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#include "tls.h"
#include "tls_rsa.h"
#include "util.h"
#if MG_TLS == MG_TLS_BUILTIN
#define NS_INTERNAL static
typedef struct _bigint bigint; /**< An alias for _bigint */
/*
* 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.
*/
/* Maintain a number of precomputed variables when doing reduction */
#define BIGINT_M_OFFSET 0 /**< Normal modulo offset. */
#define BIGINT_P_OFFSET 1 /**< p modulo offset. */
#define BIGINT_Q_OFFSET 2 /**< q module offset. */
#define BIGINT_NUM_MODS 3 /**< The number of modulus constants used. */
/* Architecture specific functions for big ints */
#if defined(CONFIG_INTEGER_8BIT)
#define COMP_RADIX 256U /**< Max component + 1 */
#define COMP_MAX 0xFFFFU /**< (Max dbl comp -1) */
#define COMP_BIT_SIZE 8 /**< Number of bits in a component. */
#define COMP_BYTE_SIZE 1 /**< Number of bytes in a component. */
#define COMP_NUM_NIBBLES 2 /**< Used For diagnostics only. */
typedef uint8_t comp; /**< A single precision component. */
typedef uint16_t long_comp; /**< A double precision component. */
typedef int16_t slong_comp; /**< A signed double precision component. */
#elif defined(CONFIG_INTEGER_16BIT)
#define COMP_RADIX 65536U /**< Max component + 1 */
#define COMP_MAX 0xFFFFFFFFU /**< (Max dbl comp -1) */
#define COMP_BIT_SIZE 16 /**< Number of bits in a component. */
#define COMP_BYTE_SIZE 2 /**< Number of bytes in a component. */
#define COMP_NUM_NIBBLES 4 /**< Used For diagnostics only. */
typedef uint16_t comp; /**< A single precision component. */
typedef uint32_t long_comp; /**< A double precision component. */
typedef int32_t slong_comp; /**< A signed double precision component. */
#else /* regular 32 bit */
#ifdef _MSC_VER
#define COMP_RADIX 4294967296i64
#define COMP_MAX 0xFFFFFFFFFFFFFFFFui64
#else
#define COMP_RADIX 4294967296 /**< Max component + 1 */
#define COMP_MAX 0xFFFFFFFFFFFFFFFF /**< (Max dbl comp -1) */
#endif
#define COMP_BIT_SIZE 32 /**< Number of bits in a component. */
#define COMP_BYTE_SIZE 4 /**< Number of bytes in a component. */
#define COMP_NUM_NIBBLES 8 /**< Used For diagnostics only. */
typedef uint32_t comp; /**< A single precision component. */
typedef uint64_t long_comp; /**< A double precision component. */
typedef int64_t slong_comp; /**< A signed double precision component. */
#endif
/**
* @struct _bigint
* @brief A big integer basic object
*/
struct _bigint {
struct _bigint *next; /**< The next bigint in the cache. */
short size; /**< The number of components in this bigint. */
short max_comps; /**< The heapsize allocated for this bigint */
int refs; /**< An internal reference count. */
comp *comps; /**< A ptr to the actual component data */
};
/**
* Maintains the state of the cache, and a number of variables used in
* reduction.
*/
struct _BI_CTX /**< A big integer "session" context. */
{
bigint *active_list; /**< Bigints currently used. */
bigint *free_list; /**< Bigints not used. */
bigint *bi_radix; /**< The radix used. */
bigint *bi_mod[BIGINT_NUM_MODS]; /**< modulus */
#if defined(CONFIG_BIGINT_MONTGOMERY)
bigint *bi_RR_mod_m[BIGINT_NUM_MODS]; /**< R^2 mod m */
bigint *bi_R_mod_m[BIGINT_NUM_MODS]; /**< R mod m */
comp N0_dash[BIGINT_NUM_MODS];
#elif defined(CONFIG_BIGINT_BARRETT)
bigint *bi_mu[BIGINT_NUM_MODS]; /**< Storage for mu */
#endif
bigint *bi_normalised_mod[BIGINT_NUM_MODS]; /**< Normalised mod storage. */
bigint **g; /**< Used by sliding-window. */
int window; /**< The size of the sliding window */
int active_count; /**< Number of active bigints. */
int free_count; /**< Number of free bigints. */
#ifdef CONFIG_BIGINT_MONTGOMERY
uint8_t use_classical; /**< Use classical reduction. */
#endif
uint8_t mod_offset; /**< The mod offset we are using */
};
typedef struct _BI_CTX BI_CTX;
#if !defined(MAX)
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define MIN(a, b) ((a) < (b) ? (a) : (b))
#endif
#define PERMANENT 0x7FFF55AA /**< A magic number for permanents. */
/*
* 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.
*/
NS_INTERNAL BI_CTX *bi_initialize(void);
NS_INTERNAL void bi_terminate(BI_CTX *ctx);
NS_INTERNAL void bi_permanent(bigint *bi);
NS_INTERNAL void bi_depermanent(bigint *bi);
NS_INTERNAL void bi_clear_cache(BI_CTX *ctx);
NS_INTERNAL void bi_free(BI_CTX *ctx, bigint *bi);
NS_INTERNAL bigint *bi_copy(bigint *bi);
NS_INTERNAL bigint *bi_clone(BI_CTX *ctx, const bigint *bi);
NS_INTERNAL void bi_export(BI_CTX *ctx, bigint *bi, uint8_t *data, int size);
NS_INTERNAL bigint *bi_import(BI_CTX *ctx, const uint8_t *data, int len);
NS_INTERNAL bigint *int_to_bi(BI_CTX *ctx, comp i);
/* the functions that actually do something interesting */
NS_INTERNAL bigint *bi_add(BI_CTX *ctx, bigint *bia, bigint *bib);
NS_INTERNAL bigint *bi_subtract(BI_CTX *ctx, bigint *bia, bigint *bib,
int *is_negative);
NS_INTERNAL bigint *bi_divide(BI_CTX *ctx, bigint *bia, bigint *bim,
int is_mod);
NS_INTERNAL bigint *bi_multiply(BI_CTX *ctx, bigint *bia, bigint *bib);
NS_INTERNAL bigint *bi_mod_power(BI_CTX *ctx, bigint *bi, bigint *biexp);
#if 0
NS_INTERNAL bigint *bi_mod_power2(BI_CTX *ctx, bigint *bi,
bigint *bim, bigint *biexp);
#endif
NS_INTERNAL int bi_compare(bigint *bia, bigint *bib);
NS_INTERNAL void bi_set_mod(BI_CTX *ctx, bigint *bim, int mod_offset);
NS_INTERNAL void bi_free_mod(BI_CTX *ctx, int mod_offset);
#ifdef CONFIG_SSL_FULL_MODE
NS_INTERNAL void bi_print(const char *label, bigint *bi);
NS_INTERNAL bigint *bi_str_import(BI_CTX *ctx, const char *data);
#endif
/**
* @def bi_mod
* Find the residue of B. bi_set_mod() must be called before hand.
*/
#define bi_mod(A, B) bi_divide(A, B, ctx->bi_mod[ctx->mod_offset], 1)
/**
* bi_residue() is technically the same as bi_mod(), but it uses the
* appropriate reduction technique (which is bi_mod() when doing classical
* reduction).
*/
#if defined(CONFIG_BIGINT_MONTGOMERY)
#define bi_residue(A, B) bi_mont(A, B)
NS_INTERNAL bigint *bi_mont(BI_CTX *ctx, bigint *bixy);
#elif defined(CONFIG_BIGINT_BARRETT)
#define bi_residue(A, B) bi_barrett(A, B)
NS_INTERNAL bigint *bi_barrett(BI_CTX *ctx, bigint *bi);
#else /* if defined(CONFIG_BIGINT_CLASSICAL) */
#define bi_residue(A, B) bi_mod(A, B)
#endif
#ifdef CONFIG_BIGINT_SQUARE
NS_INTERNAL bigint *bi_square(BI_CTX *ctx, bigint *bi);
#else
#define bi_square(A, B) bi_multiply(A, bi_copy(B), B)
#endif
//NS_INTERNAL bigint *bi_crt(BI_CTX *ctx, bigint *bi, bigint *dP, bigint *dQ,
// bigint *p, bigint *q, bigint *qInv);
/*
* 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>
* @{
*/
#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.
*/
NS_INTERNAL BI_CTX *bi_initialize(void) {
/* mg_calloc() sets everything to zero */
BI_CTX *ctx = (BI_CTX *) mg_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.
*/
NS_INTERNAL 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);
mg_free(ctx);
}
/**
*@brief Clear the memory cache.
*/
NS_INTERNAL 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;
mg_free(p->comps);
mg_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.
*/
NS_INTERNAL 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.
*/
NS_INTERNAL 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.
*/
NS_INTERNAL 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.
*/
NS_INTERNAL 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.
*
*/
NS_INTERNAL 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.
*/
NS_INTERNAL bigint *bi_clone(BI_CTX *ctx, const bigint *bi) {
bigint *biR = alloc(ctx, bi->size);
check(bi);
memcpy(biR->comps, bi->comps, (size_t) 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.
*/
NS_INTERNAL 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.
*/
NS_INTERNAL 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 = (int) 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, (size_t) ((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.
*/
NS_INTERNAL 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, (size_t) ((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],
(size_t) (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,
(size_t) (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;
(void) ctx;
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, (size_t) (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.
*/
NS_INTERNAL 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, (size_t) (biR->size * COMP_BYTE_SIZE));
for (i = size - 1; i >= 0; i--) {
biR->comps[offset] += (comp) 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.
*/
NS_INTERNAL 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, (size_t) (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;
}
NS_INTERNAL 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.
*/
NS_INTERNAL 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_t) 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 = (comp) 0xff << (j * 8);
int num = (int) (x->comps[i] & mask) >> (j * 8);
data[k--] = (uint8_t) 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().
*/
NS_INTERNAL 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, (size_t) ((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 = (comp) (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.
*/
NS_INTERNAL 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.
*/
NS_INTERNAL 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.
*/
NS_INTERNAL 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) {
int max = MAX(bi->max_comps * 2, n);
void *p = mg_calloc(1, (size_t) max * COMP_BYTE_SIZE);
if (p != NULL && bi->size > 0) memcpy(p, bi->comps, (size_t) bi->max_comps * COMP_BYTE_SIZE);
mg_free(bi->comps);
bi->max_comps = (short) max;
bi->comps = (comp *) p;
}
if (n > bi->size) {
memset(&bi->comps[bi->size], 0, (size_t) (n - bi->size) * COMP_BYTE_SIZE);
}
bi->size = (short) 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 *) mg_calloc(1, sizeof(bigint));
biR->comps = (comp *) mg_calloc(1, (size_t) size * COMP_BYTE_SIZE);
biR->max_comps = (short) size; /* give some space to spare */
}
biR->size = (short) 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.
*/
NS_INTERNAL 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.
*/
NS_INTERNAL 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 **) mg_calloc(1, 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().
*/
NS_INTERNAL 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 **) mg_calloc(1, 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]);
}
mg_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
}
/**
* @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
*/
#if 1
NS_INTERNAL 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
// Proper lib usage:
// - BI_CTX *c = bi_initialize()
// - allocate bigints (e.g.: calling bi_import(), int_to_bi(), ...)
// - function calls, allocate bigints, etc.
// - bigint *n = bi_import(c, indata, insize)
// - bi_set_mod(c, n, x)
// - mod function calls
// - bigint *nn = bi_mod_pwr(c, m, e) <-- frees m, e
// - bi_free_mod(c, x) <-- frees n
// - bi_export(c, nn, outdata, outsize) <-- frees nn
// - function calls
// - free bigints calling bi_free()
// - bi_terminate(c) <-- frees c
int mg_rsa_mod_pow(const uint8_t *mod, size_t modsz, const uint8_t *exp, size_t expsz, const uint8_t *msg, size_t msgsz, uint8_t *out, size_t outsz) {
BI_CTX *bi_ctx = bi_initialize();
bigint *m1;
bigint *n = bi_import(bi_ctx, mod, (int) modsz);
bigint *e = bi_import(bi_ctx, exp, (int) expsz);
bigint *h = bi_import(bi_ctx, msg, (int) msgsz);
bi_set_mod(bi_ctx, n, 0);
m1 = bi_mod_power(bi_ctx, h, e);
bi_free_mod(bi_ctx, 0);
bi_export(bi_ctx, m1, out, (int) outsz);
bi_terminate(bi_ctx);
return 0;
}
int mg_rsa_crt_sign(const uint8_t *em, size_t em_len,
const uint8_t *dP, size_t dP_len,
const uint8_t *dQ, size_t dQ_len,
const uint8_t *p, size_t p_len,
const uint8_t *q, size_t q_len,
const uint8_t *qInv, size_t qInv_len,
uint8_t *signature, size_t sig_len) {
BI_CTX *ctx;
bigint *em_bi, *dP_bi, *dQ_bi, *p_bi, *q_bi, *qInv_bi, *result_bi;
int ret = -1;
ctx = bi_initialize();
if (ctx == NULL) {
return -1;
}
em_bi = bi_import(ctx, em, (int) em_len);
dP_bi = bi_import(ctx, dP, (int) dP_len);
dQ_bi = bi_import(ctx, dQ, (int) dQ_len);
p_bi = bi_import(ctx, p, (int) p_len);
q_bi = bi_import(ctx, q, (int) q_len);
qInv_bi = bi_import(ctx, qInv, (int) qInv_len);
if (em_bi == NULL || dP_bi == NULL || dQ_bi == NULL ||
p_bi == NULL || q_bi == NULL || qInv_bi == NULL) {
goto cleanup;
}
bi_set_mod(ctx, bi_clone(ctx, p_bi), BIGINT_P_OFFSET);
bi_set_mod(ctx, bi_clone(ctx, q_bi), BIGINT_Q_OFFSET);
result_bi = bi_crt(ctx, em_bi, dP_bi, dQ_bi, p_bi, q_bi, qInv_bi);
if (result_bi == NULL) {
goto cleanup;
}
bi_export(ctx, result_bi, signature, (int) sig_len);
ret = 0; // Success!
cleanup:
bi_free_mod(ctx, BIGINT_P_OFFSET); // cloned p_bi stored in mod context
bi_free_mod(ctx, BIGINT_Q_OFFSET); // cloned q_bi stored in mod context
bi_terminate(ctx);
return ret;
}
#endif /* MG_TLS == MG_TLS_BUILTIN */
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