+++ /dev/null
-/*
- * 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
-/** @} */
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