precision */ + #define MP_PREC 32 /* default digits of precision */ #else #define MP_PREC 8 /* default digits of precision */ #endif @@ -518,13 +520,13 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback int mp_count_bits(mp_int *a); int mp_unsigned_bin_size(mp_int *a); -int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c); +int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); int mp_to_unsigned_bin(mp_int *a, unsigned char *b); int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); int mp_signed_bin_size(mp_int *a); -int mp_read_signed_bin(mp_int *a, unsigned char *b, int c); -int mp_to_signed_bin(mp_int *a, unsigned char *b); +int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); +int mp_to_signed_bin(mp_int *a, unsigned char *b); int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); int mp_read_radix(mp_int *a, const char *str, int radix); @@ -576,3 +578,7 @@ extern const char *mp_s_rmap; #endif + +/* $Source: /cvs/libtom/libtommath/tommath.h,v $ */ +/* $Revision: 1.8 $ */ +/* $Date: 2006/03/31 14:18:44 $ */ diff --git a/tommath.src b/tommath.src index 7a53860..4065822 100644 --- a/tommath.src +++ b/tommath.src @@ -66,7 +66,7 @@ QUALCOMM Australia \\ } } \maketitle -This text has been placed in the public domain. This text corresponds to the v0.35 release of the +This text has been placed in the public domain. This text corresponds to the v0.39 release of the LibTomMath project. \begin{alltt} @@ -77,7 +77,7 @@ K2L 1C3 Canada Phone: 1-613-836-3160 -Email: tomstdenis@iahu.ca +Email: tomstdenis@gmail.com \end{alltt} This text is formatted to the international B5 paper size of 176mm wide by 250mm tall using the \LaTeX{} @@ -268,7 +268,7 @@ and fast modular inversion, which we consider practical oversights. These optim any form of useful performance in non-trivial applications. To solve this problem the focus of this text is on the practical aspects of implementing a multiple precision integer -package. As a case study the ``LibTomMath''\footnote{Available at \url{http://math.libtomcrypt.org}} package is used +package. As a case study the ``LibTomMath''\footnote{Available at \url{http://math.libtomcrypt.com}} package is used to demonstrate algorithms with real implementations\footnote{In the ISO C programming language.} that have been field tested and work very well. The LibTomMath library is freely available on the Internet for all uses and this text discusses a very large portion of the inner workings of the library. @@ -2190,7 +2190,7 @@ left. After the digits have been shifted appropriately at most $lg(\beta) - 1$ shifts are left to perform. Step 5 calculates the number of remaining shifts required. If it is non-zero a modified shift loop is used to calculate the remaining product. -Essentially the loop is a generic version of algorith mp\_mul2 designed to handle any shift count in the range $1 \le x < lg(\beta)$. The $mask$ +Essentially the loop is a generic version of algorithm mp\_mul\_2 designed to handle any shift count in the range $1 \le x < lg(\beta)$. The $mask$ variable is used to extract the upper $d$ bits to form the carry for the next iteration. This algorithm is loosely measured as a $O(2n)$ algorithm which means that if the input is $n$-digits that it takes $2n$ ``time'' to @@ -2611,17 +2611,16 @@ Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the s \hspace{6mm}5.4.1 $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\ \hspace{3mm}5.5 $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\ \hspace{3mm}5.6 $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\ -6. $W_{pa} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\ \\ -7. $oldused \leftarrow c.used$ \\ -8. $c.used \leftarrow digs$ \\ -9. for $ix$ from $0$ to $pa$ do \\ -\hspace{3mm}9.1 $c_{ix} \leftarrow W_{ix}$ \\ -10. for $ix$ from $pa + 1$ to $oldused - 1$ do \\ -\hspace{3mm}10.1 $c_{ix} \leftarrow 0$ \\ +6. $oldused \leftarrow c.used$ \\ +7. $c.used \leftarrow digs$ \\ +8. for $ix$ from $0$ to $pa$ do \\ +\hspace{3mm}8.1 $c_{ix} \leftarrow W_{ix}$ \\ +9. for $ix$ from $pa + 1$ to $oldused - 1$ do \\ +\hspace{3mm}9.1 $c_{ix} \leftarrow 0$ \\ \\ -11. Clamp $c$. \\ -12. Return MP\_OKAY. \\ +10. Clamp $c$. \\ +11. Return MP\_OKAY. \\ \hline \end{tabular} \end{center} @@ -2775,26 +2774,25 @@ general purpose multiplication. Given two polynomial basis representations $f(x light algebra \cite{KARAP} that the following polynomial is equivalent to multiplication of the two integers the polynomials represent. \begin{equation} -f(x) \cdot g(x) = acx^2 + ((a - b)(c - d) - (ac + bd))x + bd +f(x) \cdot g(x) = acx^2 + ((a + b)(c + d) - (ac + bd))x + bd \end{equation} Using the observation that $ac$ and $bd$ could be re-used only three half sized multiplications would be required to produce the product. Applying this algorithm recursively, the work factor becomes $O(n^{lg(3)})$ which is substantially better than the work factor $O(n^2)$ of the Comba technique. It turns out what Karatsuba did not know or at least did not publish was that this is simply polynomial basis multiplication with the points -$\zeta_0$, $\zeta_{\infty}$ and $-\zeta_{-1}$. Consider the resultant system of equations. +$\zeta_0$, $\zeta_{\infty}$ and $\zeta_{1}$. Consider the resultant system of equations. \begin{center} \begin{tabular}{rcrcrcrc} $\zeta_{0}$ & $=$ & & & & & $w_0$ \\ -$-\zeta_{-1}$ & $=$ & $-w_2$ & $+$ & $w_1$ & $-$ & $w_0$ \\ +$\zeta_{1}$ & $=$ & $w_2$ & $+$ & $w_1$ & $+$ & $w_0$ \\ $\zeta_{\infty}$ & $=$ & $w_2$ & & & & \\ \end{tabular} \end{center} By adding the first and last equation to the equation in the middle the term $w_1$ can be isolated and all three coefficients solved for. The simplicity of this system of equations has made Karatsuba fairly popular. In fact the cutoff point is often fairly low\footnote{With LibTomMath 0.18 it is 70 and 109 digits for the Intel P4 and AMD Athlon respectively.} -making it an ideal algorithm to speed up certain public key cryptosystems such as RSA and Diffie-Hellman. It is worth noting that the point -$\zeta_1$ could be substituted for $-\zeta_{-1}$. In this case the first and third row are subtracted instead of added to the second row. +making it an ideal algorithm to speed up certain public key cryptosystems such as RSA and Diffie-Hellman. \newpage\begin{figure}[!here] \begin{small} @@ -2817,13 +2815,13 @@ Split the input. e.g. $a = x1 \cdot \beta^B + x0$ \\ Calculate the three products. \\ 8. $x0y0 \leftarrow x0 \cdot y0$ (\textit{mp\_mul}) \\ 9. $x1y1 \leftarrow x1 \cdot y1$ \\ -10. $t1 \leftarrow x1 - x0$ (\textit{mp\_sub}) \\ -11. $x0 \leftarrow y1 - y0$ \\ +10. $t1 \leftarrow x1 + x0$ (\textit{mp\_add}) \\ +11. $x0 \leftarrow y1 + y0$ \\ 12. $t1 \leftarrow t1 \cdot x0$ \\ \\ Calculate the middle term. \\ 13. $x0 \leftarrow x0y0 + x1y1$ \\ -14. $t1 \leftarrow x0 - t1$ \\ +14. $t1 \leftarrow t1 - x0$ (\textit{s\_mp\_sub}) \\ \\ Calculate the final product. \\ 15. $t1 \leftarrow t1 \cdot \beta^B$ (\textit{mp\_lshd}) \\ @@ -2850,7 +2848,7 @@ smallest input \textbf{used} count. After the radix point is chosen the inputs compute the lower halves. Step 6 and 7 computer the upper halves. After the halves have been computed the three intermediate half-size products must be computed. Step 8 and 9 compute the trivial products -$x0 \cdot y0$ and $x1 \cdot y1$. The mp\_int $x0$ is used as a temporary variable after $x1 - x0$ has been computed. By using $x0$ instead +$x0 \cdot y0$ and $x1 \cdot y1$. The mp\_int $x0$ is used as a temporary variable after $x1 + x0$ has been computed. By using $x0$ instead of an additional temporary variable, the algorithm can avoid an addition memory allocation operation. The remaining steps 13 through 18 compute the Karatsuba polynomial through a variety of digit shifting and addition operations. @@ -3246,10 +3244,10 @@ Let $h(x) = \left ( f(x) \right )^2$ represent the square of the polynomial. Th number with the following equation. \begin{equation} -h(x) = a^2x^2 + \left (a^2 + b^2 - (a - b)^2 \right )x + b^2 +h(x) = a^2x^2 + \left ((a + b)^2 - (a^2 + b^2) \right )x + b^2 \end{equation} -Upon closer inspection this equation only requires the calculation of three half-sized squares: $a^2$, $b^2$ and $(a - b)^2$. As in +Upon closer inspection this equation only requires the calculation of three half-sized squares: $a^2$, $b^2$ and $(a + b)^2$. As in Karatsuba multiplication, this algorithm can be applied recursively on the input and will achieve an asymptotic running time of $O \left ( n^{lg(3)} \right )$. @@ -3281,12 +3279,12 @@ Split the input. e.g. $a = x1\beta^B + x0$ \\ Calculate the three squares. \\ 6. $x0x0 \leftarrow x0^2$ (\textit{mp\_sqr}) \\ 7. $x1x1 \leftarrow x1^2$ \\ -8. $t1 \leftarrow x1 - x0$ (\textit{mp\_sub}) \\ +8. $t1 \leftarrow x1 + x0$ (\textit{s\_mp\_add}) \\ 9. $t1 \leftarrow t1^2$ \\ \\ Compute the middle term. \\ 10. $t2 \leftarrow x0x0 + x1x1$ (\textit{s\_mp\_add}) \\ -11. $t1 \leftarrow t2 - t1$ \\ +11. $t1 \leftarrow t1 - t2$ \\ \\ Compute final product. \\ 12. $t1 \leftarrow t1\beta^B$ (\textit{mp\_lshd}) \\ @@ -3309,7 +3307,7 @@ The radix point for squaring is simply placed exactly in the middle of the digit placed just below the middle. Step 3, 4 and 5 compute the two halves required using $B$ as the radix point. The first two squares in steps 6 and 7 are rather straightforward while the last square is of a more compact form. -By expanding $\left (x1 - x0 \right )^2$, the $x1^2$ and $x0^2$ terms in the middle disappear, that is $x1^2 + x0^2 - (x1 - x0)^2 = 2 \cdot x0 \cdot x1$. +By expanding $\left (x1 + x0 \right )^2$, the $x1^2$ and $x0^2$ terms in the middle disappear, that is $(x0 - x1)^2 - (x1^2 + x0^2) = 2 \cdot x0 \cdot x1$. Now if $5n$ single precision additions and a squaring of $n$-digits is faster than multiplying two $n$-digit numbers and doubling then this method is faster. Assuming no further recursions occur, the difference can be estimated with the following inequality. @@ -3732,6 +3730,7 @@ $0 \le r < \lfloor x/2^k \rfloor + n$. As a result at most a single subtraction \hline $6$ & $x/2 = 139$ \\ \hline $7$ & $x + n = 396$, $x/2 = 198$ \\ \hline $8$ & $x/2 = 99$ \\ +\hline $9$ & $x + n = 356$, $x/2 = 178$ \\ \hline \end{tabular} \end{center} @@ -3740,8 +3739,8 @@ $0 \le r < \lfloor x/2^k \rfloor + n$. As a result at most a single subtraction \label{fig:MONT1} \end{figure} -Consider the example in figure~\ref{fig:MONT1} which reduces $x = 5555$ modulo $n = 257$ when $k = 8$. The result of the algorithm $r = 99$ is -congruent to the value of $2^{-8} \cdot 5555 \mbox{ (mod }257\mbox{)}$. When $r$ is multiplied by $2^8$ modulo $257$ the correct residue +Consider the example in figure~\ref{fig:MONT1} which reduces $x = 5555$ modulo $n = 257$ when $k = 9$ (note $\beta^k = 512$ which is larger than $n$). The result of +the algorithm $r = 178$ is congruent to the value of $2^{-9} \cdot 5555 \mbox{ (mod }257\mbox{)}$. When $r$ is multiplied by $2^9$ modulo $257$ the correct residue $r \equiv 158$ is produced. Let $k = \lfloor lg(n) \rfloor + 1$ represent the number of bits in $n$. The current algorithm requires $2k^2$ single precision shifts @@ -3753,10 +3752,10 @@ Fortunately there exists an alternative representation of the algorithm. \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{Montgomery Reduction} (modified I). \\ -\textbf{Input}. Integer $x$, $n$ and $k$ \\ +\textbf{Input}. Integer $x$, $n$ and $k$ ($2^k > n$) \\ \textbf{Output}. $2^{-k}x \mbox{ (mod }n\mbox{)}$ \\ \hline \\ -1. for $t$ from $0$ to $k - 1$ do \\ +1. for $t$ from $1$ to $k$ do \\ \hspace{3mm}1.1 If the $t$'th bit of $x$ is one then \\ \hspace{6mm}1.1.1 $x \leftarrow x + 2^tn$ \\ 2. Return $x/2^k$. \\ @@ -3784,7 +3783,8 @@ precision shifts has now been reduced from $2k^2$ to $k^2 + k$ which is only a s \hline $6$ & $8896$ & $10001011000000$ \\ \hline $7$ & $x + 2^{6}n = 25344$ & $110001100000000$ \\ \hline $8$ & $25344$ & $110001100000000$ \\ -\hline -- & $x/2^k = 99$ & \\ +\hline $9$ & $x + 2^{7}n = 91136$ & $10110010000000000$ \\ +\hline -- & $x/2^k = 178$ & \\ \hline \end{tabular} \end{center} @@ -3793,7 +3793,7 @@ precision shifts has now been reduced from $2k^2$ to $k^2 + k$ which is only a s \label{fig:MONT2} \end{figure} -Figure~\ref{fig:MONT2} demonstrates the modified algorithm reducing $x = 5555$ modulo $n = 257$ with $k = 8$. +Figure~\ref{fig:MONT2} demonstrates the modified algorithm reducing $x = 5555$ modulo $n = 257$ with $k = 9$. With this algorithm a single shift right at the end is the only right shift required to reduce the input instead of $k$ right shifts inside the loop. Note that for the iterations $t = 2, 5, 6$ and $8$ where the result $x$ is not changed. In those iterations the $t$'th bit of $x$ is zero and the appropriate multiple of $n$ does not need to be added to force the $t$'th bit of the result to zero. @@ -3807,7 +3807,7 @@ previous algorithm re-written to compute the Montgomery reduction in this new fa \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{Montgomery Reduction} (modified II). \\ -\textbf{Input}. Integer $x$, $n$ and $k$ \\ +\textbf{Input}. Integer $x$, $n$ and $k$ ($\beta^k > n$) \\ \textbf{Output}. $\beta^{-k}x \mbox{ (mod }n\mbox{)}$ \\ \hline \\ 1. for $t$ from $0$ to $k - 1$ do \\ @@ -4035,7 +4035,7 @@ To calculate the variable $\rho$ a relatively simple algorithm will be required. \hline \\ 1. $b \leftarrow n_0$ \\ 2. If $b$ is even return(\textit{MP\_VAL}) \\ -3. $x \leftarrow ((b + 2) \mbox{ AND } 4) << 1) + b$ \\ +3. $x \leftarrow (((b + 2) \mbox{ AND } 4) << 1) + b$ \\ 4. for $k$ from 0 to $\lceil lg(lg(\beta)) \rceil - 2$ do \\ \hspace{3mm}4.1 $x \leftarrow x \cdot (2 - bx)$ \\ 5. $\rho \leftarrow \beta - x \mbox{ (mod }\beta\mbox{)}$ \\ @@ -4939,15 +4939,15 @@ a Left-to-Right algorithm is used to process the remaining few bits. EXAM,bn_s_mp_exptmod.c -Lines @26,if@ through @40,}@ determine the optimal window size based on the length of the exponent in bits. The window divisions are sorted +Lines @31,if@ through @45,}@ determine the optimal window size based on the length of the exponent in bits. The window divisions are sorted from smallest to greatest so that in each \textbf{if} statement only one condition must be tested. For example, by the \textbf{if} statement -on line @32,if@ the value of $x$ is already known to be greater than $140$. +on line @37,if@ the value of $x$ is already known to be greater than $140$. The conditional piece of code beginning on line @42,ifdef@ allows the window size to be restricted to five bits. This logic is used to ensure the table of precomputed powers of $G$ remains relatively small. -The for loop on line @49,for@ initializes the $M$ array while lines @59,mp_init@ and @62,mp_reduce@ compute the value of $\mu$ required for -Barrett reduction. +The for loop on line @60,for@ initializes the $M$ array while lines @71,mp_init@ and @75,mp_reduce@ through @85,}@ initialize the reduction +function that will be used for this modulus. -- More later. @@ -5230,23 +5230,23 @@ algorithm with only the quotient is mp_div(&a, &b, &c, NULL); /* c = [a/b] */ \end{verbatim} -Lines @37,if@ and @42,if@ handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor -respectively. After the two trivial cases all of the temporary variables are initialized. Line @76,neg@ determines the sign of -the quotient and line @77,sign@ ensures that both $x$ and $y$ are positive. +Lines @108,if@ and @113,if@ handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor +respectively. After the two trivial cases all of the temporary variables are initialized. Line @147,neg@ determines the sign of +the quotient and line @148,sign@ ensures that both $x$ and $y$ are positive. -The number of bits in the leading digit is calculated on line @80,norm@. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits +The number of bits in the leading digit is calculated on line @151,norm@. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits of precision which when reduced modulo $lg(\beta)$ produces the value of $k$. In this case $k$ is the number of bits in the leading digit which is exactly what is required. For the algorithm to operate $k$ must equal $lg(\beta) - 1$ and when it does not the inputs must be normalized by shifting them to the left by $lg(\beta) - 1 - k$ bits. Throughout the variables $n$ and $t$ will represent the highest digit of $x$ and $y$ respectively. These are first used to produce the -leading digit of the quotient. The loop beginning on line @113,for@ will produce the remainder of the quotient digits. +leading digit of the quotient. The loop beginning on line @184,for@ will produce the remainder of the quotient digits. -The conditional ``continue'' on line @114,if@ is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the +The conditional ``continue'' on line @186,continue@ is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the algorithm eliminates multiple non-zero digits in a single iteration. This ensures that $x_i$ is always non-zero since by definition the digits above the $i$'th position $x$ must be zero in order for the quotient to be precise\footnote{Precise as far as integer division is concerned.}. -Lines @142,t1@, @143,t1@ and @150,t2@ through @152,t2@ manually construct the high accuracy estimations by setting the digits of the two mp\_int +Lines @214,t1@, @216,t1@ and @222,t2@ through @225,t2@ manually construct the high accuracy estimations by setting the digits of the two mp\_int variables directly. \section{Single Digit Helpers} @@ -5744,33 +5744,30 @@ and will produce the greatest common divisor. \textbf{Input}. mp\_int $a$ and $b$ \\ \textbf{Output}. The greatest common divisor $c = (a, b)$. \\ \hline \\ -1. If $a = 0$ and $b \ne 0$ then \\ -\hspace{3mm}1.1 $c \leftarrow b$ \\ +1. If $a = 0$ then \\ +\hspace{3mm}1.1 $c \leftarrow \vert b \vert $ \\ \hspace{3mm}1.2 Return(\textit{MP\_OKAY}). \\ -2. If $a \ne 0$ and $b = 0$ then \\ -\hspace{3mm}2.1 $c \leftarrow a$ \\ +2. If $b = 0$ then \\ +\hspace{3mm}2.1 $c \leftarrow \vert a \vert $ \\ \hspace{3mm}2.2 Return(\textit{MP\_OKAY}). \\ -3. If $a = b = 0$ then \\ -\hspace{3mm}3.1 $c \leftarrow 1$ \\ -\hspace{3mm}3.2 Return(\textit{MP\_OKAY}). \\ -4. $u \leftarrow \vert a \vert, v \leftarrow \vert b \vert$ \\ -5. $k \leftarrow 0$ \\ -6. While $u.used > 0$ and $v.used > 0$ and $u_0 \equiv v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ -\hspace{3mm}6.1 $k \leftarrow k + 1$ \\ -\hspace{3mm}6.2 $u \leftarrow \lfloor u / 2 \rfloor$ \\ -\hspace{3mm}6.3 $v \leftarrow \lfloor v / 2 \rfloor$ \\ -7. While $u.used > 0$ and $u_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ -\hspace{3mm}7.1 $u \leftarrow \lfloor u / 2 \rfloor$ \\ -8. While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ -\hspace{3mm}8.1 $v \leftarrow \lfloor v / 2 \rfloor$ \\ -9. While $v.used > 0$ \\ -\hspace{3mm}9.1 If $\vert u \vert > \vert v \vert$ then \\ -\hspace{6mm}9.1.1 Swap $u$ and $v$. \\ -\hspace{3mm}9.2 $v \leftarrow \vert v \vert - \vert u \vert$ \\ -\hspace{3mm}9.3 While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ -\hspace{6mm}9.3.1 $v \leftarrow \lfloor v / 2 \rfloor$ \\ -10. $c \leftarrow u \cdot 2^k$ \\ -11. Return(\textit{MP\_OKAY}). \\ +3. $u \leftarrow \vert a \vert, v \leftarrow \vert b \vert$ \\ +4. $k \leftarrow 0$ \\ +5. While $u.used > 0$ and $v.used > 0$ and $u_0 \equiv v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ +\hspace{3mm}5.1 $k \leftarrow k + 1$ \\ +\hspace{3mm}5.2 $u \leftarrow \lfloor u / 2 \rfloor$ \\ +\hspace{3mm}5.3 $v \leftarrow \lfloor v / 2 \rfloor$ \\ +6. While $u.used > 0$ and $u_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ +\hspace{3mm}6.1 $u \leftarrow \lfloor u / 2 \rfloor$ \\ +7. While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ +\hspace{3mm}7.1 $v \leftarrow \lfloor v / 2 \rfloor$ \\ +8. While $v.used > 0$ \\ +\hspace{3mm}8.1 If $\vert u \vert > \vert v \vert$ then \\ +\hspace{6mm}8.1.1 Swap $u$ and $v$. \\ +\hspace{3mm}8.2 $v \leftarrow \vert v \vert - \vert u \vert$ \\ +\hspace{3mm}8.3 While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ +\hspace{6mm}8.3.1 $v \leftarrow \lfloor v / 2 \rfloor$ \\ +9. $c \leftarrow u \cdot 2^k$ \\ +10. Return(\textit{MP\_OKAY}). \\ \hline \end{tabular} \end{center} @@ -5782,17 +5779,17 @@ This algorithm will produce the greatest common divisor of two mp\_ints $a$ and Knuth \cite[pp. 338]{TAOCPV2} but has been modified to be simpler to explain. In theory it achieves the same asymptotic working time as Algorithm B and in practice this appears to be true. -The first three steps handle the cases where either one of or both inputs are zero. If either input is zero the greatest common divisor is the +The first two steps handle the cases where either one of or both inputs are zero. If either input is zero the greatest common divisor is the largest input or zero if they are both zero. If the inputs are not trivial than $u$ and $v$ are assigned the absolute values of $a$ and $b$ respectively and the algorithm will proceed to reduce the pair. -Step six will divide out any common factors of two and keep track of the count in the variable $k$. After this step two is no longer a +Step five will divide out any common factors of two and keep track of the count in the variable $k$. After this step, two is no longer a factor of the remaining greatest common divisor between $u$ and $v$ and can be safely evenly divided out of either whenever they are even. Step -seven and eight ensure that the $u$ and $v$ respectively have no more factors of two. At most only one of the while loops will iterate since +six and seven ensure that the $u$ and $v$ respectively have no more factors of two. At most only one of the while--loops will iterate since they cannot both be even. -By step nine both of $u$ and $v$ are odd which is required for the inner logic. First the pair are swapped such that $v$ is equal to -or greater than $u$. This ensures that the subtraction on step 9.2 will always produce a positive and even result. Step 9.3 removes any +By step eight both of $u$ and $v$ are odd which is required for the inner logic. First the pair are swapped such that $v$ is equal to +or greater than $u$. This ensures that the subtraction on step 8.2 will always produce a positive and even result. Step 8.3 removes any factors of two from the difference $u$ to ensure that in the next iteration of the loop both are once again odd. After $v = 0$ occurs the variable $u$ has the greatest common divisor of the pair $\left < u, v \right >$ just after step six. The result @@ -5803,17 +5800,17 @@ EXAM,bn_mp_gcd.c This function makes use of the macros mp\_iszero and mp\_iseven. The former evaluates to $1$ if the input mp\_int is equivalent to the integer zero otherwise it evaluates to $0$. The latter evaluates to $1$ if the input mp\_int represents a non-zero even integer otherwise it evaluates to $0$. Note that just because mp\_iseven may evaluate to $0$ does not mean the input is odd, it could also be zero. The three -trivial cases of inputs are handled on lines @25,zero@ through @34,}@. After those lines the inputs are assumed to be non-zero. +trivial cases of inputs are handled on lines @23,zero@ through @29,}@. After those lines the inputs are assumed to be non-zero. -Lines @36,if@ and @40,if@ make local copies $u$ and $v$ of the inputs $a$ and $b$ respectively. At this point the common factors of two -must be divided out of the two inputs. The while loop on line @49,while@ iterates so long as both are even. The local integer $k$ is used to -keep track of how many factors of $2$ are pulled out of both values. It is assumed that the number of factors will not exceed the maximum -value of a C ``int'' data type\footnote{Strictly speaking no array in C may have more than entries than are accessible by an ``int'' so this is not -a limitation.}. +Lines @32,if@ and @36,if@ make local copies $u$ and $v$ of the inputs $a$ and $b$ respectively. At this point the common factors of two +must be divided out of the two inputs. The block starting at line @43,common@ removes common factors of two by first counting the number of trailing +zero bits in both. The local integer $k$ is used to keep track of how many factors of $2$ are pulled out of both values. It is assumed that +the number of factors will not exceed the maximum value of a C ``int'' data type\footnote{Strictly speaking no array in C may have more than +entries than are accessible by an ``int'' so this is not a limitation.}. -At this point there are no more common factors of two in the two values. The while loops on lines @60,while@ and @65,while@ remove any independent -factors of two such that both $u$ and $v$ are guaranteed to be an odd integer before hitting the main body of the algorithm. The while loop -on line @71, while@ performs the reduction of the pair until $v$ is equal to zero. The unsigned comparison and subtraction algorithms are used in +At this point there are no more common factors of two in the two values. The divisions by a power of two on lines @60,div_2d@ and @67,div_2d@ remove +any independent factors of two such that both $u$ and $v$ are guaranteed to be an odd integer before hitting the main body of the algorithm. The while loop +on line @72, while@ performs the reduction of the pair until $v$ is equal to zero. The unsigned comparison and subtraction algorithms are used in place of the full signed routines since both values are guaranteed to be positive and the result of the subtraction is guaranteed to be non-negative. \section{Least Common Multiple} diff --git a/tommath.tex b/tommath.tex index b016010..c9c5976 100644 --- a/tommath.tex +++ b/tommath.tex @@ -66,7 +66,7 @@ QUALCOMM Australia \\ } } \maketitle -This text has been placed in the public domain. This text corresponds to the v0.35 release of the +This text has been placed in the public domain. This text corresponds to the v0.39 release of the LibTomMath project. \begin{alltt} @@ -77,7 +77,7 @@ K2L 1C3 Canada Phone: 1-613-836-3160 -Email: tomstdenis@iahu.ca +Email: tomstdenis@gmail.com \end{alltt} This text is formatted to the international B5 paper size of 176mm wide by 250mm tall using the \LaTeX{} @@ -268,7 +268,7 @@ and fast modular inversion, which we consider practical oversights. These optim any form of useful performance in non-trivial applications. To solve this problem the focus of this text is on the practical aspects of implementing a multiple precision integer -package. As a case study the ``LibTomMath''\footnote{Available at \url{http://math.libtomcrypt.org}} package is used +package. As a case study the ``LibTomMath''\footnote{Available at \url{http://math.libtomcrypt.com}} package is used to demonstrate algorithms with real implementations\footnote{In the ISO C programming language.} that have been field tested and work very well. The LibTomMath library is freely available on the Internet for all uses and this text discusses a very large portion of the inner workings of the library. @@ -814,6 +814,7 @@ decrementally. 039 return MP_OKAY; 040 \} 041 #endif +042 \end{alltt} \end{small} @@ -902,6 +903,7 @@ with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp 037 \} 038 \} 039 #endif +040 \end{alltt} \end{small} @@ -1008,6 +1010,7 @@ assumed to contain undefined values they are initially set to zero. 050 return MP_OKAY; 051 \} 052 #endif +053 \end{alltt} \end{small} @@ -1096,6 +1099,7 @@ correct no further memory re-allocations are required to work with the mp\_int. 041 return MP_OKAY; 042 \} 043 #endif +044 \end{alltt} \end{small} @@ -1183,6 +1187,7 @@ initialization which allows for quick recovery from runtime errors. 052 \} 053 054 #endif +055 \end{alltt} \end{small} @@ -1268,6 +1273,7 @@ when all of the digits are zero to ensure that the mp\_int is valid at all times 037 \} 038 \} 039 #endif +040 \end{alltt} \end{small} @@ -1405,6 +1411,7 @@ implement the pseudo-code. 061 return MP_OKAY; 062 \} 063 #endif +064 \end{alltt} \end{small} @@ -1519,6 +1526,7 @@ such this algorithm will perform two operations in one step. 025 return mp_copy (b, a); 026 \} 027 #endif +028 \end{alltt} \end{small} @@ -1570,6 +1578,7 @@ This algorithm simply resets a mp\_int to the default state. 029 \} 030 \} 031 #endif +032 \end{alltt} \end{small} @@ -1631,6 +1640,7 @@ logic to handle it. 036 return MP_OKAY; 037 \} 038 #endif +039 \end{alltt} \end{small} @@ -1692,6 +1702,7 @@ zero as negative. 033 return MP_OKAY; 034 \} 035 #endif +036 \end{alltt} \end{small} @@ -1739,6 +1750,7 @@ single digit is set (\textit{modulo $\beta$}) and the \textbf{used} count is adj 022 a->used = (a->dp[0] != 0) ? 1 : 0; 023 \} 024 #endif +025 \end{alltt} \end{small} @@ -1819,6 +1831,7 @@ Excess zero digits are trimmed in steps 2.1 and 3 by using higher level algorith 041 return MP_OKAY; 042 \} 043 #endif +044 \end{alltt} \end{small} @@ -1921,6 +1934,7 @@ the zero'th digit. If after all of the digits have been compared, no difference 048 return MP_EQ; 049 \} 050 #endif +051 \end{alltt} \end{small} @@ -1987,6 +2001,7 @@ $\vert a \vert < \vert b \vert$. Step number four will compare the two when the 036 \} 037 \} 038 #endif +039 \end{alltt} \end{small} @@ -2205,6 +2220,7 @@ The final carry is stored in $c_{max}$ and digits above $max$ upto $oldused$ are 102 return MP_OKAY; 103 \} 104 #endif +105 \end{alltt} \end{small} @@ -2376,6 +2392,7 @@ If $b$ has a smaller magnitude than $a$ then step 9 will force the carry and cop 082 \} 083 084 #endif +085 \end{alltt} \end{small} @@ -2511,6 +2528,7 @@ within algorithm s\_mp\_add will force $-0$ to become $0$. 046 \} 047 048 #endif +049 \end{alltt} \end{small} @@ -2623,6 +2641,7 @@ algorithm from producing $-a - -a = -0$ as a result. 052 \} 053 054 #endif +055 \end{alltt} \end{small} @@ -2757,6 +2776,7 @@ Step 8 clears any leading digits of $b$ in case it originally had a larger magni 075 return MP_OKAY; 076 \} 077 #endif +078 \end{alltt} \end{small} @@ -2857,6 +2877,7 @@ least significant bit not the most significant bit. 061 return MP_OKAY; 062 \} 063 #endif +064 \end{alltt} \end{small} @@ -2977,6 +2998,7 @@ step 8 sets the lower $b$ digits to zero. 060 return MP_OKAY; 061 \} 062 #endif +063 \end{alltt} \end{small} @@ -3088,6 +3110,7 @@ Once the window copy is complete the upper digits must be zeroed and the \textbf 065 a->used -= b; 066 \} 067 #endif +068 \end{alltt} \end{small} @@ -3146,7 +3169,7 @@ left. After the digits have been shifted appropriately at most $lg(\beta) - 1$ shifts are left to perform. Step 5 calculates the number of remaining shifts required. If it is non-zero a modified shift loop is used to calculate the remaining product. -Essentially the loop is a generic version of algorith mp\_mul2 designed to handle any shift count in the range $1 \le x < lg(\beta)$. The $mask$ +Essentially the loop is a generic version of algorithm mp\_mul\_2 designed to handle any shift count in the range $1 \le x < lg(\beta)$. The $mask$ variable is used to extract the upper $d$ bits to form the carry for the next iteration. This algorithm is loosely measured as a $O(2n)$ algorithm which means that if the input is $n$-digits that it takes $2n$ ``time'' to @@ -3221,6 +3244,7 @@ complete. It is possible to optimize this algorithm down to a $O(n)$ algorithm 078 return MP_OKAY; 079 \} 080 #endif +081 \end{alltt} \end{small} @@ -3357,6 +3381,7 @@ by using algorithm mp\_mod\_2d. 090 return MP_OKAY; 091 \} 092 #endif +093 \end{alltt} \end{small} @@ -3448,6 +3473,7 @@ is copied to $b$, leading digits are removed and the remaining leading digit is 048 return MP_OKAY; 049 \} 050 #endif +051 \end{alltt} \end{small} @@ -3687,6 +3713,7 @@ exceed the precision requested. 083 return MP_OKAY; 084 \} 085 #endif +086 \end{alltt} \end{small} @@ -3837,17 +3864,16 @@ Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the s \hspace{6mm}5.4.1 $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\ \hspace{3mm}5.5 $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\ \hspace{3mm}5.6 $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\ -6. $W_{pa} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\ \\ -7. $oldused \leftarrow c.used$ \\ -8. $c.used \leftarrow digs$ \\ -9. for $ix$ from $0$ to $pa$ do \\ -\hspace{3mm}9.1 $c_{ix} \leftarrow W_{ix}$ \\ -10. for $ix$ from $pa + 1$ to $oldused - 1$ do \\ -\hspace{3mm}10.1 $c_{ix} \leftarrow 0$ \\ +6. $oldused \leftarrow c.used$ \\ +7. $c.used \leftarrow digs$ \\ +8. for $ix$ from $0$ to $pa$ do \\ +\hspace{3mm}8.1 $c_{ix} \leftarrow W_{ix}$ \\ +9. for $ix$ from $pa + 1$ to $oldused - 1$ do \\ +\hspace{3mm}9.1 $c_{ix} \leftarrow 0$ \\ \\ -11. Clamp $c$. \\ -12. Return MP\_OKAY. \\ +10. Clamp $c$. \\ +11. Return MP\_OKAY. \\ \hline \end{tabular} \end{center} @@ -3942,39 +3968,38 @@ and addition operations in the nested loop in parallel. 069 /* execute loop */ 070 for (iz = 0; iz < iy; ++iz) \{ 071 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); -072 \} -073 -074 /* store term */ -075 W[ix] = ((mp_digit)_W) & MP_MASK; -076 -077 /* make next carry */ -078 _W = _W >> ((mp_word)DIGIT_BIT); -079 \} -080 -081 /* store final carry */ -082 W[ix] = (mp_digit)(_W & MP_MASK); -083 -084 /* setup dest */ -085 olduse = c->used; -086 c->used = pa; -087 -088 \{ -089 register mp_digit *tmpc; -090 tmpc = c->dp; -091 for (ix = 0; ix < pa+1; ix++) \{ -092 /* now extract the previous digit [below the carry] */ -093 *tmpc++ = W[ix]; -094 \} -095 -096 /* clear unused digits [that existed in the old copy of c] */ -097 for (; ix < olduse; ix++) \{ -098 *tmpc++ = 0; -099 \} -100 \} -101 mp_clamp (c); -102 return MP_OKAY; -103 \} -104 #endif +072 +073 \} +074 +075 /* store term */ +076 W[ix] = ((mp_digit)_W) & MP_MASK; +077 +078 /* make next carry */ +079 _W = _W >> ((mp_word)DIGIT_BIT); +080 \} +081 +082 /* setup dest */ +083 olduse = c->used; +084 c->used = pa; +085 +086 \{ +087 register mp_digit *tmpc; +088 tmpc = c->dp; +089 for (ix = 0; ix < pa+1; ix++) \{ +090 /* now extract the previous digit [below the carry] */ +091 *tmpc++ = W[ix]; +092 \} +093 +094 /* clear unused digits [that existed in the old copy of c] */ +095 for (; ix < olduse; ix++) \{ +096 *tmpc++ = 0; +097 \} +098 \} +099 mp_clamp (c); +100 return MP_OKAY; +101 \} +102 #endif +103 \end{alltt} \end{small} @@ -3982,7 +4007,7 @@ As per the pseudo--code we first calculate $pa$ (line 47) as the number of digit to produce the individual columns of the product. We use the two aliases $tmpx$ and $tmpy$ (lines 61, 62) to point inside the two multiplicands quickly. -The inner loop (lines 70 to 72) of this implementation is where the tradeoff come into play. Originally this comba +The inner loop (lines 70 to 73) of this implementation is where the tradeoff come into play. Originally this comba implementation was ``row--major'' which means it adds to each of the columns in each pass. After the outer loop it would then fix the carries. This was very fast except it had an annoying drawback. You had to read a mp\_word and two mp\_digits and write one mp\_word per iteration. On processors such as the Athlon XP and P4 this did not matter much since the cache bandwidth @@ -3990,8 +4015,8 @@ is very high and it can keep the ALU fed with data. It did, however, matter on slower and also often doesn't exist. This new algorithm only performs two reads per iteration under the assumption that the compiler has aliased $\_ \hat W$ to a CPU register. -After the inner loop we store the current accumulator in $W$ and shift $\_ \hat W$ (lines 75, 78) to forward it as -a carry for the next pass. After the outer loop we use the final carry (line 82) as the last digit of the product. +After the inner loop we store the current accumulator in $W$ and shift $\_ \hat W$ (lines 76, 79) to forward it as +a carry for the next pass. After the outer loop we use the final carry (line 76) as the last digit of the product. \subsection{Polynomial Basis Multiplication} To break the $O(n^2)$ barrier in multiplication requires a completely different look at integer multiplication. In the following algorithms @@ -4095,26 +4120,25 @@ general purpose multiplication. Given two polynomial basis representations $f(x light algebra \cite{KARAP} that the following polynomial is equivalent to multiplication of the two integers the polynomials represent. \begin{equation} -f(x) \cdot g(x) = acx^2 + ((a - b)(c - d) - (ac + bd))x + bd +f(x) \cdot g(x) = acx^2 + ((a + b)(c + d) - (ac + bd))x + bd \end{equation} Using the observation that $ac$ and $bd$ could be re-used only three half sized multiplications would be required to produce the product. Applying this algorithm recursively, the work factor becomes $O(n^{lg(3)})$ which is substantially better than the work factor $O(n^2)$ of the Comba technique. It turns out what Karatsuba did not know or at least did not publish was that this is simply polynomial basis multiplication with the points -$\zeta_0$, $\zeta_{\infty}$ and $-\zeta_{-1}$. Consider the resultant system of equations. +$\zeta_0$, $\zeta_{\infty}$ and $\zeta_{1}$. Consider the resultant system of equations. \begin{center} \begin{tabular}{rcrcrcrc} $\zeta_{0}$ & $=$ & & & & & $w_0$ \\ -$-\zeta_{-1}$ & $=$ & $-w_2$ & $+$ & $w_1$ & $-$ & $w_0$ \\ +$\zeta_{1}$ & $=$ & $w_2$ & $+$ & $w_1$ & $+$ & $w_0$ \\ $\zeta_{\infty}$ & $=$ & $w_2$ & & & & \\ \end{tabular} \end{center} By adding the first and last equation to the equation in the middle the term $w_1$ can be isolated and all three coefficients solved for. The simplicity of this system of equations has made Karatsuba fairly popular. In fact the cutoff point is often fairly low\footnote{With LibTomMath 0.18 it is 70 and 109 digits for the Intel P4 and AMD Athlon respectively.} -making it an ideal algorithm to speed up certain public key cryptosystems such as RSA and Diffie-Hellman. It is worth noting that the point -$\zeta_1$ could be substituted for $-\zeta_{-1}$. In this case the first and third row are subtracted instead of added to the second row. +making it an ideal algorithm to speed up certain public key cryptosystems such as RSA and Diffie-Hellman. \newpage\begin{figure}[!here] \begin{small} @@ -4137,13 +4161,13 @@ Split the input. e.g. $a = x1 \cdot \beta^B + x0$ \\ Calculate the three products. \\ 8. $x0y0 \leftarrow x0 \cdot y0$ (\textit{mp\_mul}) \\ 9. $x1y1 \leftarrow x1 \cdot y1$ \\ -10. $t1 \leftarrow x1 - x0$ (\textit{mp\_sub}) \\ -11. $x0 \leftarrow y1 - y0$ \\ +10. $t1 \leftarrow x1 + x0$ (\textit{mp\_add}) \\ +11. $x0 \leftarrow y1 + y0$ \\ 12. $t1 \leftarrow t1 \cdot x0$ \\ \\ Calculate the middle term. \\ 13. $x0 \leftarrow x0y0 + x1y1$ \\ -14. $t1 \leftarrow x0 - t1$ \\ +14. $t1 \leftarrow t1 - x0$ (\textit{s\_mp\_sub}) \\ \\ Calculate the final product. \\ 15. $t1 \leftarrow t1 \cdot \beta^B$ (\textit{mp\_lshd}) \\ @@ -4170,7 +4194,7 @@ smallest input \textbf{used} count. After the radix point is chosen the inputs compute the lower halves. Step 6 and 7 computer the upper halves. After the halves have been computed the three intermediate half-size products must be computed. Step 8 and 9 compute the trivial products -$x0 \cdot y0$ and $x1 \cdot y1$. The mp\_int $x0$ is used as a temporary variable after $x1 - x0$ has been computed. By using $x0$ instead +$x0 \cdot y0$ and $x1 \cdot y1$. The mp\_int $x0$ is used as a temporary variable after $x1 + x0$ has been computed. By using $x0$ instead of an additional temporary variable, the algorithm can avoid an addition memory allocation operation. The remaining steps 13 through 18 compute the Karatsuba polynomial through a variety of digit shifting and addition operations. @@ -4191,12 +4215,12 @@ The remaining steps 13 through 18 compute the Karatsuba polynomial through a var 025 * b = b1 * B**n + b0 026 * 027 * Then, a * b => -028 a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0 +028 a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 029 * 030 * Note that a1b1 and a0b0 are used twice and only need to be 031 * computed once. So in total three half size (half # of 032 * digit) multiplications are performed, a0b0, a1b1 and -033 * (a1-b1)(a0-b0) +033 * (a1+b1)(a0+b0) 034 * 035 * Note that a multiplication of half the digits requires 036 * 1/4th the number of single precision multiplications so in @@ -4287,19 +4311,19 @@ The remaining steps 13 through 18 compute the Karatsuba polynomial through a var 121 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) 122 goto X1Y1; /* x1y1 = x1*y1 */ 123 -124 /* now calc x1-x0 and y1-y0 */ -125 if (mp_sub (&x1, &x0, &t1) != MP_OKAY) +124 /* now calc x1+x0 and y1+y0 */ +125 if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) 126 goto X1Y1; /* t1 = x1 - x0 */ -127 if (mp_sub (&y1, &y0, &x0) != MP_OKAY) +127 if (s_mp_add (&y1, &y0, &x0) != MP_OKAY) 128 goto X1Y1; /* t2 = y1 - y0 */ 129 if (mp_mul (&t1, &x0, &t1) != MP_OKAY) -130 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */ +130 goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ 131 132 /* add x0y0 */ 133 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) 134 goto X1Y1; /* t2 = x0y0 + x1y1 */ -135 if (mp_sub (&x0, &t1, &t1) != MP_OKAY) -136 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */ +135 if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY) +136 goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ 137 138 /* shift by B */ 139 if (mp_lshd (&t1, B) != MP_OKAY) @@ -4326,6 +4350,7 @@ The remaining steps 13 through 18 compute the Karatsuba polynomial through a var 160 return err; 161 \} 162 #endif +163 \end{alltt} \end{small} @@ -4729,6 +4754,7 @@ result $a \cdot b$ is produced. 277 \} 278 279 #endif +280 \end{alltt} \end{small} @@ -4837,6 +4863,7 @@ s\_mp\_mul\_digs will clear it. 059 return res; 060 \} 061 #endif +062 \end{alltt} \end{small} @@ -5006,6 +5033,7 @@ results calculated so far. This involves expensive carry propagation which will 077 return MP_OKAY; 078 \} 079 #endif +080 \end{alltt} \end{small} @@ -5188,6 +5216,7 @@ only to even outputs and it is the square of the term at the $\lfloor ix / 2 \rf 107 return MP_OKAY; 108 \} 109 #endif +110 \end{alltt} \end{small} @@ -5205,10 +5234,10 @@ Let $h(x) = \left ( f(x) \right )^2$ represent the square of the polynomial. Th number with the following equation. \begin{equation} -h(x) = a^2x^2 + \left (a^2 + b^2 - (a - b)^2 \right )x + b^2 +h(x) = a^2x^2 + \left ((a + b)^2 - (a^2 + b^2) \right )x + b^2 \end{equation} -Upon closer inspection this equation only requires the calculation of three half-sized squares: $a^2$, $b^2$ and $(a - b)^2$. As in +Upon closer inspection this equation only requires the calculation of three half-sized squares: $a^2$, $b^2$ and $(a + b)^2$. As in Karatsuba multiplication, this algorithm can be applied recursively on the input and will achieve an asymptotic running time of $O \left ( n^{lg(3)} \right )$. @@ -5240,12 +5269,12 @@ Split the input. e.g. $a = x1\beta^B + x0$ \\ Calculate the three squares. \\ 6. $x0x0 \leftarrow x0^2$ (\textit{mp\_sqr}) \\ 7. $x1x1 \leftarrow x1^2$ \\ -8. $t1 \leftarrow x1 - x0$ (\textit{mp\_sub}) \\ +8. $t1 \leftarrow x1 + x0$ (\textit{s\_mp\_add}) \\ 9. $t1 \leftarrow t1^2$ \\ \\ Compute the middle term. \\ 10. $t2 \leftarrow x0x0 + x1x1$ (\textit{s\_mp\_add}) \\ -11. $t1 \leftarrow t2 - t1$ \\ +11. $t1 \leftarrow t1 - t2$ \\ \\ Compute final product. \\ 12. $t1 \leftarrow t1\beta^B$ (\textit{mp\_lshd}) \\ @@ -5268,7 +5297,7 @@ The radix point for squaring is simply placed exactly in the middle of the digit placed just below the middle. Step 3, 4 and 5 compute the two halves required using $B$ as the radix point. The first two squares in steps 6 and 7 are rather straightforward while the last square is of a more compact form. -By expanding $\left (x1 - x0 \right )^2$, the $x1^2$ and $x0^2$ terms in the middle disappear, that is $x1^2 + x0^2 - (x1 - x0)^2 = 2 \cdot x0 \cdot x1$. +By expanding $\left (x1 + x0 \right )^2$, the $x1^2$ and $x0^2$ terms in the middle disappear, that is $(x0 - x1)^2 - (x1^2 + x0^2) = 2 \cdot x0 \cdot x1$. Now if $5n$ single precision additions and a squaring of $n$-digits is faster than multiplying two $n$-digit numbers and doubling then this method is faster. Assuming no further recursions occur, the difference can be estimated with the following inequality. @@ -5363,8 +5392,8 @@ ratio of 1:7. } than simpler operations such as addition. 079 if (mp_sqr (&x1, &x1x1) != MP_OKAY) 080 goto X1X1; /* x1x1 = x1*x1 */ 081 -082 /* now calc (x1-x0)**2 */ -083 if (mp_sub (&x1, &x0, &t1) != MP_OKAY) +082 /* now calc (x1+x0)**2 */ +083 if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) 084 goto X1X1; /* t1 = x1 - x0 */ 085 if (mp_sqr (&t1, &t1) != MP_OKAY) 086 goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ @@ -5372,8 +5401,8 @@ ratio of 1:7. } than simpler operations such as addition. 088 /* add x0y0 */ 089 if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) 090 goto X1X1; /* t2 = x0x0 + x1x1 */ -091 if (mp_sub (&t2, &t1, &t1) != MP_OKAY) -092 goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */ +091 if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY) +092 goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ 093 094 /* shift by B */ 095 if (mp_lshd (&t1, B) != MP_OKAY) @@ -5398,6 +5427,7 @@ ratio of 1:7. } than simpler operations such as addition. 114 return err; 115 \} 116 #endif +117 \end{alltt} \end{small} @@ -5494,6 +5524,7 @@ neither of the polynomial basis algorithms should be used then either the Comba 051 return res; 052 \} 053 #endif +054 \end{alltt} \end{small} @@ -5827,6 +5858,7 @@ performed at most twice, and on average once. However, if $a \ge b^2$ than it wi 093 return res; 094 \} 095 #endif +096 \end{alltt} \end{small} @@ -5879,6 +5911,7 @@ is equivalent and much faster. The final value is computed by taking the intege 027 return mp_div (a, b, a, NULL); 028 \} 029 #endif +030 \end{alltt} \end{small} @@ -5943,6 +5976,7 @@ $0 \le r < \lfloor x/2^k \rfloor + n$. As a result at most a single subtraction \hline $6$ & $x/2 = 139$ \\ \hline $7$ & $x + n = 396$, $x/2 = 198$ \\ \hline $8$ & $x/2 = 99$ \\ +\hline $9$ & $x + n = 356$, $x/2 = 178$ \\ \hline \end{tabular} \end{center} @@ -5951,8 +5985,8 @@ $0 \le r < \lfloor x/2^k \rfloor + n$. As a result at most a single subtraction \label{fig:MONT1} \end{figure} -Consider the example in figure~\ref{fig:MONT1} which reduces $x = 5555$ modulo $n = 257$ when $k = 8$. The result of the algorithm $r = 99$ is -congruent to the value of $2^{-8} \cdot 5555 \mbox{ (mod }257\mbox{)}$. When $r$ is multiplied by $2^8$ modulo $257$ the correct residue +Consider the example in figure~\ref{fig:MONT1} which reduces $x = 5555$ modulo $n = 257$ when $k = 9$ (note $\beta^k = 512$ which is larger than $n$). The result of +the algorithm $r = 178$ is congruent to the value of $2^{-9} \cdot 5555 \mbox{ (mod }257\mbox{)}$. When $r$ is multiplied by $2^9$ modulo $257$ the correct residue $r \equiv 158$ is produced. Let $k = \lfloor lg(n) \rfloor + 1$ represent the number of bits in $n$. The current algorithm requires $2k^2$ single precision shifts @@ -5964,10 +5998,10 @@ Fortunately there exists an alternative representation of the algorithm. \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{Montgomery Reduction} (modified I). \\ -\textbf{Input}. Integer $x$, $n$ and $k$ \\ +\textbf{Input}. Integer $x$, $n$ and $k$ ($2^k > n$) \\ \textbf{Output}. $2^{-k}x \mbox{ (mod }n\mbox{)}$ \\ \hline \\ -1. for $t$ from $0$ to $k - 1$ do \\ +1. for $t$ from $1$ to $k$ do \\ \hspace{3mm}1.1 If the $t$'th bit of $x$ is one then \\ \hspace{6mm}1.1.1 $x \leftarrow x + 2^tn$ \\ 2. Return $x/2^k$. \\ @@ -5995,7 +6029,8 @@ precision shifts has now been reduced from $2k^2$ to $k^2 + k$ which is only a s \hline $6$ & $8896$ & $10001011000000$ \\ \hline $7$ & $x + 2^{6}n = 25344$ & $110001100000000$ \\ \hline $8$ & $25344$ & $110001100000000$ \\ -\hline -- & $x/2^k = 99$ & \\ +\hline $9$ & $x + 2^{7}n = 91136$ & $10110010000000000$ \\ +\hline -- & $x/2^k = 178$ & \\ \hline \end{tabular} \end{center} @@ -6004,7 +6039,7 @@ precision shifts has now been reduced from $2k^2$ to $k^2 + k$ which is only a s \label{fig:MONT2} \end{figure} -Figure~\ref{fig:MONT2} demonstrates the modified algorithm reducing $x = 5555$ modulo $n = 257$ with $k = 8$. +Figure~\ref{fig:MONT2} demonstrates the modified algorithm reducing $x = 5555$ modulo $n = 257$ with $k = 9$. With this algorithm a single shift right at the end is the only right shift required to reduce the input instead of $k$ right shifts inside the loop. Note that for the iterations $t = 2, 5, 6$ and $8$ where the result $x$ is not changed. In those iterations the $t$'th bit of $x$ is zero and the appropriate multiple of $n$ does not need to be added to force the $t$'th bit of the result to zero. @@ -6018,7 +6053,7 @@ previous algorithm re-written to compute the Montgomery reduction in this new fa \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{Montgomery Reduction} (modified II). \\ -\textbf{Input}. Integer $x$, $n$ and $k$ \\ +\textbf{Input}. Integer $x$, $n$ and $k$ ($\beta^k > n$) \\ \textbf{Output}. $\beta^{-k}x \mbox{ (mod }n\mbox{)}$ \\ \hline \\ 1. for $t$ from $0$ to $k - 1$ do \\ @@ -6234,6 +6269,7 @@ multiplications. 111 return MP_OKAY; 112 \} 113 #endif +114 \end{alltt} \end{small} @@ -6478,6 +6514,7 @@ stored in the destination $x$. 165 return MP_OKAY; 166 \} 167 #endif +168 \end{alltt} \end{small} @@ -6505,7 +6542,7 @@ To calculate the variable $\rho$ a relatively simple algorithm will be required. \hline \\ 1. $b \leftarrow n_0$ \\ 2. If $b$ is even return(\textit{MP\_VAL}) \\ -3. $x \leftarrow ((b + 2) \mbox{ AND } 4) << 1) + b$ \\ +3. $x \leftarrow (((b + 2) \mbox{ AND } 4) << 1) + b$ \\ 4. for $k$ from 0 to $\lceil lg(lg(\beta)) \rceil - 2$ do \\ \hspace{3mm}4.1 $x \leftarrow x \cdot (2 - bx)$ \\ 5. $\rho \leftarrow \beta - x \mbox{ (mod }\beta\mbox{)}$ \\ @@ -6559,11 +6596,13 @@ to calculate $1/n_0$ when $\beta$ is a power of two. 047 #endif 048 049 /* rho = -1/m mod b */ -050 *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; +050 *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MAS + K; 051 052 return MP_OKAY; 053 \} 054 #endif +055 \end{alltt} \end{small} @@ -6830,6 +6869,7 @@ at step 3. 087 return MP_OKAY; 088 \} 089 #endif +090 \end{alltt} \end{small} @@ -6885,6 +6925,7 @@ completeness. 025 \} 026 027 #endif +028 \end{alltt} \end{small} @@ -6943,6 +6984,7 @@ step 3 then $n$ must be of Diminished Radix form. 036 \} 037 038 #endif +039 \end{alltt} \end{small} @@ -7027,6 +7069,7 @@ shift which makes the algorithm fairly inexpensive to use. 054 \} 055 056 #endif +057 \end{alltt} \end{small} @@ -7096,6 +7139,7 @@ is sufficient to solve for $k$. Alternatively if $n$ has more than one digit th 040 return MP_OKAY; 041 \} 042 #endif +043 \end{alltt} \end{small} @@ -7172,6 +7216,7 @@ This algorithm quickly determines if a modulus is of the form required for algor 045 \} 046 047 #endif +048 \end{alltt} \end{small} @@ -7381,6 +7426,7 @@ iteration of the loop moves the bits of the exponent $b$ upwards to the most sig 050 return MP_OKAY; 051 \} 052 #endif +053 \end{alltt} \end{small} @@ -7620,7 +7666,8 @@ algorithm since their arguments are essentially the same (\textit{two mp\_ints a 065 \} 066 067 /* modified diminished radix reduction */ -068 #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) +068 #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defin + ed(BN_S_MP_EXPTMOD_C) 069 if (mp_reduce_is_2k_l(P) == MP_YES) \{ 070 return s_mp_exptmod(G, X, P, Y, 1); 071 \} @@ -7660,6 +7707,7 @@ algorithm since their arguments are essentially the same (\textit{two mp\_ints a 105 \} 106 107 #endif +108 \end{alltt} \end{small} @@ -7839,252 +7887,252 @@ a Left-to-Right algorithm is used to process the remaining few bits. \hspace{-5.1mm}{\bf File}: bn\_s\_mp\_exptmod.c \vspace{-3mm} \begin{alltt} -016 -017 #ifdef MP_LOW_MEM -018 #define TAB_SIZE 32 -019 #else -020 #define TAB_SIZE 256 -021 #endif -022 -023 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmod +016 #ifdef MP_LOW_MEM +017 #define TAB_SIZE 32 +018 #else +019 #define TAB_SIZE 256 +020 #endif +021 +022 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmod e) -024 \{ -025 mp_int M[TAB_SIZE], res, mu; -026 mp_digit buf; -027 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; -028 int (*redux)(mp_int*,mp_int*,mp_int*); -029 -030 /* find window size */ -031 x = mp_count_bits (X); -032 if (x <= 7) \{ -033 winsize = 2; -034 \} else if (x <= 36) \{ -035 winsize = 3; -036 \} else if (x <= 140) \{ -037 winsize = 4; -038 \} else if (x <= 450) \{ -039 winsize = 5; -040 \} else if (x <= 1303) \{ -041 winsize = 6; -042 \} else if (x <= 3529) \{ -043 winsize = 7; -044 \} else \{ -045 winsize = 8; -046 \} -047 -048 #ifdef MP_LOW_MEM -049 if (winsize > 5) \{ -050 winsize = 5; -051 \} -052 #endif -053 -054 /* init M array */ -055 /* init first cell */ -056 if ((err = mp_init(&M[1])) != MP_OKAY) \{ -057 return err; -058 \} -059 -060 /* now init the second half of the array */ -061 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{ -062 if ((err = mp_init(&M[x])) != MP_OKAY) \{ -063 for (y = 1<<(winsize-1); y < x; y++) \{ -064 mp_clear (&M[y]); -065 \} -066 mp_clear(&M[1]); -067 return err; -068 \} -069 \} -070 -071 /* create mu, used for Barrett reduction */ -072 if ((err = mp_init (&mu)) != MP_OKAY) \{ -073 goto LBL_M; -074 \} -075 -076 if (redmode == 0) \{ -077 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) \{ -078 goto LBL_MU; -079 \} -080 redux = mp_reduce; -081 \} else \{ -082 if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) \{ -083 goto LBL_MU; -084 \} -085 redux = mp_reduce_2k_l; -086 \} -087 -088 /* create M table -089 * -090 * The M table contains powers of the base, -091 * e.g. M[x] = G**x mod P -092 * -093 * The first half of the table is not -094 * computed though accept for M[0] and M[1] -095 */ -096 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) \{ -097 goto LBL_MU; -098 \} -099 -100 /* compute the value at M[1<<(winsize-1)] by squaring -101 * M[1] (winsize-1) times -102 */ -103 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) \{ -104 goto LBL_MU; -105 \} -106 -107 for (x = 0; x < (winsize - 1); x++) \{ -108 /* square it */ -109 if ((err = mp_sqr (&M[1 << (winsize - 1)], -110 &M[1 << (winsize - 1)])) != MP_OKAY) \{ -111 goto LBL_MU; -112 \} -113 -114 /* reduce modulo P */ -115 if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) \{ -116 goto LBL_MU; -117 \} -118 \} -119 -120 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) -121 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) -122 */ -123 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) \{ -124 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) \{ -125 goto LBL_MU; -126 \} -127 if ((err = redux (&M[x], P, &mu)) != MP_OKAY) \{ -128 goto LBL_MU; -129 \} -130 \} -131 -132 /* setup result */ -133 if ((err = mp_init (&res)) != MP_OKAY) \{ -134 goto LBL_MU; -135 \} -136 mp_set (&res, 1); -137 -138 /* set initial mode and bit cnt */ -139 mode = 0; -140 bitcnt = 1; -141 buf = 0; -142 digidx = X->used - 1; -143 bitcpy = 0; -144 bitbuf = 0; -145 -146 for (;;) \{ -147 /* grab next digit as required */ -148 if (--bitcnt == 0) \{ -149 /* if digidx == -1 we are out of digits */ -150 if (digidx == -1) \{ -151 break; -152 \} -153 /* read next digit and reset the bitcnt */ -154 buf = X->dp[digidx--]; -155 bitcnt = (int) DIGIT_BIT; -156 \} -157 -158 /* grab the next msb from the exponent */ -159 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1; -160 buf <<= (mp_digit)1; -161 -162 /* if the bit is zero and mode == 0 then we ignore it -163 * These represent the leading zero bits before the first 1 bit -164 * in the exponent. Technically this opt is not required but it -165 * does lower the # of trivial squaring/reductions used -166 */ -167 if (mode == 0 && y == 0) \{ -168 continue; -169 \} -170 -171 /* if the bit is zero and mode == 1 then we square */ -172 if (mode == 1 && y == 0) \{ -173 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ -174 goto LBL_RES; -175 \} -176 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ -177 goto LBL_RES; -178 \} -179 continue; -180 \} -181 -182 /* else we add it to the window */ -183 bitbuf |= (y << (winsize - ++bitcpy)); -184 mode = 2; -185 -186 if (bitcpy == winsize) \{ -187 /* ok window is filled so square as required and multiply */ -188 /* square first */ -189 for (x = 0; x < winsize; x++) \{ -190 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ -191 goto LBL_RES; -192 \} -193 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ -194 goto LBL_RES; -195 \} -196 \} -197 -198 /* then multiply */ -199 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) \{ -200 goto LBL_RES; -201 \} -202 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ -203 goto LBL_RES; -204 \} -205 -206 /* empty window and reset */ -207 bitcpy = 0; -208 bitbuf = 0; -209 mode = 1; -210 \} -211 \} -212 -213 /* if bits remain then square/multiply */ -214 if (mode == 2 && bitcpy > 0) \{ -215 /* square then multiply if the bit is set */ -216 for (x = 0; x < bitcpy; x++) \{ -217 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ -218 goto LBL_RES; -219 \} -220 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ -221 goto LBL_RES; -222 \} -223 -224 bitbuf <<= 1; -225 if ((bitbuf & (1 << winsize)) != 0) \{ -226 /* then multiply */ -227 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) \{ -228 goto LBL_RES; -229 \} -230 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ -231 goto LBL_RES; -232 \} -233 \} -234 \} -235 \} -236 -237 mp_exch (&res, Y); -238 err = MP_OKAY; -239 LBL_RES:mp_clear (&res); -240 LBL_MU:mp_clear (&mu); -241 LBL_M: -242 mp_clear(&M[1]); -243 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{ -244 mp_clear (&M[x]); -245 \} -246 return err; -247 \} -248 #endif +023 \{ +024 mp_int M[TAB_SIZE], res, mu; +025 mp_digit buf; +026 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; +027 int (*redux)(mp_int*,mp_int*,mp_int*); +028 +029 /* find window size */ +030 x = mp_count_bits (X); +031 if (x <= 7) \{ +032 winsize = 2; +033 \} else if (x <= 36) \{ +034 winsize = 3; +035 \} else if (x <= 140) \{ +036 winsize = 4; +037 \} else if (x <= 450) \{ +038 winsize = 5; +039 \} else if (x <= 1303) \{ +040 winsize = 6; +041 \} else if (x <= 3529) \{ +042 winsize = 7; +043 \} else \{ +044 winsize = 8; +045 \} +046 +047 #ifdef MP_LOW_MEM +048 if (winsize > 5) \{ +049 winsize = 5; +050 \} +051 #endif +052 +053 /* init M array */ +054 /* init first cell */ +055 if ((err = mp_init(&M[1])) != MP_OKAY) \{ +056 return err; +057 \} +058 +059 /* now init the second half of the array */ +060 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{ +061 if ((err = mp_init(&M[x])) != MP_OKAY) \{ +062 for (y = 1<<(winsize-1); y < x; y++) \{ +063 mp_clear (&M[y]); +064 \} +065 mp_clear(&M[1]); +066 return err; +067 \} +068 \} +069 +070 /* create mu, used for Barrett reduction */ +071 if ((err = mp_init (&mu)) != MP_OKAY) \{ +072 goto LBL_M; +073 \} +074 +075 if (redmode == 0) \{ +076 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) \{ +077 goto LBL_MU; +078 \} +079 redux = mp_reduce; +080 \} else \{ +081 if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) \{ +082 goto LBL_MU; +083 \} +084 redux = mp_reduce_2k_l; +085 \} +086 +087 /* create M table +088 * +089 * The M table contains powers of the base, +090 * e.g. M[x] = G**x mod P +091 * +092 * The first half of the table is not +093 * computed though accept for M[0] and M[1] +094 */ +095 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) \{ +096 goto LBL_MU; +097 \} +098 +099 /* compute the value at M[1<<(winsize-1)] by squaring +100 * M[1] (winsize-1) times +101 */ +102 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) \{ +103 goto LBL_MU; +104 \} +105 +106 for (x = 0; x < (winsize - 1); x++) \{ +107 /* square it */ +108 if ((err = mp_sqr (&M[1 << (winsize - 1)], +109 &M[1 << (winsize - 1)])) != MP_OKAY) \{ +110 goto LBL_MU; +111 \} +112 +113 /* reduce modulo P */ +114 if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) \{ +115 goto LBL_MU; +116 \} +117 \} +118 +119 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) +120 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) +121 */ +122 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) \{ +123 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) \{ +124 goto LBL_MU; +125 \} +126 if ((err = redux (&M[x], P, &mu)) != MP_OKAY) \{ +127 goto LBL_MU; +128 \} +129 \} +130 +131 /* setup result */ +132 if ((err = mp_init (&res)) != MP_OKAY) \{ +133 goto LBL_MU; +134 \} +135 mp_set (&res, 1); +136 +137 /* set initial mode and bit cnt */ +138 mode = 0; +139 bitcnt = 1; +140 buf = 0; +141 digidx = X->used - 1; +142 bitcpy = 0; +143 bitbuf = 0; +144 +145 for (;;) \{ +146 /* grab next digit as required */ +147 if (--bitcnt == 0) \{ +148 /* if digidx == -1 we are out of digits */ +149 if (digidx == -1) \{ +150 break; +151 \} +152 /* read next digit and reset the bitcnt */ +153 buf = X->dp[digidx--]; +154 bitcnt = (int) DIGIT_BIT; +155 \} +156 +157 /* grab the next msb from the exponent */ +158 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1; +159 buf <<= (mp_digit)1; +160 +161 /* if the bit is zero and mode == 0 then we ignore it +162 * These represent the leading zero bits before the first 1 bit +163 * in the exponent. Technically this opt is not required but it +164 * does lower the # of trivial squaring/reductions used +165 */ +166 if (mode == 0 && y == 0) \{ +167 continue; +168 \} +169 +170 /* if the bit is zero and mode == 1 then we square */ +171 if (mode == 1 && y == 0) \{ +172 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ +173 goto LBL_RES; +174 \} +175 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +176 goto LBL_RES; +177 \} +178 continue; +179 \} +180 +181 /* else we add it to the window */ +182 bitbuf |= (y << (winsize - ++bitcpy)); +183 mode = 2; +184 +185 if (bitcpy == winsize) \{ +186 /* ok window is filled so square as required and multiply */ +187 /* square first */ +188 for (x = 0; x < winsize; x++) \{ +189 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ +190 goto LBL_RES; +191 \} +192 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +193 goto LBL_RES; +194 \} +195 \} +196 +197 /* then multiply */ +198 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) \{ +199 goto LBL_RES; +200 \} +201 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +202 goto LBL_RES; +203 \} +204 +205 /* empty window and reset */ +206 bitcpy = 0; +207 bitbuf = 0; +208 mode = 1; +209 \} +210 \} +211 +212 /* if bits remain then square/multiply */ +213 if (mode == 2 && bitcpy > 0) \{ +214 /* square then multiply if the bit is set */ +215 for (x = 0; x < bitcpy; x++) \{ +216 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ +217 goto LBL_RES; +218 \} +219 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +220 goto LBL_RES; +221 \} +222 +223 bitbuf <<= 1; +224 if ((bitbuf & (1 << winsize)) != 0) \{ +225 /* then multiply */ +226 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) \{ +227 goto LBL_RES; +228 \} +229 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +230 goto LBL_RES; +231 \} +232 \} +233 \} +234 \} +235 +236 mp_exch (&res, Y); +237 err = MP_OKAY; +238 LBL_RES:mp_clear (&res); +239 LBL_MU:mp_clear (&mu); +240 LBL_M: +241 mp_clear(&M[1]); +242 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{ +243 mp_clear (&M[x]); +244 \} +245 return err; +246 \} +247 #endif +248 \end{alltt} \end{small} -Lines 21 through 40 determine the optimal window size based on the length of the exponent in bits. The window divisions are sorted +Lines 31 through 45 determine the optimal window size based on the length of the exponent in bits. The window divisions are sorted from smallest to greatest so that in each \textbf{if} statement only one condition must be tested. For example, by the \textbf{if} statement -on line 32 the value of $x$ is already known to be greater than $140$. +on line 37 the value of $x$ is already known to be greater than $140$. -The conditional piece of code beginning on line 48 allows the window size to be restricted to five bits. This logic is used to ensure +The conditional piece of code beginning on line 47 allows the window size to be restricted to five bits. This logic is used to ensure the table of precomputed powers of $G$ remains relatively small. -The for loop on line 61 initializes the $M$ array while lines 62 and 77 compute the value of $\mu$ required for -Barrett reduction. +The for loop on line 60 initializes the $M$ array while lines 71 and 76 through 85 initialize the reduction +function that will be used for this modulus. -- More later. @@ -8146,6 +8194,7 @@ equivalent to $m \cdot 2^k$. By this logic when $m = 1$ a quick power of two ca 041 return MP_OKAY; 042 \} 043 #endif +044 \end{alltt} \end{small} @@ -8666,6 +8715,7 @@ respectively be replaced with a zero. 285 #endif 286 287 #endif +288 \end{alltt} \end{small} @@ -8677,23 +8727,23 @@ algorithm with only the quotient is mp_div(&a, &b, &c, NULL); /* c = [a/b] */ \end{verbatim} -Lines 37 and 44 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor -respectively. After the two trivial cases all of the temporary variables are initialized. Line 105 determines the sign of -the quotient and line 76 ensures that both $x$ and $y$ are positive. +Lines 108 and 113 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor +respectively. After the two trivial cases all of the temporary variables are initialized. Line 147 determines the sign of +the quotient and line 148 ensures that both $x$ and $y$ are positive. -The number of bits in the leading digit is calculated on line 105. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits +The number of bits in the leading digit is calculated on line 151. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits of precision which when reduced modulo $lg(\beta)$ produces the value of $k$. In this case $k$ is the number of bits in the leading digit which is exactly what is required. For the algorithm to operate $k$ must equal $lg(\beta) - 1$ and when it does not the inputs must be normalized by shifting them to the left by $lg(\beta) - 1 - k$ bits. Throughout the variables $n$ and $t$ will represent the highest digit of $x$ and $y$ respectively. These are first used to produce the -leading digit of the quotient. The loop beginning on line 183 will produce the remainder of the quotient digits. +leading digit of the quotient. The loop beginning on line 184 will produce the remainder of the quotient digits. -The conditional ``continue'' on line 114 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the +The conditional ``continue'' on line 186 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the algorithm eliminates multiple non-zero digits in a single iteration. This ensures that $x_i$ is always non-zero since by definition the digits above the $i$'th position $x$ must be zero in order for the quotient to be precise\footnote{Precise as far as integer division is concerned.}. -Lines 130, 130 and 134 through 134 manually construct the high accuracy estimations by setting the digits of the two mp\_int +Lines 214, 216 and 222 through 225 manually construct the high accuracy estimations by setting the digits of the two mp\_int variables directly. \section{Single Digit Helpers} @@ -8757,69 +8807,73 @@ This algorithm initiates a temporary mp\_int with the value of the single digit 039 /* fix sign */ 040 a->sign = c->sign = MP_NEG; 041 -042 return res; -043 \} +042 /* clamp */ +043 mp_clamp(c); 044 -045 /* old number of used digits in c */ -046 oldused = c->used; +045 return res; +046 \} 047 -048 /* sign always positive */ -049 c->sign = MP_ZPOS; +048 /* old number of used digits in c */ +049 oldused = c->used; 050 -051 /* source alias */ -052 tmpa = a->dp; +051 /* sign always positive */ +052 c->sign = MP_ZPOS; 053 -054 /* destination alias */ -055 tmpc = c->dp; +054 /* source alias */ +055 tmpa = a->dp; 056 -057 /* if a is positive */ -058 if (a->sign == MP_ZPOS) \{ -059 /* add digit, after this we're propagating -060 * the carry. -061 */ -062 *tmpc = *tmpa++ + b; -063 mu = *tmpc >> DIGIT_BIT; -064 *tmpc++ &= MP_MASK; -065 -066 /* now handle rest of the digits */ -067 for (ix = 1; ix < a->used; ix++) \{ -068 *tmpc = *tmpa++ + mu; -069 mu = *tmpc >> DIGIT_BIT; -070 *tmpc++ &= MP_MASK; -071 \} -072 /* set final carry */ -073 ix++; -074 *tmpc++ = mu; -075 -076 /* setup size */ -077 c->used = a->used + 1; -078 \} else \{ -079 /* a was negative and |a| < b */ -080 c->used = 1; -081 -082 /* the result is a single digit */ -083 if (a->used == 1) \{ -084 *tmpc++ = b - a->dp[0]; -085 \} else \{ -086 *tmpc++ = b; -087 \} -088 -089 /* setup count so the clearing of oldused -090 * can fall through correctly -091 */ -092 ix = 1; -093 \} -094 -095 /* now zero to oldused */ -096 while (ix++ < oldused) \{ -097 *tmpc++ = 0; -098 \} -099 mp_clamp(c); -100 -101 return MP_OKAY; -102 \} +057 /* destination alias */ +058 tmpc = c->dp; +059 +060 /* if a is positive */ +061 if (a->sign == MP_ZPOS) \{ +062 /* add digit, after this we're propagating +063 * the carry. +064 */ +065 *tmpc = *tmpa++ + b; +066 mu = *tmpc >> DIGIT_BIT; +067 *tmpc++ &= MP_MASK; +068 +069 /* now handle rest of the digits */ +070 for (ix = 1; ix < a->used; ix++) \{ +071 *tmpc = *tmpa++ + mu; +072 mu = *tmpc >> DIGIT_BIT; +073 *tmpc++ &= MP_MASK; +074 \} +075 /* set final carry */ +076 ix++; +077 *tmpc++ = mu; +078 +079 /* setup size */ +080 c->used = a->used + 1; +081 \} else \{ +082 /* a was negative and |a| < b */ +083 c->used = 1; +084 +085 /* the result is a single digit */ +086 if (a->used == 1) \{ +087 *tmpc++ = b - a->dp[0]; +088 \} else \{ +089 *tmpc++ = b; +090 \} +091 +092 /* setup count so the clearing of oldused +093 * can fall through correctly +094 */ +095 ix = 1; +096 \} +097 +098 /* now zero to oldused */ +099 while (ix++ < oldused) \{ +100 *tmpc++ = 0; +101 \} +102 mp_clamp(c); 103 -104 #endif +104 return MP_OKAY; +105 \} +106 +107 #endif +108 \end{alltt} \end{small} @@ -8929,6 +8983,7 @@ Unlike the full multiplication algorithms this algorithm does not require any si 072 return MP_OKAY; 073 \} 074 #endif +075 \end{alltt} \end{small} @@ -9074,6 +9129,7 @@ from chapter seven. 103 \} 104 105 #endif +106 \end{alltt} \end{small} @@ -9260,6 +9316,7 @@ root. Ideally this algorithm is meant to find the $n$'th root of an input where 125 return res; 126 \} 127 #endif +128 \end{alltt} \end{small} @@ -9336,6 +9393,7 @@ the integers from $0$ to $\beta - 1$. 048 return MP_OKAY; 049 \} 050 #endif +051 \end{alltt} \end{small} @@ -9425,61 +9483,65 @@ as part of larger input without any significant problem. 020 int y, res, neg; 021 char ch; 022 -023 /* make sure the radix is ok */ -024 if (radix < 2 || radix > 64) \{ -025 return MP_VAL; -026 \} -027 -028 /* if the leading digit is a -029 * minus set the sign to negative. -030 */ -031 if (*str == '-') \{ -032 ++str; -033 neg = MP_NEG; -034 \} else \{ -035 neg = MP_ZPOS; -036 \} -037 -038 /* set the integer to the default of zero */ -039 mp_zero (a); -040 -041 /* process each digit of the string */ -042 while (*str) \{ -043 /* if the radix < 36 the conversion is case insensitive -044 * this allows numbers like 1AB and 1ab to represent the same value -045 * [e.g. in hex] -046 */ -047 ch = (char) ((radix < 36) ? toupper (*str) : *str); -048 for (y = 0; y < 64; y++) \{ -049 if (ch == mp_s_rmap[y]) \{ -050 break; -051 \} -052 \} -053 -054 /* if the char was found in the map -055 * and is less than the given radix add it -056 * to the number, otherwise exit the loop. -057 */ -058 if (y < radix) \{ -059 if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) \{ -060 return res; -061 \} -062 if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) \{ +023 /* zero the digit bignum */ +024 mp_zero(a); +025 +026 /* make sure the radix is ok */ +027 if (radix < 2 || radix > 64) \{ +028 return MP_VAL; +029 \} +030 +031 /* if the leading digit is a +032 * minus set the sign to negative. +033 */ +034 if (*str == '-') \{ +035 ++str; +036 neg = MP_NEG; +037 \} else \{ +038 neg = MP_ZPOS; +039 \} +040 +041 /* set the integer to the default of zero */ +042 mp_zero (a); +043 +044 /* process each digit of the string */ +045 while (*str) \{ +046 /* if the radix < 36 the conversion is case insensitive +047 * this allows numbers like 1AB and 1ab to represent the same value +048 * [e.g. in hex] +049 */ +050 ch = (char) ((radix < 36) ? toupper (*str) : *str); +051 for (y = 0; y < 64; y++) \{ +052 if (ch == mp_s_rmap[y]) \{ +053 break; +054 \} +055 \} +056 +057 /* if the char was found in the map +058 * and is less than the given radix add it +059 * to the number, otherwise exit the loop. +060 */ +061 if (y < radix) \{ +062 if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) \{ 063 return res; 064 \} -065 \} else \{ -066 break; -067 \} -068 ++str; -069 \} -070 -071 /* set the sign only if a != 0 */ -072 if (mp_iszero(a) != 1) \{ -073 a->sign = neg; -074 \} -075 return MP_OKAY; -076 \} -077 #endif +065 if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) \{ +066 return res; +067 \} +068 \} else \{ +069 break; +070 \} +071 ++str; +072 \} +073 +074 /* set the sign only if a != 0 */ +075 if (mp_iszero(a) != 1) \{ +076 a->sign = neg; +077 \} +078 return MP_OKAY; +079 \} +080 #endif +081 \end{alltt} \end{small} @@ -9599,6 +9661,7 @@ are required instead of a series of $n \times k$ divisions. One design flaw of 068 \} 069 070 #endif +071 \end{alltt} \end{small} @@ -9728,33 +9791,30 @@ and will produce the greatest common divisor. \textbf{Input}. mp\_int $a$ and $b$ \\ \textbf{Output}. The greatest common divisor $c = (a, b)$. \\ \hline \\ -1. If $a = 0$ and $b \ne 0$ then \\ -\hspace{3mm}1.1 $c \leftarrow b$ \\ +1. If $a = 0$ then \\ +\hspace{3mm}1.1 $c \leftarrow \vert b \vert $ \\ \hspace{3mm}1.2 Return(\textit{MP\_OKAY}). \\ -2. If $a \ne 0$ and $b = 0$ then \\ -\hspace{3mm}2.1 $c \leftarrow a$ \\ +2. If $b = 0$ then \\ +\hspace{3mm}2.1 $c \leftarrow \vert a \vert $ \\ \hspace{3mm}2.2 Return(\textit{MP\_OKAY}). \\ -3. If $a = b = 0$ then \\ -\hspace{3mm}3.1 $c \leftarrow 1$ \\ -\hspace{3mm}3.2 Return(\textit{MP\_OKAY}). \\ -4. $u \leftarrow \vert a \vert, v \leftarrow \vert b \vert$ \\ -5. $k \leftarrow 0$ \\ -6. While $u.used > 0$ and $v.used > 0$ and $u_0 \equiv v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ -\hspace{3mm}6.1 $k \leftarrow k + 1$ \\ -\hspace{3mm}6.2 $u \leftarrow \lfloor u / 2 \rfloor$ \\ -\hspace{3mm}6.3 $v \leftarrow \lfloor v / 2 \rfloor$ \\ -7. While $u.used > 0$ and $u_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ -\hspace{3mm}7.1 $u \leftarrow \lfloor u / 2 \rfloor$ \\ -8. While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ -\hspace{3mm}8.1 $v \leftarrow \lfloor v / 2 \rfloor$ \\ -9. While $v.used > 0$ \\ -\hspace{3mm}9.1 If $\vert u \vert > \vert v \vert$ then \\ -\hspace{6mm}9.1.1 Swap $u$ and $v$. \\ -\hspace{3mm}9.2 $v \leftarrow \vert v \vert - \vert u \vert$ \\ -\hspace{3mm}9.3 While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ -\hspace{6mm}9.3.1 $v \leftarrow \lfloor v / 2 \rfloor$ \\ -10. $c \leftarrow u \cdot 2^k$ \\ -11. Return(\textit{MP\_OKAY}). \\ +3. $u \leftarrow \vert a \vert, v \leftarrow \vert b \vert$ \\ +4. $k \leftarrow 0$ \\ +5. While $u.used > 0$ and $v.used > 0$ and $u_0 \equiv v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ +\hspace{3mm}5.1 $k \leftarrow k + 1$ \\ +\hspace{3mm}5.2 $u \leftarrow \lfloor u / 2 \rfloor$ \\ +\hspace{3mm}5.3 $v \leftarrow \lfloor v / 2 \rfloor$ \\ +6. While $u.used > 0$ and $u_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ +\hspace{3mm}6.1 $u \leftarrow \lfloor u / 2 \rfloor$ \\ +7. While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ +\hspace{3mm}7.1 $v \leftarrow \lfloor v / 2 \rfloor$ \\ +8. While $v.used > 0$ \\ +\hspace{3mm}8.1 If $\vert u \vert > \vert v \vert$ then \\ +\hspace{6mm}8.1.1 Swap $u$ and $v$. \\ +\hspace{3mm}8.2 $v \leftarrow \vert v \vert - \vert u \vert$ \\ +\hspace{3mm}8.3 While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\ +\hspace{6mm}8.3.1 $v \leftarrow \lfloor v / 2 \rfloor$ \\ +9. $c \leftarrow u \cdot 2^k$ \\ +10. Return(\textit{MP\_OKAY}). \\ \hline \end{tabular} \end{center} @@ -9766,17 +9826,17 @@ This algorithm will produce the greatest common divisor of two mp\_ints $a$ and Knuth \cite[pp. 338]{TAOCPV2} but has been modified to be simpler to explain. In theory it achieves the same asymptotic working time as Algorithm B and in practice this appears to be true. -The first three steps handle the cases where either one of or both inputs are zero. If either input is zero the greatest common divisor is the +The first two steps handle the cases where either one of or both inputs are zero. If either input is zero the greatest common divisor is the largest input or zero if they are both zero. If the inputs are not trivial than $u$ and $v$ are assigned the absolute values of $a$ and $b$ respectively and the algorithm will proceed to reduce the pair. -Step six will divide out any common factors of two and keep track of the count in the variable $k$. After this step two is no longer a +Step five will divide out any common factors of two and keep track of the count in the variable $k$. After this step, two is no longer a factor of the remaining greatest common divisor between $u$ and $v$ and can be safely evenly divided out of either whenever they are even. Step -seven and eight ensure that the $u$ and $v$ respectively have no more factors of two. At most only one of the while loops will iterate since +six and seven ensure that the $u$ and $v$ respectively have no more factors of two. At most only one of the while--loops will iterate since they cannot both be even. -By step nine both of $u$ and $v$ are odd which is required for the inner logic. First the pair are swapped such that $v$ is equal to -or greater than $u$. This ensures that the subtraction on step 9.2 will always produce a positive and even result. Step 9.3 removes any +By step eight both of $u$ and $v$ are odd which is required for the inner logic. First the pair are swapped such that $v$ is equal to +or greater than $u$. This ensures that the subtraction on step 8.2 will always produce a positive and even result. Step 8.3 removes any factors of two from the difference $u$ to ensure that in the next iteration of the loop both are once again odd. After $v = 0$ occurs the variable $u$ has the greatest common divisor of the pair $\left < u, v \right >$ just after step six. The result @@ -9794,108 +9854,101 @@ must be adjusted by multiplying by the common factors of two ($2^k$) removed ear 021 int k, u_lsb, v_lsb, res; 022 023 /* either zero than gcd is the largest */ -024 if (mp_iszero (a) == 1 && mp_iszero (b) == 0) \{ +024 if (mp_iszero (a) == MP_YES) \{ 025 return mp_abs (b, c); 026 \} -027 if (mp_iszero (a) == 0 && mp_iszero (b) == 1) \{ +027 if (mp_iszero (b) == MP_YES) \{ 028 return mp_abs (a, c); 029 \} 030 -031 /* optimized. At this point if a == 0 then -032 * b must equal zero too -033 */ -034 if (mp_iszero (a) == 1) \{ -035 mp_zero(c); -036 return MP_OKAY; -037 \} -038 -039 /* get copies of a and b we can modify */ -040 if ((res = mp_init_copy (&u, a)) != MP_OKAY) \{ -041 return res; -042 \} -043 -044 if ((res = mp_init_copy (&v, b)) != MP_OKAY) \{ -045 goto LBL_U; -046 \} +031 /* get copies of a and b we can modify */ +032 if ((res = mp_init_copy (&u, a)) != MP_OKAY) \{ +033 return res; +034 \} +035 +036 if ((res = mp_init_copy (&v, b)) != MP_OKAY) \{ +037 goto LBL_U; +038 \} +039 +040 /* must be positive for the remainder of the algorithm */ +041 u.sign = v.sign = MP_ZPOS; +042 +043 /* B1. Find the common power of two for u and v */ +044 u_lsb = mp_cnt_lsb(&u); +045 v_lsb = mp_cnt_lsb(&v); +046 k = MIN(u_lsb, v_lsb); 047 -048 /* must be positive for the remainder of the algorithm */ -049 u.sign = v.sign = MP_ZPOS; -050 -051 /* B1. Find the common power of two for u and v */ -052 u_lsb = mp_cnt_lsb(&u); -053 v_lsb = mp_cnt_lsb(&v); -054 k = MIN(u_lsb, v_lsb); -055 -056 if (k > 0) \{ -057 /* divide the power of two out */ -058 if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) \{ -059 goto LBL_V; -060 \} -061 -062 if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) \{ -063 goto LBL_V; -064 \} -065 \} -066 -067 /* divide any remaining factors of two out */ -068 if (u_lsb != k) \{ -069 if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) \{ -070 goto LBL_V; -071 \} -072 \} -073 -074 if (v_lsb != k) \{ -075 if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) \{ -076 goto LBL_V; +048 if (k > 0) \{ +049 /* divide the power of two out */ +050 if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) \{ +051 goto LBL_V; +052 \} +053 +054 if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) \{ +055 goto LBL_V; +056 \} +057 \} +058 +059 /* divide any remaining factors of two out */ +060 if (u_lsb != k) \{ +061 if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) \{ +062 goto LBL_V; +063 \} +064 \} +065 +066 if (v_lsb != k) \{ +067 if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) \{ +068 goto LBL_V; +069 \} +070 \} +071 +072 while (mp_iszero(&v) == 0) \{ +073 /* make sure v is the largest */ +074 if (mp_cmp_mag(&u, &v) == MP_GT) \{ +075 /* swap u and v to make sure v is >= u */ +076 mp_exch(&u, &v); 077 \} -078 \} -079 -080 while (mp_iszero(&v) == 0) \{ -081 /* make sure v is the largest */ -082 if (mp_cmp_mag(&u, &v) == MP_GT) \{ -083 /* swap u and v to make sure v is >= u */ -084 mp_exch(&u, &v); -085 \} -086 -087 /* subtract smallest from largest */ -088 if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) \{ -089 goto LBL_V; -090 \} -091 -092 /* Divide out all factors of two */ -093 if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) \{ -094 goto LBL_V; -095 \} -096 \} -097 -098 /* multiply by 2**k which we divided out at the beginning */ -099 if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) \{ -100 goto LBL_V; -101 \} -102 c->sign = MP_ZPOS; -103 res = MP_OKAY; -104 LBL_V:mp_clear (&u); -105 LBL_U:mp_clear (&v); -106 return res; -107 \} -108 #endif +078 +079 /* subtract smallest from largest */ +080 if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) \{ +081 goto LBL_V; +082 \} +083 +084 /* Divide out all factors of two */ +085 if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) \{ +086 goto LBL_V; +087 \} +088 \} +089 +090 /* multiply by 2**k which we divided out at the beginning */ +091 if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) \{ +092 goto LBL_V; +093 \} +094 c->sign = MP_ZPOS; +095 res = MP_OKAY; +096 LBL_V:mp_clear (&u); +097 LBL_U:mp_clear (&v); +098 return res; +099 \} +100 #endif +101 \end{alltt} \end{small} This function makes use of the macros mp\_iszero and mp\_iseven. The former evaluates to $1$ if the input mp\_int is equivalent to the integer zero otherwise it evaluates to $0$. The latter evaluates to $1$ if the input mp\_int represents a non-zero even integer otherwise it evaluates to $0$. Note that just because mp\_iseven may evaluate to $0$ does not mean the input is odd, it could also be zero. The three -trivial cases of inputs are handled on lines 24 through 37. After those lines the inputs are assumed to be non-zero. +trivial cases of inputs are handled on lines 23 through 29. After those lines the inputs are assumed to be non-zero. -Lines 34 and 40 make local copies $u$ and $v$ of the inputs $a$ and $b$ respectively. At this point the common factors of two -must be divided out of the two inputs. The while loop on line 80 iterates so long as both are even. The local integer $k$ is used to -keep track of how many factors of $2$ are pulled out of both values. It is assumed that the number of factors will not exceed the maximum -value of a C ``int'' data type\footnote{Strictly speaking no array in C may have more than entries than are accessible by an ``int'' so this is not -a limitation.}. +Lines 32 and 36 make local copies $u$ and $v$ of the inputs $a$ and $b$ respectively. At this point the common factors of two +must be divided out of the two inputs. The block starting at line 43 removes common factors of two by first counting the number of trailing +zero bits in both. The local integer $k$ is used to keep track of how many factors of $2$ are pulled out of both values. It is assumed that +the number of factors will not exceed the maximum value of a C ``int'' data type\footnote{Strictly speaking no array in C may have more than +entries than are accessible by an ``int'' so this is not a limitation.}. -At this point there are no more common factors of two in the two values. The while loops on lines 80 and 80 remove any independent -factors of two such that both $u$ and $v$ are guaranteed to be an odd integer before hitting the main body of the algorithm. The while loop -on line 80 performs the reduction of the pair until $v$ is equal to zero. The unsigned comparison and subtraction algorithms are used in +At this point there are no more common factors of two in the two values. The divisions by a power of two on lines 61 and 67 remove +any independent factors of two such that both $u$ and $v$ are guaranteed to be an odd integer before hitting the main body of the algorithm. The while loop +on line 72 performs the reduction of the pair until $v$ is equal to zero. The unsigned comparison and subtraction algorithms are used in place of the full signed routines since both values are guaranteed to be positive and the result of the subtraction is guaranteed to be non-negative. \section{Least Common Multiple} @@ -9974,6 +10027,7 @@ dividing the product of the two inputs by their greatest common divisor. 053 return res; 054 \} 055 #endif +056 \end{alltt} \end{small} @@ -10218,6 +10272,7 @@ $\left ( {p' \over a'} \right )$ which is multiplied against the current Jacobi 098 return res; 099 \} 100 #endif +101 \end{alltt} \end{small} @@ -10366,6 +10421,7 @@ then only a couple of additions or subtractions will be required to adjust the i 036 return MP_VAL; 037 \} 038 #endif +039 \end{alltt} \end{small} @@ -10467,6 +10523,7 @@ This algorithm attempts to determine if a candidate integer $n$ is composite by 043 return MP_OKAY; 044 \} 045 #endif +046 \end{alltt} \end{small} @@ -10518,6 +10575,7 @@ mp\_digit. The table \_\_prime\_tab is defined in the following file. 054 #endif 055 \}; 056 #endif +057 \end{alltt} \end{small} @@ -10606,6 +10664,7 @@ determine the result. 055 return err; 056 \} 057 #endif +058 \end{alltt} \end{small} @@ -10741,6 +10800,7 @@ composite then it is \textit{probably} prime. 096 return err; 097 \} 098 #endif +099 \end{alltt} \end{small} diff --git a/tommath_class.h b/tommath_class.h index a9ae034..a4e275a 100644 --- a/tommath_class.h +++ b/tommath_class.h @@ -687,6 +687,7 @@ #if defined(BN_MP_READ_RADIX_C) #define BN_MP_ZERO_C #define BN_MP_S_RMAP_C + #define BN_MP_RADIX_SMAP_C #define BN_MP_MUL_D_C #define BN_MP_ADD_D_C #define BN_MP_ISZERO_C @@ -998,3 +999,7 @@ #undef BN_MP_KARATSUBA_SQR_C #undef BN_MP_TOOM_MUL_C #undef BN_MP_TOOM_SQR_C + +/* $Source: /cvs/libtom/libtommath/tommath_class.h,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2005/07/28 11:59:32 $ */ diff --git a/tommath_superclass.h b/tommath_superclass.h index b50ecb0..2fdebe6 100644 --- a/tommath_superclass.h +++ b/tommath_superclass.h @@ -4,7 +4,7 @@ #define LTM_ALL /* RSA only (does not support DH/DSA/ECC) */ -// #define SC_RSA_1 +/* #define SC_RSA_1 */ /* For reference.... On an Athlon64 optimizing for speed... @@ -70,3 +70,7 @@ #endif #endif + +/* $Source: /cvs/libtom/libtommath/tommath_superclass.h,v $ */ +/* $Revision: 1.3 $ */ +/* $Date: 2005/05/14 13:29:17 $ */ |