--- /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
+/** @} */
projects / project / luci.git / blobdiff