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Diffstat (limited to 'axTLS/src/crypto/bigint.c')
| -rw-r--r-- | axTLS/src/crypto/bigint.c | 1512 |
1 files changed, 0 insertions, 1512 deletions
diff --git a/axTLS/src/crypto/bigint.c b/axTLS/src/crypto/bigint.c deleted file mode 100644 index e9ca04c..0000000 --- a/axTLS/src/crypto/bigint.c +++ /dev/null @@ -1,1512 +0,0 @@ -/* - * 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 "os_port.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) - { - goto buf_done; - } - } - } -buf_done: - - 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. - * - * 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 *regular_multiply(BI_CTX *ctx, bigint *bia, bigint *bib, - int inner_partial, int outer_partial) -{ - int i = 0, 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)); - - do - { - long_comp tmp; - comp carry = 0; - int r_index = i; - j = 0; - - if (outer_partial && outer_partial-i > 0 && outer_partial < n) - { - r_index = outer_partial-1; - j = outer_partial-i-1; - } - - do - { - if (inner_partial && r_index >= inner_partial) - { - break; - } - - tmp = sr[r_index] + ((long_comp)sa[j])*sb[i] + carry; - sr[r_index++] = (comp)tmp; /* downsize */ - carry = tmp >> COMP_BIT_SIZE; - } while (++j < n); - - sr[r_index] = 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, 0, 0); - } - - return karatsuba(ctx, bia, bib, 0); -#else - return regular_multiply(ctx, bia, bib, 0, 0); -#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+1); - comp *w = biR->comps; - comp *x = bi->comps; - long_comp carry; - memset(w, 0, biR->size*COMP_BYTE_SIZE); - - do - { - long_comp tmp = w[2*i] + (long_comp)x[i]*x[i]; - w[2*i] = (comp)tmp; - carry = tmp >> COMP_BIT_SIZE; - - for (j = i+1; j < t; j++) - { - uint8_t c = 0; - long_comp xx = (long_comp)x[i]*x[j]; - if ((COMP_MAX-xx) < xx) - c = 1; - - tmp = (xx<<1); - - if ((COMP_MAX-tmp) < w[i+j]) - c = 1; - - tmp += w[i+j]; - - if ((COMP_MAX-tmp) < carry) - c = 1; - - tmp += carry; - w[i+j] = (comp)tmp; - carry = tmp >> COMP_BIT_SIZE; - - if (c) - carry += COMP_RADIX; - } - - tmp = w[i+t] + carry; - w[i+t] = (comp)tmp; - w[i+t+1] = tmp >> COMP_BIT_SIZE; - } 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) != 0; -} - -#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; -} - -/** - * @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 = regular_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(regular_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 -/** @} */ |