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Diffstat (limited to 'libs/nixio/axTLS/crypto/bigint.c')
| -rw-r--r-- | libs/nixio/axTLS/crypto/bigint.c | 1575 |
1 files changed, 1575 insertions, 0 deletions
diff --git a/libs/nixio/axTLS/crypto/bigint.c b/libs/nixio/axTLS/crypto/bigint.c new file mode 100644 index 0000000000..53a5839293 --- /dev/null +++ b/libs/nixio/axTLS/crypto/bigint.c @@ -0,0 +1,1575 @@ +/* + * Copyright (c) 2007, Cameron Rich + * + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions are met: + * + * * Redistributions of source code must retain the above copyright notice, + * this list of conditions and the following disclaimer. + * * Redistributions in binary form must reproduce the above copyright notice, + * this list of conditions and the following disclaimer in the documentation + * and/or other materials provided with the distribution. + * * Neither the name of the axTLS project nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR + * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR + * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, + * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, + * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR + * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF + * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING + * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS + * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/** + * @defgroup bigint_api Big Integer API + * @brief The bigint implementation as used by the axTLS project. + * + * The bigint library is for RSA encryption/decryption as well as signing. + * This code tries to minimise use of malloc/free by maintaining a small + * cache. A bigint context may maintain state by being made "permanent". + * It be be later released with a bi_depermanent() and bi_free() call. + * + * It supports the following reduction techniques: + * - Classical + * - Barrett + * - Montgomery + * + * It also implements the following: + * - Karatsuba multiplication + * - Squaring + * - Sliding window exponentiation + * - Chinese Remainder Theorem (implemented in rsa.c). + * + * All the algorithms used are pretty standard, and designed for different + * data bus sizes. Negative numbers are not dealt with at all, so a subtraction + * may need to be tested for negativity. + * + * This library steals some ideas from Jef Poskanzer + * <http://cs.marlboro.edu/term/cs-fall02/algorithms/crypto/RSA/bigint> + * and GMP <http://www.swox.com/gmp>. It gets most of its implementation + * detail from "The Handbook of Applied Cryptography" + * <http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf> + * @{ + */ + +#include <stdlib.h> +#include <limits.h> +#include <string.h> +#include <stdio.h> +#include <time.h> +#include "bigint.h" + +#define V1 v->comps[v->size-1] /**< v1 for division */ +#define V2 v->comps[v->size-2] /**< v2 for division */ +#define U(j) tmp_u->comps[tmp_u->size-j-1] /**< uj for division */ +#define Q(j) quotient->comps[quotient->size-j-1] /**< qj for division */ + +static bigint *bi_int_multiply(BI_CTX *ctx, bigint *bi, comp i); +static bigint *bi_int_divide(BI_CTX *ctx, bigint *biR, comp denom); +static bigint *alloc(BI_CTX *ctx, int size); +static bigint *trim(bigint *bi); +static void more_comps(bigint *bi, int n); +#if defined(CONFIG_BIGINT_KARATSUBA) || defined(CONFIG_BIGINT_BARRETT) || \ + defined(CONFIG_BIGINT_MONTGOMERY) +static bigint *comp_right_shift(bigint *biR, int num_shifts); +static bigint *comp_left_shift(bigint *biR, int num_shifts); +#endif + +#ifdef CONFIG_BIGINT_CHECK_ON +static void check(const bigint *bi); +#else +#define check(A) /**< disappears in normal production mode */ +#endif + + +/** + * @brief Start a new bigint context. + * @return A bigint context. + */ +BI_CTX *bi_initialize(void) +{ + /* calloc() sets everything to zero */ + BI_CTX *ctx = (BI_CTX *)calloc(1, sizeof(BI_CTX)); + + /* the radix */ + ctx->bi_radix = alloc(ctx, 2); + ctx->bi_radix->comps[0] = 0; + ctx->bi_radix->comps[1] = 1; + bi_permanent(ctx->bi_radix); + return ctx; +} + +/** + * @brief Close the bigint context and free any resources. + * + * Free up any used memory - a check is done if all objects were not + * properly freed. + * @param ctx [in] The bigint session context. + */ +void bi_terminate(BI_CTX *ctx) +{ + bi_depermanent(ctx->bi_radix); + bi_free(ctx, ctx->bi_radix); + + if (ctx->active_count != 0) + { +#ifdef CONFIG_SSL_FULL_MODE + printf("bi_terminate: there were %d un-freed bigints\n", + ctx->active_count); +#endif + abort(); + } + + bi_clear_cache(ctx); + free(ctx); +} + +/** + *@brief Clear the memory cache. + */ +void bi_clear_cache(BI_CTX *ctx) +{ + bigint *p, *pn; + + if (ctx->free_list == NULL) + return; + + for (p = ctx->free_list; p != NULL; p = pn) + { + pn = p->next; + free(p->comps); + free(p); + } + + ctx->free_count = 0; + ctx->free_list = NULL; +} + +/** + * @brief Increment the number of references to this object. + * It does not do a full copy. + * @param bi [in] The bigint to copy. + * @return A reference to the same bigint. + */ +bigint *bi_copy(bigint *bi) +{ + check(bi); + if (bi->refs != PERMANENT) + bi->refs++; + return bi; +} + +/** + * @brief Simply make a bigint object "unfreeable" if bi_free() is called on it. + * + * For this object to be freed, bi_depermanent() must be called. + * @param bi [in] The bigint to be made permanent. + */ +void bi_permanent(bigint *bi) +{ + check(bi); + if (bi->refs != 1) + { +#ifdef CONFIG_SSL_FULL_MODE + printf("bi_permanent: refs was not 1\n"); +#endif + abort(); + } + + bi->refs = PERMANENT; +} + +/** + * @brief Take a permanent object and make it eligible for freedom. + * @param bi [in] The bigint to be made back to temporary. + */ +void bi_depermanent(bigint *bi) +{ + check(bi); + if (bi->refs != PERMANENT) + { +#ifdef CONFIG_SSL_FULL_MODE + printf("bi_depermanent: bigint was not permanent\n"); +#endif + abort(); + } + + bi->refs = 1; +} + +/** + * @brief Free a bigint object so it can be used again. + * + * The memory itself it not actually freed, just tagged as being available + * @param ctx [in] The bigint session context. + * @param bi [in] The bigint to be freed. + */ +void bi_free(BI_CTX *ctx, bigint *bi) +{ + check(bi); + if (bi->refs == PERMANENT) + { + return; + } + + if (--bi->refs > 0) + { + return; + } + + bi->next = ctx->free_list; + ctx->free_list = bi; + ctx->free_count++; + + if (--ctx->active_count < 0) + { +#ifdef CONFIG_SSL_FULL_MODE + printf("bi_free: active_count went negative " + "- double-freed bigint?\n"); +#endif + abort(); + } +} + +/** + * @brief Convert an (unsigned) integer into a bigint. + * @param ctx [in] The bigint session context. + * @param i [in] The (unsigned) integer to be converted. + * + */ +bigint *int_to_bi(BI_CTX *ctx, comp i) +{ + bigint *biR = alloc(ctx, 1); + biR->comps[0] = i; + return biR; +} + +/** + * @brief Do a full copy of the bigint object. + * @param ctx [in] The bigint session context. + * @param bi [in] The bigint object to be copied. + */ +bigint *bi_clone(BI_CTX *ctx, const bigint *bi) +{ + bigint *biR = alloc(ctx, bi->size); + check(bi); + memcpy(biR->comps, bi->comps, bi->size*COMP_BYTE_SIZE); + return biR; +} + +/** + * @brief Perform an addition operation between two bigints. + * @param ctx [in] The bigint session context. + * @param bia [in] A bigint. + * @param bib [in] Another bigint. + * @return The result of the addition. + */ +bigint *bi_add(BI_CTX *ctx, bigint *bia, bigint *bib) +{ + int n; + comp carry = 0; + comp *pa, *pb; + + check(bia); + check(bib); + + n = max(bia->size, bib->size); + more_comps(bia, n+1); + more_comps(bib, n); + pa = bia->comps; + pb = bib->comps; + + do + { + comp sl, rl, cy1; + sl = *pa + *pb++; + rl = sl + carry; + cy1 = sl < *pa; + carry = cy1 | (rl < sl); + *pa++ = rl; + } while (--n != 0); + + *pa = carry; /* do overflow */ + bi_free(ctx, bib); + return trim(bia); +} + +/** + * @brief Perform a subtraction operation between two bigints. + * @param ctx [in] The bigint session context. + * @param bia [in] A bigint. + * @param bib [in] Another bigint. + * @param is_negative [out] If defined, indicates that the result was negative. + * is_negative may be null. + * @return The result of the subtraction. The result is always positive. + */ +bigint *bi_subtract(BI_CTX *ctx, + bigint *bia, bigint *bib, int *is_negative) +{ + int n = bia->size; + comp *pa, *pb, carry = 0; + + check(bia); + check(bib); + + more_comps(bib, n); + pa = bia->comps; + pb = bib->comps; + + do + { + comp sl, rl, cy1; + sl = *pa - *pb++; + rl = sl - carry; + cy1 = sl > *pa; + carry = cy1 | (rl > sl); + *pa++ = rl; + } while (--n != 0); + + if (is_negative) /* indicate a negative result */ + { + *is_negative = carry; + } + + bi_free(ctx, trim(bib)); /* put bib back to the way it was */ + return trim(bia); +} + +/** + * Perform a multiply between a bigint an an (unsigned) integer + */ +static bigint *bi_int_multiply(BI_CTX *ctx, bigint *bia, comp b) +{ + int j = 0, n = bia->size; + bigint *biR = alloc(ctx, n + 1); + comp carry = 0; + comp *r = biR->comps; + comp *a = bia->comps; + + check(bia); + + /* clear things to start with */ + memset(r, 0, ((n+1)*COMP_BYTE_SIZE)); + + do + { + long_comp tmp = *r + (long_comp)a[j]*b + carry; + *r++ = (comp)tmp; /* downsize */ + carry = (comp)(tmp >> COMP_BIT_SIZE); + } while (++j < n); + + *r = carry; + bi_free(ctx, bia); + return trim(biR); +} + +/** + * @brief Does both division and modulo calculations. + * + * Used extensively when doing classical reduction. + * @param ctx [in] The bigint session context. + * @param u [in] A bigint which is the numerator. + * @param v [in] Either the denominator or the modulus depending on the mode. + * @param is_mod [n] Determines if this is a normal division (0) or a reduction + * (1). + * @return The result of the division/reduction. + */ +bigint *bi_divide(BI_CTX *ctx, bigint *u, bigint *v, int is_mod) +{ + int n = v->size, m = u->size-n; + int j = 0, orig_u_size = u->size; + uint8_t mod_offset = ctx->mod_offset; + comp d; + bigint *quotient, *tmp_u; + comp q_dash; + + check(u); + check(v); + + /* if doing reduction and we are < mod, then return mod */ + if (is_mod && bi_compare(v, u) > 0) + { + bi_free(ctx, v); + return u; + } + + quotient = alloc(ctx, m+1); + tmp_u = alloc(ctx, n+1); + v = trim(v); /* make sure we have no leading 0's */ + d = (comp)((long_comp)COMP_RADIX/(V1+1)); + + /* clear things to start with */ + memset(quotient->comps, 0, ((quotient->size)*COMP_BYTE_SIZE)); + + /* normalise */ + if (d > 1) + { + u = bi_int_multiply(ctx, u, d); + + if (is_mod) + { + v = ctx->bi_normalised_mod[mod_offset]; + } + else + { + v = bi_int_multiply(ctx, v, d); + } + } + + if (orig_u_size == u->size) /* new digit position u0 */ + { + more_comps(u, orig_u_size + 1); + } + + do + { + /* get a temporary short version of u */ + memcpy(tmp_u->comps, &u->comps[u->size-n-1-j], (n+1)*COMP_BYTE_SIZE); + + /* calculate q' */ + if (U(0) == V1) + { + q_dash = COMP_RADIX-1; + } + else + { + q_dash = (comp)(((long_comp)U(0)*COMP_RADIX + U(1))/V1); + } + + if (v->size > 1 && V2) + { + /* we are implementing the following: + if (V2*q_dash > (((U(0)*COMP_RADIX + U(1) - + q_dash*V1)*COMP_RADIX) + U(2))) ... */ + comp inner = (comp)((long_comp)COMP_RADIX*U(0) + U(1) - + (long_comp)q_dash*V1); + if ((long_comp)V2*q_dash > (long_comp)inner*COMP_RADIX + U(2)) + { + q_dash--; + } + } + + /* multiply and subtract */ + if (q_dash) + { + int is_negative; + tmp_u = bi_subtract(ctx, tmp_u, + bi_int_multiply(ctx, bi_copy(v), q_dash), &is_negative); + more_comps(tmp_u, n+1); + + Q(j) = q_dash; + + /* add back */ + if (is_negative) + { + Q(j)--; + tmp_u = bi_add(ctx, tmp_u, bi_copy(v)); + + /* lop off the carry */ + tmp_u->size--; + v->size--; + } + } + else + { + Q(j) = 0; + } + + /* copy back to u */ + memcpy(&u->comps[u->size-n-1-j], tmp_u->comps, (n+1)*COMP_BYTE_SIZE); + } while (++j <= m); + + bi_free(ctx, tmp_u); + bi_free(ctx, v); + + if (is_mod) /* get the remainder */ + { + bi_free(ctx, quotient); + return bi_int_divide(ctx, trim(u), d); + } + else /* get the quotient */ + { + bi_free(ctx, u); + return trim(quotient); + } +} + +/* + * Perform an integer divide on a bigint. + */ +static bigint *bi_int_divide(BI_CTX *ctx, bigint *biR, comp denom) +{ + int i = biR->size - 1; + long_comp r = 0; + + check(biR); + + do + { + r = (r<<COMP_BIT_SIZE) + biR->comps[i]; + biR->comps[i] = (comp)(r / denom); + r %= denom; + } while (--i >= 0); + + return trim(biR); +} + +#ifdef CONFIG_BIGINT_MONTGOMERY +/** + * There is a need for the value of integer N' such that B^-1(B-1)-N^-1N'=1, + * where B^-1(B-1) mod N=1. Actually, only the least significant part of + * N' is needed, hence the definition N0'=N' mod b. We reproduce below the + * simple algorithm from an article by Dusse and Kaliski to efficiently + * find N0' from N0 and b */ +static comp modular_inverse(bigint *bim) +{ + int i; + comp t = 1; + comp two_2_i_minus_1 = 2; /* 2^(i-1) */ + long_comp two_2_i = 4; /* 2^i */ + comp N = bim->comps[0]; + + for (i = 2; i <= COMP_BIT_SIZE; i++) + { + if ((long_comp)N*t%two_2_i >= two_2_i_minus_1) + { + t += two_2_i_minus_1; + } + + two_2_i_minus_1 <<= 1; + two_2_i <<= 1; + } + + return (comp)(COMP_RADIX-t); +} +#endif + +#if defined(CONFIG_BIGINT_KARATSUBA) || defined(CONFIG_BIGINT_BARRETT) || \ + defined(CONFIG_BIGINT_MONTGOMERY) +/** + * Take each component and shift down (in terms of components) + */ +static bigint *comp_right_shift(bigint *biR, int num_shifts) +{ + int i = biR->size-num_shifts; + comp *x = biR->comps; + comp *y = &biR->comps[num_shifts]; + + check(biR); + + if (i <= 0) /* have we completely right shifted? */ + { + biR->comps[0] = 0; /* return 0 */ + biR->size = 1; + return biR; + } + + do + { + *x++ = *y++; + } while (--i > 0); + + biR->size -= num_shifts; + return biR; +} + +/** + * Take each component and shift it up (in terms of components) + */ +static bigint *comp_left_shift(bigint *biR, int num_shifts) +{ + int i = biR->size-1; + comp *x, *y; + + check(biR); + + if (num_shifts <= 0) + { + return biR; + } + + more_comps(biR, biR->size + num_shifts); + + x = &biR->comps[i+num_shifts]; + y = &biR->comps[i]; + + do + { + *x-- = *y--; + } while (i--); + + memset(biR->comps, 0, num_shifts*COMP_BYTE_SIZE); /* zero LS comps */ + return biR; +} +#endif + +/** + * @brief Allow a binary sequence to be imported as a bigint. + * @param ctx [in] The bigint session context. + * @param data [in] The data to be converted. + * @param size [in] The number of bytes of data. + * @return A bigint representing this data. + */ +bigint *bi_import(BI_CTX *ctx, const uint8_t *data, int size) +{ + bigint *biR = alloc(ctx, (size+COMP_BYTE_SIZE-1)/COMP_BYTE_SIZE); + int i, j = 0, offset = 0; + + memset(biR->comps, 0, biR->size*COMP_BYTE_SIZE); + + for (i = size-1; i >= 0; i--) + { + biR->comps[offset] += data[i] << (j*8); + + if (++j == COMP_BYTE_SIZE) + { + j = 0; + offset ++; + } + } + + return trim(biR); +} + +#ifdef CONFIG_SSL_FULL_MODE +/** + * @brief The testharness uses this code to import text hex-streams and + * convert them into bigints. + * @param ctx [in] The bigint session context. + * @param data [in] A string consisting of hex characters. The characters must + * be in upper case. + * @return A bigint representing this data. + */ +bigint *bi_str_import(BI_CTX *ctx, const char *data) +{ + int size = strlen(data); + bigint *biR = alloc(ctx, (size+COMP_NUM_NIBBLES-1)/COMP_NUM_NIBBLES); + int i, j = 0, offset = 0; + memset(biR->comps, 0, biR->size*COMP_BYTE_SIZE); + + for (i = size-1; i >= 0; i--) + { + int num = (data[i] <= '9') ? (data[i] - '0') : (data[i] - 'A' + 10); + biR->comps[offset] += num << (j*4); + + if (++j == COMP_NUM_NIBBLES) + { + j = 0; + offset ++; + } + } + + return biR; +} + +void bi_print(const char *label, bigint *x) +{ + int i, j; + + if (x == NULL) + { + printf("%s: (null)\n", label); + return; + } + + printf("%s: (size %d)\n", label, x->size); + for (i = x->size-1; i >= 0; i--) + { + for (j = COMP_NUM_NIBBLES-1; j >= 0; j--) + { + comp mask = 0x0f << (j*4); + comp num = (x->comps[i] & mask) >> (j*4); + putc((num <= 9) ? (num + '0') : (num + 'A' - 10), stdout); + } + } + + printf("\n"); +} +#endif + +/** + * @brief Take a bigint and convert it into a byte sequence. + * + * This is useful after a decrypt operation. + * @param ctx [in] The bigint session context. + * @param x [in] The bigint to be converted. + * @param data [out] The converted data as a byte stream. + * @param size [in] The maximum size of the byte stream. Unused bytes will be + * zeroed. + */ +void bi_export(BI_CTX *ctx, bigint *x, uint8_t *data, int size) +{ + int i, j, k = size-1; + + check(x); + memset(data, 0, size); /* ensure all leading 0's are cleared */ + + for (i = 0; i < x->size; i++) + { + for (j = 0; j < COMP_BYTE_SIZE; j++) + { + comp mask = 0xff << (j*8); + int num = (x->comps[i] & mask) >> (j*8); + data[k--] = num; + + if (k < 0) + { + break; + } + } + } + + bi_free(ctx, x); +} + +/** + * @brief Pre-calculate some of the expensive steps in reduction. + * + * This function should only be called once (normally when a session starts). + * When the session is over, bi_free_mod() should be called. bi_mod_power() + * relies on this function being called. + * @param ctx [in] The bigint session context. + * @param bim [in] The bigint modulus that will be used. + * @param mod_offset [in] There are three moduluii that can be stored - the + * standard modulus, and its two primes p and q. This offset refers to which + * modulus we are referring to. + * @see bi_free_mod(), bi_mod_power(). + */ +void bi_set_mod(BI_CTX *ctx, bigint *bim, int mod_offset) +{ + int k = bim->size; + comp d = (comp)((long_comp)COMP_RADIX/(bim->comps[k-1]+1)); +#ifdef CONFIG_BIGINT_MONTGOMERY + bigint *R, *R2; +#endif + + ctx->bi_mod[mod_offset] = bim; + bi_permanent(ctx->bi_mod[mod_offset]); + ctx->bi_normalised_mod[mod_offset] = bi_int_multiply(ctx, bim, d); + bi_permanent(ctx->bi_normalised_mod[mod_offset]); + +#if defined(CONFIG_BIGINT_MONTGOMERY) + /* set montgomery variables */ + R = comp_left_shift(bi_clone(ctx, ctx->bi_radix), k-1); /* R */ + R2 = comp_left_shift(bi_clone(ctx, ctx->bi_radix), k*2-1); /* R^2 */ + ctx->bi_RR_mod_m[mod_offset] = bi_mod(ctx, R2); /* R^2 mod m */ + ctx->bi_R_mod_m[mod_offset] = bi_mod(ctx, R); /* R mod m */ + + bi_permanent(ctx->bi_RR_mod_m[mod_offset]); + bi_permanent(ctx->bi_R_mod_m[mod_offset]); + + ctx->N0_dash[mod_offset] = modular_inverse(ctx->bi_mod[mod_offset]); + +#elif defined (CONFIG_BIGINT_BARRETT) + ctx->bi_mu[mod_offset] = + bi_divide(ctx, comp_left_shift( + bi_clone(ctx, ctx->bi_radix), k*2-1), ctx->bi_mod[mod_offset], 0); + bi_permanent(ctx->bi_mu[mod_offset]); +#endif +} + +/** + * @brief Used when cleaning various bigints at the end of a session. + * @param ctx [in] The bigint session context. + * @param mod_offset [in] The offset to use. + * @see bi_set_mod(). + */ +void bi_free_mod(BI_CTX *ctx, int mod_offset) +{ + bi_depermanent(ctx->bi_mod[mod_offset]); + bi_free(ctx, ctx->bi_mod[mod_offset]); +#if defined (CONFIG_BIGINT_MONTGOMERY) + bi_depermanent(ctx->bi_RR_mod_m[mod_offset]); + bi_depermanent(ctx->bi_R_mod_m[mod_offset]); + bi_free(ctx, ctx->bi_RR_mod_m[mod_offset]); + bi_free(ctx, ctx->bi_R_mod_m[mod_offset]); +#elif defined(CONFIG_BIGINT_BARRETT) + bi_depermanent(ctx->bi_mu[mod_offset]); + bi_free(ctx, ctx->bi_mu[mod_offset]); +#endif + bi_depermanent(ctx->bi_normalised_mod[mod_offset]); + bi_free(ctx, ctx->bi_normalised_mod[mod_offset]); +} + +/** + * Perform a standard multiplication between two bigints. + */ +static bigint *regular_multiply(BI_CTX *ctx, bigint *bia, bigint *bib) +{ + int i, j, i_plus_j; + int n = bia->size; + int t = bib->size; + bigint *biR = alloc(ctx, n + t); + comp *sr = biR->comps; + comp *sa = bia->comps; + comp *sb = bib->comps; + + check(bia); + check(bib); + + /* clear things to start with */ + memset(biR->comps, 0, ((n+t)*COMP_BYTE_SIZE)); + i = 0; + + do + { + comp carry = 0; + comp b = *sb++; + i_plus_j = i; + j = 0; + + do + { + long_comp tmp = sr[i_plus_j] + (long_comp)sa[j]*b + carry; + sr[i_plus_j++] = (comp)tmp; /* downsize */ + carry = (comp)(tmp >> COMP_BIT_SIZE); + } while (++j < n); + + sr[i_plus_j] = carry; + } while (++i < t); + + bi_free(ctx, bia); + bi_free(ctx, bib); + return trim(biR); +} + +#ifdef CONFIG_BIGINT_KARATSUBA +/* + * Karatsuba improves on regular multiplication due to only 3 multiplications + * being done instead of 4. The additional additions/subtractions are O(N) + * rather than O(N^2) and so for big numbers it saves on a few operations + */ +static bigint *karatsuba(BI_CTX *ctx, bigint *bia, bigint *bib, int is_square) +{ + bigint *x0, *x1; + bigint *p0, *p1, *p2; + int m; + + if (is_square) + { + m = (bia->size + 1)/2; + } + else + { + m = (max(bia->size, bib->size) + 1)/2; + } + + x0 = bi_clone(ctx, bia); + x0->size = m; + x1 = bi_clone(ctx, bia); + comp_right_shift(x1, m); + bi_free(ctx, bia); + + /* work out the 3 partial products */ + if (is_square) + { + p0 = bi_square(ctx, bi_copy(x0)); + p2 = bi_square(ctx, bi_copy(x1)); + p1 = bi_square(ctx, bi_add(ctx, x0, x1)); + } + else /* normal multiply */ + { + bigint *y0, *y1; + y0 = bi_clone(ctx, bib); + y0->size = m; + y1 = bi_clone(ctx, bib); + comp_right_shift(y1, m); + bi_free(ctx, bib); + + p0 = bi_multiply(ctx, bi_copy(x0), bi_copy(y0)); + p2 = bi_multiply(ctx, bi_copy(x1), bi_copy(y1)); + p1 = bi_multiply(ctx, bi_add(ctx, x0, x1), bi_add(ctx, y0, y1)); + } + + p1 = bi_subtract(ctx, + bi_subtract(ctx, p1, bi_copy(p2), NULL), bi_copy(p0), NULL); + + comp_left_shift(p1, m); + comp_left_shift(p2, 2*m); + return bi_add(ctx, p1, bi_add(ctx, p0, p2)); +} +#endif + +/** + * @brief Perform a multiplication operation between two bigints. + * @param ctx [in] The bigint session context. + * @param bia [in] A bigint. + * @param bib [in] Another bigint. + * @return The result of the multiplication. + */ +bigint *bi_multiply(BI_CTX *ctx, bigint *bia, bigint *bib) +{ + check(bia); + check(bib); + +#ifdef CONFIG_BIGINT_KARATSUBA + if (min(bia->size, bib->size) < MUL_KARATSUBA_THRESH) + { + return regular_multiply(ctx, bia, bib); + } + + return karatsuba(ctx, bia, bib, 0); +#else + return regular_multiply(ctx, bia, bib); +#endif +} + +#ifdef CONFIG_BIGINT_SQUARE +/* + * Perform the actual square operion. It takes into account overflow. + */ +static bigint *regular_square(BI_CTX *ctx, bigint *bi) +{ + int t = bi->size; + int i = 0, j; + bigint *biR = alloc(ctx, t*2); + comp *w = biR->comps; + comp *x = bi->comps; + comp carry; + + memset(w, 0, biR->size*COMP_BYTE_SIZE); + + do + { + long_comp tmp = w[2*i] + (long_comp)x[i]*x[i]; + comp u = 0; + w[2*i] = (comp)tmp; + carry = (comp)(tmp >> COMP_BIT_SIZE); + + for (j = i+1; j < t; j++) + { + long_comp xx = (long_comp)x[i]*x[j]; + long_comp xx2 = 2*xx; + long_comp blob = (long_comp)w[i+j]+carry; + + if (u) /* previous overflow */ + { + blob += COMP_RADIX; + } + + + u = 0; + tmp = xx2 + blob; + + /* check for overflow */ + if ((COMP_MAX-xx) < xx || (COMP_MAX-xx2) < blob) + { + u = 1; + } + + w[i+j] = (comp)tmp; + carry = (comp)(tmp >> COMP_BIT_SIZE); + } + + w[i+t] += carry; + + if (u) + { + w[i+t+1] = 1; /* add carry */ + } + } while (++i < t); + + bi_free(ctx, bi); + return trim(biR); +} + +/** + * @brief Perform a square operation on a bigint. + * @param ctx [in] The bigint session context. + * @param bia [in] A bigint. + * @return The result of the multiplication. + */ +bigint *bi_square(BI_CTX *ctx, bigint *bia) +{ + check(bia); + +#ifdef CONFIG_BIGINT_KARATSUBA + if (bia->size < SQU_KARATSUBA_THRESH) + { + return regular_square(ctx, bia); + } + + return karatsuba(ctx, bia, NULL, 1); +#else + return regular_square(ctx, bia); +#endif +} +#endif + +/** + * @brief Compare two bigints. + * @param bia [in] A bigint. + * @param bib [in] Another bigint. + * @return -1 if smaller, 1 if larger and 0 if equal. + */ +int bi_compare(bigint *bia, bigint *bib) +{ + int r, i; + + check(bia); + check(bib); + + if (bia->size > bib->size) + r = 1; + else if (bia->size < bib->size) + r = -1; + else + { + comp *a = bia->comps; + comp *b = bib->comps; + + /* Same number of components. Compare starting from the high end + * and working down. */ + r = 0; + i = bia->size - 1; + + do + { + if (a[i] > b[i]) + { + r = 1; + break; + } + else if (a[i] < b[i]) + { + r = -1; + break; + } + } while (--i >= 0); + } + + return r; +} + +/* + * Allocate and zero more components. Does not consume bi. + */ +static void more_comps(bigint *bi, int n) +{ + if (n > bi->max_comps) + { + bi->max_comps = max(bi->max_comps * 2, n); + bi->comps = (comp*)realloc(bi->comps, bi->max_comps * COMP_BYTE_SIZE); + } + + if (n > bi->size) + { + memset(&bi->comps[bi->size], 0, (n-bi->size)*COMP_BYTE_SIZE); + } + + bi->size = n; +} + +/* + * Make a new empty bigint. It may just use an old one if one is available. + * Otherwise get one off the heap. + */ +static bigint *alloc(BI_CTX *ctx, int size) +{ + bigint *biR; + + /* Can we recycle an old bigint? */ + if (ctx->free_list != NULL) + { + biR = ctx->free_list; + ctx->free_list = biR->next; + ctx->free_count--; + + if (biR->refs != 0) + { +#ifdef CONFIG_SSL_FULL_MODE + printf("alloc: refs was not 0\n"); +#endif + abort(); /* create a stack trace from a core dump */ + } + + more_comps(biR, size); + } + else + { + /* No free bigints available - create a new one. */ + biR = (bigint *)malloc(sizeof(bigint)); + biR->comps = (comp*)malloc(size * COMP_BYTE_SIZE); + biR->max_comps = size; /* give some space to spare */ + } + + biR->size = size; + biR->refs = 1; + biR->next = NULL; + ctx->active_count++; + return biR; +} + +/* + * Work out the highest '1' bit in an exponent. Used when doing sliding-window + * exponentiation. + */ +static int find_max_exp_index(bigint *biexp) +{ + int i = COMP_BIT_SIZE-1; + comp shift = COMP_RADIX/2; + comp test = biexp->comps[biexp->size-1]; /* assume no leading zeroes */ + + check(biexp); + + do + { + if (test & shift) + { + return i+(biexp->size-1)*COMP_BIT_SIZE; + } + + shift >>= 1; + } while (--i != 0); + + return -1; /* error - must have been a leading 0 */ +} + +/* + * Is a particular bit is an exponent 1 or 0? Used when doing sliding-window + * exponentiation. + */ +static int exp_bit_is_one(bigint *biexp, int offset) +{ + comp test = biexp->comps[offset / COMP_BIT_SIZE]; + int num_shifts = offset % COMP_BIT_SIZE; + comp shift = 1; + int i; + + check(biexp); + + for (i = 0; i < num_shifts; i++) + { + shift <<= 1; + } + + return test & shift; +} + +#ifdef CONFIG_BIGINT_CHECK_ON +/* + * Perform a sanity check on bi. + */ +static void check(const bigint *bi) +{ + if (bi->refs <= 0) + { + printf("check: zero or negative refs in bigint\n"); + abort(); + } + + if (bi->next != NULL) + { + printf("check: attempt to use a bigint from " + "the free list\n"); + abort(); + } +} +#endif + +/* + * Delete any leading 0's (and allow for 0). + */ +static bigint *trim(bigint *bi) +{ + check(bi); + + while (bi->comps[bi->size-1] == 0 && bi->size > 1) + { + bi->size--; + } + + return bi; +} + +#if defined(CONFIG_BIGINT_MONTGOMERY) +/** + * @brief Perform a single montgomery reduction. + * @param ctx [in] The bigint session context. + * @param bixy [in] A bigint. + * @return The result of the montgomery reduction. + */ +bigint *bi_mont(BI_CTX *ctx, bigint *bixy) +{ + int i = 0, n; + uint8_t mod_offset = ctx->mod_offset; + bigint *bim = ctx->bi_mod[mod_offset]; + comp mod_inv = ctx->N0_dash[mod_offset]; + + check(bixy); + + if (ctx->use_classical) /* just use classical instead */ + { + return bi_mod(ctx, bixy); + } + + n = bim->size; + + do + { + bixy = bi_add(ctx, bixy, comp_left_shift( + bi_int_multiply(ctx, bim, bixy->comps[i]*mod_inv), i)); + } while (++i < n); + + comp_right_shift(bixy, n); + + if (bi_compare(bixy, bim) >= 0) + { + bixy = bi_subtract(ctx, bixy, bim, NULL); + } + + return bixy; +} + +#elif defined(CONFIG_BIGINT_BARRETT) +/* + * Stomp on the most significant components to give the illusion of a "mod base + * radix" operation + */ +static bigint *comp_mod(bigint *bi, int mod) +{ + check(bi); + + if (bi->size > mod) + { + bi->size = mod; + } + + return bi; +} + +/* + * Barrett reduction has no need for some parts of the product, so ignore bits + * of the multiply. This routine gives Barrett its big performance + * improvements over Classical/Montgomery reduction methods. + */ +static bigint *partial_multiply(BI_CTX *ctx, bigint *bia, bigint *bib, + int inner_partial, int outer_partial) +{ + int i = 0, j, n = bia->size, t = bib->size; + bigint *biR; + comp carry; + comp *sr, *sa, *sb; + + check(bia); + check(bib); + + biR = alloc(ctx, n + t); + sa = bia->comps; + sb = bib->comps; + sr = biR->comps; + + if (inner_partial) + { + memset(sr, 0, inner_partial*COMP_BYTE_SIZE); + } + else /* outer partial */ + { + if (n < outer_partial || t < outer_partial) /* should we bother? */ + { + bi_free(ctx, bia); + bi_free(ctx, bib); + biR->comps[0] = 0; /* return 0 */ + biR->size = 1; + return biR; + } + + memset(&sr[outer_partial], 0, (n+t-outer_partial)*COMP_BYTE_SIZE); + } + + do + { + comp *a = sa; + comp b = *sb++; + long_comp tmp; + int i_plus_j = i; + carry = 0; + j = n; + + if (outer_partial && i_plus_j < outer_partial) + { + i_plus_j = outer_partial; + a = &sa[outer_partial-i]; + j = n-(outer_partial-i); + } + + do + { + if (inner_partial && i_plus_j >= inner_partial) + { + break; + } + + tmp = sr[i_plus_j] + ((long_comp)*a++)*b + carry; + sr[i_plus_j++] = (comp)tmp; /* downsize */ + carry = (comp)(tmp >> COMP_BIT_SIZE); + } while (--j != 0); + + sr[i_plus_j] = carry; + } while (++i < t); + + bi_free(ctx, bia); + bi_free(ctx, bib); + return trim(biR); +} + +/** + * @brief Perform a single Barrett reduction. + * @param ctx [in] The bigint session context. + * @param bi [in] A bigint. + * @return The result of the Barrett reduction. + */ +bigint *bi_barrett(BI_CTX *ctx, bigint *bi) +{ + bigint *q1, *q2, *q3, *r1, *r2, *r; + uint8_t mod_offset = ctx->mod_offset; + bigint *bim = ctx->bi_mod[mod_offset]; + int k = bim->size; + + check(bi); + check(bim); + + /* use Classical method instead - Barrett cannot help here */ + if (bi->size > k*2) + { + return bi_mod(ctx, bi); + } + + q1 = comp_right_shift(bi_clone(ctx, bi), k-1); + + /* do outer partial multiply */ + q2 = partial_multiply(ctx, q1, ctx->bi_mu[mod_offset], 0, k-1); + q3 = comp_right_shift(q2, k+1); + r1 = comp_mod(bi, k+1); + + /* do inner partial multiply */ + r2 = comp_mod(partial_multiply(ctx, q3, bim, k+1, 0), k+1); + r = bi_subtract(ctx, r1, r2, NULL); + + /* if (r >= m) r = r - m; */ + if (bi_compare(r, bim) >= 0) + { + r = bi_subtract(ctx, r, bim, NULL); + } + + return r; +} +#endif /* CONFIG_BIGINT_BARRETT */ + +#ifdef CONFIG_BIGINT_SLIDING_WINDOW +/* + * Work out g1, g3, g5, g7... etc for the sliding-window algorithm + */ +static void precompute_slide_window(BI_CTX *ctx, int window, bigint *g1) +{ + int k = 1, i; + bigint *g2; + + for (i = 0; i < window-1; i++) /* compute 2^(window-1) */ + { + k <<= 1; + } + + ctx->g = (bigint **)malloc(k*sizeof(bigint *)); + ctx->g[0] = bi_clone(ctx, g1); + bi_permanent(ctx->g[0]); + g2 = bi_residue(ctx, bi_square(ctx, ctx->g[0])); /* g^2 */ + + for (i = 1; i < k; i++) + { + ctx->g[i] = bi_residue(ctx, bi_multiply(ctx, ctx->g[i-1], bi_copy(g2))); + bi_permanent(ctx->g[i]); + } + + bi_free(ctx, g2); + ctx->window = k; +} +#endif + +/** + * @brief Perform a modular exponentiation. + * + * This function requires bi_set_mod() to have been called previously. This is + * one of the optimisations used for performance. + * @param ctx [in] The bigint session context. + * @param bi [in] The bigint on which to perform the mod power operation. + * @param biexp [in] The bigint exponent. + * @return The result of the mod exponentiation operation + * @see bi_set_mod(). + */ +bigint *bi_mod_power(BI_CTX *ctx, bigint *bi, bigint *biexp) +{ + int i = find_max_exp_index(biexp), j, window_size = 1; + bigint *biR = int_to_bi(ctx, 1); + +#if defined(CONFIG_BIGINT_MONTGOMERY) + uint8_t mod_offset = ctx->mod_offset; + if (!ctx->use_classical) + { + /* preconvert */ + bi = bi_mont(ctx, + bi_multiply(ctx, bi, ctx->bi_RR_mod_m[mod_offset])); /* x' */ + bi_free(ctx, biR); + biR = ctx->bi_R_mod_m[mod_offset]; /* A */ + } +#endif + + check(bi); + check(biexp); + +#ifdef CONFIG_BIGINT_SLIDING_WINDOW + for (j = i; j > 32; j /= 5) /* work out an optimum size */ + window_size++; + + /* work out the slide constants */ + precompute_slide_window(ctx, window_size, bi); +#else /* just one constant */ + ctx->g = (bigint **)malloc(sizeof(bigint *)); + ctx->g[0] = bi_clone(ctx, bi); + ctx->window = 1; + bi_permanent(ctx->g[0]); +#endif + + /* if sliding-window is off, then only one bit will be done at a time and + * will reduce to standard left-to-right exponentiation */ + do + { + if (exp_bit_is_one(biexp, i)) + { + int l = i-window_size+1; + int part_exp = 0; + + if (l < 0) /* LSB of exponent will always be 1 */ + l = 0; + else + { + while (exp_bit_is_one(biexp, l) == 0) + l++; /* go back up */ + } + + /* build up the section of the exponent */ + for (j = i; j >= l; j--) + { + biR = bi_residue(ctx, bi_square(ctx, biR)); + if (exp_bit_is_one(biexp, j)) + part_exp++; + + if (j != l) + part_exp <<= 1; + } + + part_exp = (part_exp-1)/2; /* adjust for array */ + biR = bi_residue(ctx, bi_multiply(ctx, biR, ctx->g[part_exp])); + i = l-1; + } + else /* square it */ + { + biR = bi_residue(ctx, bi_square(ctx, biR)); + i--; + } + } while (i >= 0); + + /* cleanup */ + for (i = 0; i < ctx->window; i++) + { + bi_depermanent(ctx->g[i]); + bi_free(ctx, ctx->g[i]); + } + + free(ctx->g); + bi_free(ctx, bi); + bi_free(ctx, biexp); +#if defined CONFIG_BIGINT_MONTGOMERY + return ctx->use_classical ? biR : bi_mont(ctx, biR); /* convert back */ +#else /* CONFIG_BIGINT_CLASSICAL or CONFIG_BIGINT_BARRETT */ + return biR; +#endif +} + +#ifdef CONFIG_SSL_CERT_VERIFICATION +/** + * @brief Perform a modular exponentiation using a temporary modulus. + * + * We need this function to check the signatures of certificates. The modulus + * of this function is temporary as it's just used for authentication. + * @param ctx [in] The bigint session context. + * @param bi [in] The bigint to perform the exp/mod. + * @param bim [in] The temporary modulus. + * @param biexp [in] The bigint exponent. + * @return The result of the mod exponentiation operation + * @see bi_set_mod(). + */ +bigint *bi_mod_power2(BI_CTX *ctx, bigint *bi, bigint *bim, bigint *biexp) +{ + bigint *biR, *tmp_biR; + + /* Set up a temporary bigint context and transfer what we need between + * them. We need to do this since we want to keep the original modulus + * which is already in this context. This operation is only called when + * doing peer verification, and so is not expensive :-) */ + BI_CTX *tmp_ctx = bi_initialize(); + bi_set_mod(tmp_ctx, bi_clone(tmp_ctx, bim), BIGINT_M_OFFSET); + tmp_biR = bi_mod_power(tmp_ctx, + bi_clone(tmp_ctx, bi), + bi_clone(tmp_ctx, biexp)); + biR = bi_clone(ctx, tmp_biR); + bi_free(tmp_ctx, tmp_biR); + bi_free_mod(tmp_ctx, BIGINT_M_OFFSET); + bi_terminate(tmp_ctx); + + bi_free(ctx, bi); + bi_free(ctx, bim); + bi_free(ctx, biexp); + return biR; +} +#endif + +#ifdef CONFIG_BIGINT_CRT +/** + * @brief Use the Chinese Remainder Theorem to quickly perform RSA decrypts. + * + * @param ctx [in] The bigint session context. + * @param bi [in] The bigint to perform the exp/mod. + * @param dP [in] CRT's dP bigint + * @param dQ [in] CRT's dQ bigint + * @param p [in] CRT's p bigint + * @param q [in] CRT's q bigint + * @param qInv [in] CRT's qInv bigint + * @return The result of the CRT operation + */ +bigint *bi_crt(BI_CTX *ctx, bigint *bi, + bigint *dP, bigint *dQ, + bigint *p, bigint *q, bigint *qInv) +{ + bigint *m1, *m2, *h; + + /* Montgomery has a condition the 0 < x, y < m and these products violate + * that condition. So disable Montgomery when using CRT */ +#if defined(CONFIG_BIGINT_MONTGOMERY) + ctx->use_classical = 1; +#endif + ctx->mod_offset = BIGINT_P_OFFSET; + m1 = bi_mod_power(ctx, bi_copy(bi), dP); + + ctx->mod_offset = BIGINT_Q_OFFSET; + m2 = bi_mod_power(ctx, bi, dQ); + + h = bi_subtract(ctx, bi_add(ctx, m1, p), bi_copy(m2), NULL); + h = bi_multiply(ctx, h, qInv); + ctx->mod_offset = BIGINT_P_OFFSET; + h = bi_residue(ctx, h); +#if defined(CONFIG_BIGINT_MONTGOMERY) + ctx->use_classical = 0; /* reset for any further operation */ +#endif + return bi_add(ctx, m2, bi_multiply(ctx, q, h)); +} +#endif +/** @} */ |