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-rw-r--r--libtommath/etc/2kprime.12
-rw-r--r--libtommath/etc/2kprime.c80
-rw-r--r--libtommath/etc/drprime.c60
-rw-r--r--libtommath/etc/drprimes.2825
-rw-r--r--libtommath/etc/drprimes.txt6
-rw-r--r--libtommath/etc/makefile50
-rw-r--r--libtommath/etc/makefile.icc67
-rw-r--r--libtommath/etc/makefile.msvc23
-rw-r--r--libtommath/etc/mersenne.c140
-rw-r--r--libtommath/etc/mont.c46
-rw-r--r--libtommath/etc/pprime.c396
-rw-r--r--libtommath/etc/prime.1024414
-rw-r--r--libtommath/etc/prime.512205
-rw-r--r--libtommath/etc/timer.asm37
-rw-r--r--libtommath/etc/tune.c138
15 files changed, 1689 insertions, 0 deletions
diff --git a/libtommath/etc/2kprime.1 b/libtommath/etc/2kprime.1
new file mode 100644
index 0000000..c41ded1
--- /dev/null
+++ b/libtommath/etc/2kprime.1
@@ -0,0 +1,2 @@
+256-bits (k = 36113) = 115792089237316195423570985008687907853269984665640564039457584007913129603823
+512-bits (k = 38117) = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006045979
diff --git a/libtommath/etc/2kprime.c b/libtommath/etc/2kprime.c
new file mode 100644
index 0000000..d48b83e
--- /dev/null
+++ b/libtommath/etc/2kprime.c
@@ -0,0 +1,80 @@
+/* Makes safe primes of a 2k nature */
+#include <tommath.h>
+#include <time.h>
+
+int sizes[] = {256, 512, 768, 1024, 1536, 2048, 3072, 4096};
+
+int main(void)
+{
+ char buf[2000];
+ int x, y;
+ mp_int q, p;
+ FILE *out;
+ clock_t t1;
+ mp_digit z;
+
+ mp_init_multi(&q, &p, NULL);
+
+ out = fopen("2kprime.1", "w");
+ for (x = 0; x < (int)(sizeof(sizes) / sizeof(sizes[0])); x++) {
+ top:
+ mp_2expt(&q, sizes[x]);
+ mp_add_d(&q, 3, &q);
+ z = -3;
+
+ t1 = clock();
+ for(;;) {
+ mp_sub_d(&q, 4, &q);
+ z += 4;
+
+ if (z > MP_MASK) {
+ printf("No primes of size %d found\n", sizes[x]);
+ break;
+ }
+
+ if (clock() - t1 > CLOCKS_PER_SEC) {
+ printf("."); fflush(stdout);
+// sleep((clock() - t1 + CLOCKS_PER_SEC/2)/CLOCKS_PER_SEC);
+ t1 = clock();
+ }
+
+ /* quick test on q */
+ mp_prime_is_prime(&q, 1, &y);
+ if (y == 0) {
+ continue;
+ }
+
+ /* find (q-1)/2 */
+ mp_sub_d(&q, 1, &p);
+ mp_div_2(&p, &p);
+ mp_prime_is_prime(&p, 3, &y);
+ if (y == 0) {
+ continue;
+ }
+
+ /* test on q */
+ mp_prime_is_prime(&q, 3, &y);
+ if (y == 0) {
+ continue;
+ }
+
+ break;
+ }
+
+ if (y == 0) {
+ ++sizes[x];
+ goto top;
+ }
+
+ mp_toradix(&q, buf, 10);
+ printf("\n\n%d-bits (k = %lu) = %s\n", sizes[x], z, buf);
+ fprintf(out, "%d-bits (k = %lu) = %s\n", sizes[x], z, buf); fflush(out);
+ }
+
+ return 0;
+}
+
+
+
+
+
diff --git a/libtommath/etc/drprime.c b/libtommath/etc/drprime.c
new file mode 100644
index 0000000..0ab8ea6
--- /dev/null
+++ b/libtommath/etc/drprime.c
@@ -0,0 +1,60 @@
+/* Makes safe primes of a DR nature */
+#include <tommath.h>
+
+int sizes[] = { 1+256/DIGIT_BIT, 1+512/DIGIT_BIT, 1+768/DIGIT_BIT, 1+1024/DIGIT_BIT, 1+2048/DIGIT_BIT, 1+4096/DIGIT_BIT };
+int main(void)
+{
+ int res, x, y;
+ char buf[4096];
+ FILE *out;
+ mp_int a, b;
+
+ mp_init(&a);
+ mp_init(&b);
+
+ out = fopen("drprimes.txt", "w");
+ for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) {
+ top:
+ printf("Seeking a %d-bit safe prime\n", sizes[x] * DIGIT_BIT);
+ mp_grow(&a, sizes[x]);
+ mp_zero(&a);
+ for (y = 1; y < sizes[x]; y++) {
+ a.dp[y] = MP_MASK;
+ }
+
+ /* make a DR modulus */
+ a.dp[0] = -1;
+ a.used = sizes[x];
+
+ /* now loop */
+ res = 0;
+ for (;;) {
+ a.dp[0] += 4;
+ if (a.dp[0] >= MP_MASK) break;
+ mp_prime_is_prime(&a, 1, &res);
+ if (res == 0) continue;
+ printf("."); fflush(stdout);
+ mp_sub_d(&a, 1, &b);
+ mp_div_2(&b, &b);
+ mp_prime_is_prime(&b, 3, &res);
+ if (res == 0) continue;
+ mp_prime_is_prime(&a, 3, &res);
+ if (res == 1) break;
+ }
+
+ if (res != 1) {
+ printf("Error not DR modulus\n"); sizes[x] += 1; goto top;
+ } else {
+ mp_toradix(&a, buf, 10);
+ printf("\n\np == %s\n\n", buf);
+ fprintf(out, "%d-bit prime:\np == %s\n\n", mp_count_bits(&a), buf); fflush(out);
+ }
+ }
+ fclose(out);
+
+ mp_clear(&a);
+ mp_clear(&b);
+
+ return 0;
+}
+
diff --git a/libtommath/etc/drprimes.28 b/libtommath/etc/drprimes.28
new file mode 100644
index 0000000..9d438ad
--- /dev/null
+++ b/libtommath/etc/drprimes.28
@@ -0,0 +1,25 @@
+DR safe primes for 28-bit digits.
+
+224-bit prime:
+p == 26959946667150639794667015087019630673637144422540572481103341844143
+
+532-bit prime:
+p == 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368691747
+
+784-bit prime:
+p == 101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039
+
+1036-bit prime:
+p == 736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821798437127
+
+1540-bit prime:
+p == 38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783
+
+2072-bit prime:
+p == 542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147
+
+3080-bit prime:
+p == 1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503
+
+4116-bit prime:
+p == 1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679
diff --git a/libtommath/etc/drprimes.txt b/libtommath/etc/drprimes.txt
new file mode 100644
index 0000000..2c887ea
--- /dev/null
+++ b/libtommath/etc/drprimes.txt
@@ -0,0 +1,6 @@
+280-bit prime:
+p == 1942668892225729070919461906823518906642406839052139521251812409738904285204940164839
+
+532-bit prime:
+p == 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368691747
+
diff --git a/libtommath/etc/makefile b/libtommath/etc/makefile
new file mode 100644
index 0000000..99154d8
--- /dev/null
+++ b/libtommath/etc/makefile
@@ -0,0 +1,50 @@
+CFLAGS += -Wall -W -Wshadow -O3 -fomit-frame-pointer -funroll-loops -I../
+
+# default lib name (requires install with root)
+# LIBNAME=-ltommath
+
+# libname when you can't install the lib with install
+LIBNAME=../libtommath.a
+
+#provable primes
+pprime: pprime.o
+ $(CC) pprime.o $(LIBNAME) -o pprime
+
+# portable [well requires clock()] tuning app
+tune: tune.o
+ $(CC) tune.o $(LIBNAME) -o tune
+
+# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
+tune86: tune.c
+ nasm -f coff timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+# for cygwin
+tune86c: tune.c
+ nasm -f gnuwin32 timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+#make tune86 for linux or any ELF format
+tune86l: tune.c
+ nasm -f elf -DUSE_ELF timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
+
+# spits out mersenne primes
+mersenne: mersenne.o
+ $(CC) mersenne.o $(LIBNAME) -o mersenne
+
+# fines DR safe primes for the given config
+drprime: drprime.o
+ $(CC) drprime.o $(LIBNAME) -o drprime
+
+# fines 2k safe primes for the given config
+2kprime: 2kprime.o
+ $(CC) 2kprime.o $(LIBNAME) -o 2kprime
+
+mont: mont.o
+ $(CC) mont.o $(LIBNAME) -o mont
+
+
+clean:
+ rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat \
+ *.da *.dyn *.dpi *~
diff --git a/libtommath/etc/makefile.icc b/libtommath/etc/makefile.icc
new file mode 100644
index 0000000..0a50728
--- /dev/null
+++ b/libtommath/etc/makefile.icc
@@ -0,0 +1,67 @@
+CC = icc
+
+CFLAGS += -I../
+
+# optimize for SPEED
+#
+# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
+# -ax? specifies make code specifically for ? but compatible with IA-32
+# -x? specifies compile solely for ? [not specifically IA-32 compatible]
+#
+# where ? is
+# K - PIII
+# W - first P4 [Williamette]
+# N - P4 Northwood
+# P - P4 Prescott
+# B - Blend of P4 and PM [mobile]
+#
+# Default to just generic max opts
+CFLAGS += -O3 -xN -ip
+
+# default lib name (requires install with root)
+# LIBNAME=-ltommath
+
+# libname when you can't install the lib with install
+LIBNAME=../libtommath.a
+
+#provable primes
+pprime: pprime.o
+ $(CC) pprime.o $(LIBNAME) -o pprime
+
+# portable [well requires clock()] tuning app
+tune: tune.o
+ $(CC) tune.o $(LIBNAME) -o tune
+
+# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
+tune86: tune.c
+ nasm -f coff timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+# for cygwin
+tune86c: tune.c
+ nasm -f gnuwin32 timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+#make tune86 for linux or any ELF format
+tune86l: tune.c
+ nasm -f elf -DUSE_ELF timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
+
+# spits out mersenne primes
+mersenne: mersenne.o
+ $(CC) mersenne.o $(LIBNAME) -o mersenne
+
+# fines DR safe primes for the given config
+drprime: drprime.o
+ $(CC) drprime.o $(LIBNAME) -o drprime
+
+# fines 2k safe primes for the given config
+2kprime: 2kprime.o
+ $(CC) 2kprime.o $(LIBNAME) -o 2kprime
+
+mont: mont.o
+ $(CC) mont.o $(LIBNAME) -o mont
+
+
+clean:
+ rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat *.il
diff --git a/libtommath/etc/makefile.msvc b/libtommath/etc/makefile.msvc
new file mode 100644
index 0000000..2833372
--- /dev/null
+++ b/libtommath/etc/makefile.msvc
@@ -0,0 +1,23 @@
+#MSVC Makefile
+#
+#Tom St Denis
+
+CFLAGS = /I../ /Ox /DWIN32 /W3
+
+pprime: pprime.obj
+ cl pprime.obj ../tommath.lib
+
+mersenne: mersenne.obj
+ cl mersenne.obj ../tommath.lib
+
+tune: tune.obj
+ cl tune.obj ../tommath.lib
+
+mont: mont.obj
+ cl mont.obj ../tommath.lib
+
+drprime: drprime.obj
+ cl drprime.obj ../tommath.lib
+
+2kprime: 2kprime.obj
+ cl 2kprime.obj ../tommath.lib
diff --git a/libtommath/etc/mersenne.c b/libtommath/etc/mersenne.c
new file mode 100644
index 0000000..1cd5b50
--- /dev/null
+++ b/libtommath/etc/mersenne.c
@@ -0,0 +1,140 @@
+/* Finds Mersenne primes using the Lucas-Lehmer test
+ *
+ * Tom St Denis, tomstdenis@iahu.ca
+ */
+#include <time.h>
+#include <tommath.h>
+
+int
+is_mersenne (long s, int *pp)
+{
+ mp_int n, u;
+ int res, k;
+
+ *pp = 0;
+
+ if ((res = mp_init (&n)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&u)) != MP_OKAY) {
+ goto LBL_N;
+ }
+
+ /* n = 2^s - 1 */
+ if ((res = mp_2expt(&n, s)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* set u=4 */
+ mp_set (&u, 4);
+
+ /* for k=1 to s-2 do */
+ for (k = 1; k <= s - 2; k++) {
+ /* u = u^2 - 2 mod n */
+ if ((res = mp_sqr (&u, &u)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* make sure u is positive */
+ while (u.sign == MP_NEG) {
+ if ((res = mp_add (&u, &n, &u)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* reduce */
+ if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* if u == 0 then its prime */
+ if (mp_iszero (&u) == 1) {
+ mp_prime_is_prime(&n, 8, pp);
+ if (*pp != 1) printf("FAILURE\n");
+ }
+
+ res = MP_OKAY;
+LBL_MU:mp_clear (&u);
+LBL_N:mp_clear (&n);
+ return res;
+}
+
+/* square root of a long < 65536 */
+long
+i_sqrt (long x)
+{
+ long x1, x2;
+
+ x2 = 16;
+ do {
+ x1 = x2;
+ x2 = x1 - ((x1 * x1) - x) / (2 * x1);
+ } while (x1 != x2);
+
+ if (x1 * x1 > x) {
+ --x1;
+ }
+
+ return x1;
+}
+
+/* is the long prime by brute force */
+int
+isprime (long k)
+{
+ long y, z;
+
+ y = i_sqrt (k);
+ for (z = 2; z <= y; z++) {
+ if ((k % z) == 0)
+ return 0;
+ }
+ return 1;
+}
+
+
+int
+main (void)
+{
+ int pp;
+ long k;
+ clock_t tt;
+
+ k = 3;
+
+ for (;;) {
+ /* start time */
+ tt = clock ();
+
+ /* test if 2^k - 1 is prime */
+ if (is_mersenne (k, &pp) != MP_OKAY) {
+ printf ("Whoa error\n");
+ return -1;
+ }
+
+ if (pp == 1) {
+ /* count time */
+ tt = clock () - tt;
+
+ /* display if prime */
+ printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt);
+ }
+
+ /* goto next odd exponent */
+ k += 2;
+
+ /* but make sure its prime */
+ while (isprime (k) == 0) {
+ k += 2;
+ }
+ }
+ return 0;
+}
diff --git a/libtommath/etc/mont.c b/libtommath/etc/mont.c
new file mode 100644
index 0000000..dbf1735
--- /dev/null
+++ b/libtommath/etc/mont.c
@@ -0,0 +1,46 @@
+/* tests the montgomery routines */
+#include <tommath.h>
+
+int main(void)
+{
+ mp_int modulus, R, p, pp;
+ mp_digit mp;
+ long x, y;
+
+ srand(time(NULL));
+ mp_init_multi(&modulus, &R, &p, &pp, NULL);
+
+ /* loop through various sizes */
+ for (x = 4; x < 256; x++) {
+ printf("DIGITS == %3ld...", x); fflush(stdout);
+
+ /* make up the odd modulus */
+ mp_rand(&modulus, x);
+ modulus.dp[0] |= 1;
+
+ /* now find the R value */
+ mp_montgomery_calc_normalization(&R, &modulus);
+ mp_montgomery_setup(&modulus, &mp);
+
+ /* now run through a bunch tests */
+ for (y = 0; y < 1000; y++) {
+ mp_rand(&p, x/2); /* p = random */
+ mp_mul(&p, &R, &pp); /* pp = R * p */
+ mp_montgomery_reduce(&pp, &modulus, mp);
+
+ /* should be equal to p */
+ if (mp_cmp(&pp, &p) != MP_EQ) {
+ printf("FAILURE!\n");
+ exit(-1);
+ }
+ }
+ printf("PASSED\n");
+ }
+
+ return 0;
+}
+
+
+
+
+
diff --git a/libtommath/etc/pprime.c b/libtommath/etc/pprime.c
new file mode 100644
index 0000000..26e0d84
--- /dev/null
+++ b/libtommath/etc/pprime.c
@@ -0,0 +1,396 @@
+/* Generates provable primes
+ *
+ * See http://iahu.ca:8080/papers/pp.pdf for more info.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://tom.iahu.ca
+ */
+#include <time.h>
+#include "tommath.h"
+
+int n_prime;
+FILE *primes;
+
+/* fast square root */
+static mp_digit
+i_sqrt (mp_word x)
+{
+ mp_word x1, x2;
+
+ x2 = x;
+ do {
+ x1 = x2;
+ x2 = x1 - ((x1 * x1) - x) / (2 * x1);
+ } while (x1 != x2);
+
+ if (x1 * x1 > x) {
+ --x1;
+ }
+
+ return x1;
+}
+
+
+/* generates a prime digit */
+static void gen_prime (void)
+{
+ mp_digit r, x, y, next;
+ FILE *out;
+
+ out = fopen("pprime.dat", "wb");
+
+ /* write first set of primes */
+ r = 3; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 5; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 7; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 11; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 13; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 17; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 19; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 23; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 29; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 31; fwrite(&r, 1, sizeof(mp_digit), out);
+
+ /* get square root, since if 'r' is composite its factors must be < than this */
+ y = i_sqrt (r);
+ next = (y + 1) * (y + 1);
+
+ for (;;) {
+ do {
+ r += 2; /* next candidate */
+ r &= MP_MASK;
+ if (r < 31) break;
+
+ /* update sqrt ? */
+ if (next <= r) {
+ ++y;
+ next = (y + 1) * (y + 1);
+ }
+
+ /* loop if divisible by 3,5,7,11,13,17,19,23,29 */
+ if ((r % 3) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 5) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 7) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 11) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 13) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 17) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 19) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 23) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 29) == 0) {
+ x = 0;
+ continue;
+ }
+
+ /* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */
+ for (x = 30; x <= y; x += 30) {
+ if ((r % (x + 1)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 7)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 11)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 13)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 17)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 19)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 23)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 29)) == 0) {
+ x = 0;
+ break;
+ }
+ }
+ } while (x == 0);
+ if (r > 31) { fwrite(&r, 1, sizeof(mp_digit), out); printf("%9d\r", r); fflush(stdout); }
+ if (r < 31) break;
+ }
+
+ fclose(out);
+}
+
+void load_tab(void)
+{
+ primes = fopen("pprime.dat", "rb");
+ if (primes == NULL) {
+ gen_prime();
+ primes = fopen("pprime.dat", "rb");
+ }
+ fseek(primes, 0, SEEK_END);
+ n_prime = ftell(primes) / sizeof(mp_digit);
+}
+
+mp_digit prime_digit(void)
+{
+ int n;
+ mp_digit d;
+
+ n = abs(rand()) % n_prime;
+ fseek(primes, n * sizeof(mp_digit), SEEK_SET);
+ fread(&d, 1, sizeof(mp_digit), primes);
+ return d;
+}
+
+
+/* makes a prime of at least k bits */
+int
+pprime (int k, int li, mp_int * p, mp_int * q)
+{
+ mp_int a, b, c, n, x, y, z, v;
+ int res, ii;
+ static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
+
+ /* single digit ? */
+ if (k <= (int) DIGIT_BIT) {
+ mp_set (p, prime_digit ());
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init (&c)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&v)) != MP_OKAY) {
+ goto LBL_C;
+ }
+
+ /* product of first 50 primes */
+ if ((res =
+ mp_read_radix (&v,
+ "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
+ 10)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ if ((res = mp_init (&a)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ /* set the prime */
+ mp_set (&a, prime_digit ());
+
+ if ((res = mp_init (&b)) != MP_OKAY) {
+ goto LBL_A;
+ }
+
+ if ((res = mp_init (&n)) != MP_OKAY) {
+ goto LBL_B;
+ }
+
+ if ((res = mp_init (&x)) != MP_OKAY) {
+ goto LBL_N;
+ }
+
+ if ((res = mp_init (&y)) != MP_OKAY) {
+ goto LBL_X;
+ }
+
+ if ((res = mp_init (&z)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* now loop making the single digit */
+ while (mp_count_bits (&a) < k) {
+ fprintf (stderr, "prime has %4d bits left\r", k - mp_count_bits (&a));
+ fflush (stderr);
+ top:
+ mp_set (&b, prime_digit ());
+
+ /* now compute z = a * b * 2 */
+ if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) { /* z = a * b */
+ goto LBL_Z;
+ }
+
+ if ((res = mp_copy (&z, &c)) != MP_OKAY) { /* c = a * b */
+ goto LBL_Z;
+ }
+
+ if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) { /* z = 2 * a * b */
+ goto LBL_Z;
+ }
+
+ /* n = z + 1 */
+ if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) { /* n = z + 1 */
+ goto LBL_Z;
+ }
+
+ /* check (n, v) == 1 */
+ if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */
+ goto LBL_Z;
+ }
+
+ if (mp_cmp_d (&y, 1) != MP_EQ)
+ goto top;
+
+ /* now try base x=bases[ii] */
+ for (ii = 0; ii < li; ii++) {
+ mp_set (&x, bases[ii]);
+
+ /* compute x^a mod n */
+ if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) { /* y = x^a mod n */
+ goto LBL_Z;
+ }
+
+ /* if y == 1 loop */
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* now x^2a mod n */
+ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */
+ goto LBL_Z;
+ }
+
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* compute x^b mod n */
+ if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */
+ goto LBL_Z;
+ }
+
+ /* if y == 1 loop */
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* now x^2b mod n */
+ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */
+ goto LBL_Z;
+ }
+
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* compute x^c mod n == x^ab mod n */
+ if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) { /* y = x^ab mod n */
+ goto LBL_Z;
+ }
+
+ /* if y == 1 loop */
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* now compute (x^c mod n)^2 */
+ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */
+ goto LBL_Z;
+ }
+
+ /* y should be 1 */
+ if (mp_cmp_d (&y, 1) != MP_EQ)
+ continue;
+ break;
+ }
+
+ /* no bases worked? */
+ if (ii == li)
+ goto top;
+
+{
+ char buf[4096];
+
+ mp_toradix(&n, buf, 10);
+ printf("Certificate of primality for:\n%s\n\n", buf);
+ mp_toradix(&a, buf, 10);
+ printf("A == \n%s\n\n", buf);
+ mp_toradix(&b, buf, 10);
+ printf("B == \n%s\n\nG == %d\n", buf, bases[ii]);
+ printf("----------------------------------------------------------------\n");
+}
+
+ /* a = n */
+ mp_copy (&n, &a);
+ }
+
+ /* get q to be the order of the large prime subgroup */
+ mp_sub_d (&n, 1, q);
+ mp_div_2 (q, q);
+ mp_div (q, &b, q, NULL);
+
+ mp_exch (&n, p);
+
+ res = MP_OKAY;
+LBL_Z:mp_clear (&z);
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_N:mp_clear (&n);
+LBL_B:mp_clear (&b);
+LBL_A:mp_clear (&a);
+LBL_V:mp_clear (&v);
+LBL_C:mp_clear (&c);
+ return res;
+}
+
+
+int
+main (void)
+{
+ mp_int p, q;
+ char buf[4096];
+ int k, li;
+ clock_t t1;
+
+ srand (time (NULL));
+ load_tab();
+
+ printf ("Enter # of bits: \n");
+ fgets (buf, sizeof (buf), stdin);
+ sscanf (buf, "%d", &k);
+
+ printf ("Enter number of bases to try (1 to 8):\n");
+ fgets (buf, sizeof (buf), stdin);
+ sscanf (buf, "%d", &li);
+
+
+ mp_init (&p);
+ mp_init (&q);
+
+ t1 = clock ();
+ pprime (k, li, &p, &q);
+ t1 = clock () - t1;
+
+ printf ("\n\nTook %ld ticks, %d bits\n", t1, mp_count_bits (&p));
+
+ mp_toradix (&p, buf, 10);
+ printf ("P == %s\n", buf);
+ mp_toradix (&q, buf, 10);
+ printf ("Q == %s\n", buf);
+
+ return 0;
+}
diff --git a/libtommath/etc/prime.1024 b/libtommath/etc/prime.1024
new file mode 100644
index 0000000..5636e2d
--- /dev/null
+++ b/libtommath/etc/prime.1024
@@ -0,0 +1,414 @@
+Enter # of bits:
+Enter number of bases to try (1 to 8):
+Certificate of primality for:
+36360080703173363
+
+A ==
+89963569
+
+B ==
+202082249
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+4851595597739856136987139
+
+A ==
+36360080703173363
+
+B ==
+66715963
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+19550639734462621430325731591027
+
+A ==
+4851595597739856136987139
+
+B ==
+2014867
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+10409036141344317165691858509923818734539
+
+A ==
+19550639734462621430325731591027
+
+B ==
+266207047
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1049829549988285012736475602118094726647504414203
+
+A ==
+10409036141344317165691858509923818734539
+
+B ==
+50428759
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+77194737385528288387712399596835459931920358844586615003
+
+A ==
+1049829549988285012736475602118094726647504414203
+
+B ==
+36765367
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+35663756695365208574443215955488689578374232732893628896541201763
+
+A ==
+77194737385528288387712399596835459931920358844586615003
+
+B ==
+230998627
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+16711831463502165169495622246023119698415848120292671294127567620396469803
+
+A ==
+35663756695365208574443215955488689578374232732893628896541201763
+
+B ==
+234297127
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+6163534781560285962890718925972249753147470953579266394395432475622345597103528739
+
+A ==
+16711831463502165169495622246023119698415848120292671294127567620396469803
+
+B ==
+184406323
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787
+
+A ==
+6163534781560285962890718925972249753147470953579266394395432475622345597103528739
+
+B ==
+66054487
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187
+
+A ==
+814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787
+
+B ==
+108362239
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419
+
+A ==
+176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187
+
+B ==
+127286707
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059
+
+A ==
+44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419
+
+B ==
+229284691
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979
+
+A ==
+20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059
+
+B ==
+152800771
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123
+
+A ==
+6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979
+
+B ==
+246595759
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499
+
+A ==
+3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123
+
+B ==
+4252063
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163
+
+A ==
+26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499
+
+B ==
+210605419
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187
+
+A ==
+11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163
+
+B ==
+74170111
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363
+
+A ==
+1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187
+
+B ==
+260016763
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283
+
+A ==
+857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363
+
+B ==
+102563707
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283
+
+A ==
+175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283
+
+B ==
+137747527
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403
+
+A ==
+48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283
+
+B ==
+135672847
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123
+
+A ==
+13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403
+
+B ==
+241523587
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083
+
+A ==
+6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123
+
+B ==
+248388667
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067
+
+A ==
+3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083
+
+B ==
+61849651
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739
+
+A ==
+390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067
+
+B ==
+62201707
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419
+
+A ==
+48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739
+
+B ==
+264832231
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387
+
+A ==
+25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419
+
+B ==
+54494047
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547
+
+A ==
+2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387
+
+B ==
+131594179
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683
+
+A ==
+738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547
+
+B ==
+266107603
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627
+
+A ==
+392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683
+
+B ==
+214408111
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643
+
+A ==
+168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627
+
+B ==
+44122723
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019
+
+A ==
+14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643
+
+B ==
+40808563
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843
+
+A ==
+1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019
+
+B ==
+77035759
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683
+
+A ==
+186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843
+
+B ==
+222383587
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
+
+A ==
+83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683
+
+B ==
+23407687
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723
+
+A ==
+3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
+
+B ==
+213701827
+
+G == 2
+----------------------------------------------------------------
+
+
+Took 33057 ticks, 1048 bits
+P == 1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723
+Q == 3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
diff --git a/libtommath/etc/prime.512 b/libtommath/etc/prime.512
new file mode 100644
index 0000000..cb6ec30
--- /dev/null
+++ b/libtommath/etc/prime.512
@@ -0,0 +1,205 @@
+Enter # of bits:
+Enter number of bases to try (1 to 8):
+Certificate of primality for:
+85933926807634727
+
+A ==
+253758023
+
+B ==
+169322581
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+23930198825086241462113799
+
+A ==
+85933926807634727
+
+B ==
+139236037
+
+G == 11
+----------------------------------------------------------------
+Certificate of primality for:
+6401844647261612602378676572510019
+
+A ==
+23930198825086241462113799
+
+B ==
+133760791
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+269731366027728777712034888684015329354259
+
+A ==
+6401844647261612602378676572510019
+
+B ==
+21066691
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+37942338209025571690075025099189467992329684223707
+
+A ==
+269731366027728777712034888684015329354259
+
+B ==
+70333567
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+15306904714258982484473490774101705363308327436988160248323
+
+A ==
+37942338209025571690075025099189467992329684223707
+
+B ==
+201712723
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1616744757018513392810355191503853040357155275733333124624513530099
+
+A ==
+15306904714258982484473490774101705363308327436988160248323
+
+B ==
+52810963
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+464222094814208047161771036072622485188658077940154689939306386289983787983
+
+A ==
+1616744757018513392810355191503853040357155275733333124624513530099
+
+B ==
+143566909
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+187429931674053784626487560729643601208757374994177258429930699354770049369025096447
+
+A ==
+464222094814208047161771036072622485188658077940154689939306386289983787983
+
+B ==
+201875281
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563
+
+A ==
+187429931674053784626487560729643601208757374994177258429930699354770049369025096447
+
+B ==
+268311523
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163
+
+A ==
+100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563
+
+B ==
+5834287
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623
+
+A ==
+1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163
+
+B ==
+81567097
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519
+
+A ==
+191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623
+
+B ==
+151095433
+
+G == 7
+----------------------------------------------------------------
+Certificate of primality for:
+13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803
+
+A ==
+57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519
+
+B ==
+119178679
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979
+
+A ==
+13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803
+
+B ==
+256552363
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463
+
+A ==
+7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979
+
+B ==
+86720989
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
+
+A ==
+1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463
+
+B ==
+182015287
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243
+
+A ==
+446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
+
+B ==
+5920567
+
+G == 2
+----------------------------------------------------------------
+
+
+Took 3454 ticks, 521 bits
+P == 5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243
+Q == 446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
diff --git a/libtommath/etc/timer.asm b/libtommath/etc/timer.asm
new file mode 100644
index 0000000..35890d9
--- /dev/null
+++ b/libtommath/etc/timer.asm
@@ -0,0 +1,37 @@
+; x86 timer in NASM
+;
+; Tom St Denis, tomstdenis@iahu.ca
+[bits 32]
+[section .data]
+time dd 0, 0
+
+[section .text]
+
+%ifdef USE_ELF
+[global t_start]
+t_start:
+%else
+[global _t_start]
+_t_start:
+%endif
+ push edx
+ push eax
+ rdtsc
+ mov [time+0],edx
+ mov [time+4],eax
+ pop eax
+ pop edx
+ ret
+
+%ifdef USE_ELF
+[global t_read]
+t_read:
+%else
+[global _t_read]
+_t_read:
+%endif
+ rdtsc
+ sub eax,[time+4]
+ sbb edx,[time+0]
+ ret
+ \ No newline at end of file
diff --git a/libtommath/etc/tune.c b/libtommath/etc/tune.c
new file mode 100644
index 0000000..d054d10
--- /dev/null
+++ b/libtommath/etc/tune.c
@@ -0,0 +1,138 @@
+/* Tune the Karatsuba parameters
+ *
+ * Tom St Denis, tomstdenis@iahu.ca
+ */
+#include <tommath.h>
+#include <time.h>
+
+/* how many times todo each size mult. Depends on your computer. For slow computers
+ * this can be low like 5 or 10. For fast [re: Athlon] should be 25 - 50 or so
+ */
+#define TIMES (1UL<<14UL)
+
+/* RDTSC from Scott Duplichan */
+static ulong64 TIMFUNC (void)
+ {
+ #if defined __GNUC__
+ #if defined(__i386__) || defined(__x86_64__)
+ unsigned long long a;
+ __asm__ __volatile__ ("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::"m"(a):"%eax","%edx");
+ return a;
+ #else /* gcc-IA64 version */
+ unsigned long result;
+ __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
+ while (__builtin_expect ((int) result == -1, 0))
+ __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
+ return result;
+ #endif
+
+ // Microsoft and Intel Windows compilers
+ #elif defined _M_IX86
+ __asm rdtsc
+ #elif defined _M_AMD64
+ return __rdtsc ();
+ #elif defined _M_IA64
+ #if defined __INTEL_COMPILER
+ #include <ia64intrin.h>
+ #endif
+ return __getReg (3116);
+ #else
+ #error need rdtsc function for this build
+ #endif
+ }
+
+
+#ifndef X86_TIMER
+
+/* generic ISO C timer */
+ulong64 LBL_T;
+void t_start(void) { LBL_T = TIMFUNC(); }
+ulong64 t_read(void) { return TIMFUNC() - LBL_T; }
+
+#else
+extern void t_start(void);
+extern ulong64 t_read(void);
+#endif
+
+ulong64 time_mult(int size, int s)
+{
+ unsigned long x;
+ mp_int a, b, c;
+ ulong64 t1;
+
+ mp_init (&a);
+ mp_init (&b);
+ mp_init (&c);
+
+ mp_rand (&a, size);
+ mp_rand (&b, size);
+
+ if (s == 1) {
+ KARATSUBA_MUL_CUTOFF = size;
+ } else {
+ KARATSUBA_MUL_CUTOFF = 100000;
+ }
+
+ t_start();
+ for (x = 0; x < TIMES; x++) {
+ mp_mul(&a,&b,&c);
+ }
+ t1 = t_read();
+ mp_clear (&a);
+ mp_clear (&b);
+ mp_clear (&c);
+ return t1;
+}
+
+ulong64 time_sqr(int size, int s)
+{
+ unsigned long x;
+ mp_int a, b;
+ ulong64 t1;
+
+ mp_init (&a);
+ mp_init (&b);
+
+ mp_rand (&a, size);
+
+ if (s == 1) {
+ KARATSUBA_SQR_CUTOFF = size;
+ } else {
+ KARATSUBA_SQR_CUTOFF = 100000;
+ }
+
+ t_start();
+ for (x = 0; x < TIMES; x++) {
+ mp_sqr(&a,&b);
+ }
+ t1 = t_read();
+ mp_clear (&a);
+ mp_clear (&b);
+ return t1;
+}
+
+int
+main (void)
+{
+ ulong64 t1, t2;
+ int x, y;
+
+ for (x = 8; ; x += 2) {
+ t1 = time_mult(x, 0);
+ t2 = time_mult(x, 1);
+ printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
+ if (t2 < t1) break;
+ }
+ y = x;
+
+ for (x = 8; ; x += 2) {
+ t1 = time_sqr(x, 0);
+ t2 = time_sqr(x, 1);
+ printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
+ if (t2 < t1) break;
+ }
+ printf("KARATSUBA_MUL_CUTOFF = %d\n", y);
+ printf("KARATSUBA_SQR_CUTOFF = %d\n", x);
+
+ return 0;
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-27 12:40:00 +0000