1020 lines
33 KiB
C
1020 lines
33 KiB
C
/*
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* Core bignum functions
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*
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* Copyright The Mbed TLS Contributors
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* SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
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*/
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#include "common.h"
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#if defined(MBEDTLS_BIGNUM_C)
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#include <string.h>
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#include "mbedtls/error.h"
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#include "mbedtls/platform_util.h"
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#include "constant_time_internal.h"
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#include "mbedtls/platform.h"
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#include "bignum_core.h"
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#include "bn_mul.h"
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#include "constant_time_internal.h"
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size_t mbedtls_mpi_core_clz(mbedtls_mpi_uint a)
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{
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#if defined(__has_builtin)
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#if (MBEDTLS_MPI_UINT_MAX == UINT_MAX) && __has_builtin(__builtin_clz)
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#define core_clz __builtin_clz
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#elif (MBEDTLS_MPI_UINT_MAX == ULONG_MAX) && __has_builtin(__builtin_clzl)
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#define core_clz __builtin_clzl
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#elif (MBEDTLS_MPI_UINT_MAX == ULLONG_MAX) && __has_builtin(__builtin_clzll)
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#define core_clz __builtin_clzll
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#endif
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#endif
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#if defined(core_clz)
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return (size_t) core_clz(a);
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#else
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size_t j;
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mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);
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for (j = 0; j < biL; j++) {
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if (a & mask) {
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break;
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}
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mask >>= 1;
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}
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return j;
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#endif
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}
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size_t mbedtls_mpi_core_bitlen(const mbedtls_mpi_uint *A, size_t A_limbs)
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{
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int i;
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size_t j;
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for (i = ((int) A_limbs) - 1; i >= 0; i--) {
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if (A[i] != 0) {
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j = biL - mbedtls_mpi_core_clz(A[i]);
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return (i * biL) + j;
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}
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}
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return 0;
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}
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static mbedtls_mpi_uint mpi_bigendian_to_host(mbedtls_mpi_uint a)
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{
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if (MBEDTLS_IS_BIG_ENDIAN) {
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/* Nothing to do on bigendian systems. */
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return a;
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} else {
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#if defined(MBEDTLS_HAVE_INT32)
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return (mbedtls_mpi_uint) MBEDTLS_BSWAP32(a);
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#elif defined(MBEDTLS_HAVE_INT64)
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return (mbedtls_mpi_uint) MBEDTLS_BSWAP64(a);
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#endif
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}
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}
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void mbedtls_mpi_core_bigendian_to_host(mbedtls_mpi_uint *A,
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size_t A_limbs)
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{
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mbedtls_mpi_uint *cur_limb_left;
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mbedtls_mpi_uint *cur_limb_right;
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if (A_limbs == 0) {
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return;
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}
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/*
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* Traverse limbs and
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* - adapt byte-order in each limb
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* - swap the limbs themselves.
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* For that, simultaneously traverse the limbs from left to right
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* and from right to left, as long as the left index is not bigger
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* than the right index (it's not a problem if limbs is odd and the
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* indices coincide in the last iteration).
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*/
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for (cur_limb_left = A, cur_limb_right = A + (A_limbs - 1);
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cur_limb_left <= cur_limb_right;
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cur_limb_left++, cur_limb_right--) {
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mbedtls_mpi_uint tmp;
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/* Note that if cur_limb_left == cur_limb_right,
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* this code effectively swaps the bytes only once. */
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tmp = mpi_bigendian_to_host(*cur_limb_left);
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*cur_limb_left = mpi_bigendian_to_host(*cur_limb_right);
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*cur_limb_right = tmp;
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}
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}
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/* Whether min <= A, in constant time.
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* A_limbs must be at least 1. */
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mbedtls_ct_condition_t mbedtls_mpi_core_uint_le_mpi(mbedtls_mpi_uint min,
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const mbedtls_mpi_uint *A,
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size_t A_limbs)
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{
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/* min <= least significant limb? */
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mbedtls_ct_condition_t min_le_lsl = mbedtls_ct_uint_ge(A[0], min);
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/* limbs other than the least significant one are all zero? */
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mbedtls_ct_condition_t msll_mask = MBEDTLS_CT_FALSE;
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for (size_t i = 1; i < A_limbs; i++) {
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msll_mask = mbedtls_ct_bool_or(msll_mask, mbedtls_ct_bool(A[i]));
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}
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/* min <= A iff the lowest limb of A is >= min or the other limbs
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* are not all zero. */
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return mbedtls_ct_bool_or(msll_mask, min_le_lsl);
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}
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mbedtls_ct_condition_t mbedtls_mpi_core_lt_ct(const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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size_t limbs)
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{
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mbedtls_ct_condition_t ret = MBEDTLS_CT_FALSE, cond = MBEDTLS_CT_FALSE, done = MBEDTLS_CT_FALSE;
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for (size_t i = limbs; i > 0; i--) {
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/*
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* If B[i - 1] < A[i - 1] then A < B is false and the result must
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* remain 0.
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*
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* Again even if we can make a decision, we just mark the result and
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* the fact that we are done and continue looping.
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*/
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cond = mbedtls_ct_uint_lt(B[i - 1], A[i - 1]);
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done = mbedtls_ct_bool_or(done, cond);
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/*
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* If A[i - 1] < B[i - 1] then A < B is true.
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*
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* Again even if we can make a decision, we just mark the result and
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* the fact that we are done and continue looping.
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*/
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cond = mbedtls_ct_uint_lt(A[i - 1], B[i - 1]);
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ret = mbedtls_ct_bool_or(ret, mbedtls_ct_bool_and(cond, mbedtls_ct_bool_not(done)));
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done = mbedtls_ct_bool_or(done, cond);
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}
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/*
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* If all the limbs were equal, then the numbers are equal, A < B is false
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* and leaving the result 0 is correct.
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*/
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return ret;
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}
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void mbedtls_mpi_core_cond_assign(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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size_t limbs,
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mbedtls_ct_condition_t assign)
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{
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if (X == A) {
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return;
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}
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/* This function is very performance-sensitive for RSA. For this reason
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* we have the loop below, instead of calling mbedtls_ct_memcpy_if
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* (this is more optimal since here we don't have to handle the case where
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* we copy awkwardly sized data).
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*/
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for (size_t i = 0; i < limbs; i++) {
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X[i] = mbedtls_ct_mpi_uint_if(assign, A[i], X[i]);
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}
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}
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void mbedtls_mpi_core_cond_swap(mbedtls_mpi_uint *X,
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mbedtls_mpi_uint *Y,
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size_t limbs,
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mbedtls_ct_condition_t swap)
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{
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if (X == Y) {
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return;
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}
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for (size_t i = 0; i < limbs; i++) {
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mbedtls_mpi_uint tmp = X[i];
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X[i] = mbedtls_ct_mpi_uint_if(swap, Y[i], X[i]);
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Y[i] = mbedtls_ct_mpi_uint_if(swap, tmp, Y[i]);
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}
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}
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int mbedtls_mpi_core_read_le(mbedtls_mpi_uint *X,
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size_t X_limbs,
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const unsigned char *input,
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size_t input_length)
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{
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const size_t limbs = CHARS_TO_LIMBS(input_length);
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if (X_limbs < limbs) {
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return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
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}
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if (X != NULL) {
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memset(X, 0, X_limbs * ciL);
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for (size_t i = 0; i < input_length; i++) {
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size_t offset = ((i % ciL) << 3);
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X[i / ciL] |= ((mbedtls_mpi_uint) input[i]) << offset;
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}
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}
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return 0;
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}
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int mbedtls_mpi_core_read_be(mbedtls_mpi_uint *X,
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size_t X_limbs,
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const unsigned char *input,
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size_t input_length)
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{
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const size_t limbs = CHARS_TO_LIMBS(input_length);
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if (X_limbs < limbs) {
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return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
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}
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/* If X_limbs is 0, input_length must also be 0 (from previous test).
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* Nothing to do. */
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if (X_limbs == 0) {
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return 0;
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}
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memset(X, 0, X_limbs * ciL);
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/* memcpy() with (NULL, 0) is undefined behaviour */
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if (input_length != 0) {
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size_t overhead = (X_limbs * ciL) - input_length;
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unsigned char *Xp = (unsigned char *) X;
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memcpy(Xp + overhead, input, input_length);
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}
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mbedtls_mpi_core_bigendian_to_host(X, X_limbs);
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return 0;
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}
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int mbedtls_mpi_core_write_le(const mbedtls_mpi_uint *A,
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size_t A_limbs,
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unsigned char *output,
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size_t output_length)
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{
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size_t stored_bytes = A_limbs * ciL;
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size_t bytes_to_copy;
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if (stored_bytes < output_length) {
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bytes_to_copy = stored_bytes;
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} else {
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bytes_to_copy = output_length;
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/* The output buffer is smaller than the allocated size of A.
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* However A may fit if its leading bytes are zero. */
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for (size_t i = bytes_to_copy; i < stored_bytes; i++) {
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if (GET_BYTE(A, i) != 0) {
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return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
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}
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}
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}
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for (size_t i = 0; i < bytes_to_copy; i++) {
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output[i] = GET_BYTE(A, i);
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}
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if (stored_bytes < output_length) {
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/* Write trailing 0 bytes */
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memset(output + stored_bytes, 0, output_length - stored_bytes);
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}
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return 0;
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}
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int mbedtls_mpi_core_write_be(const mbedtls_mpi_uint *X,
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size_t X_limbs,
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unsigned char *output,
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size_t output_length)
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{
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size_t stored_bytes;
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size_t bytes_to_copy;
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unsigned char *p;
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stored_bytes = X_limbs * ciL;
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if (stored_bytes < output_length) {
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/* There is enough space in the output buffer. Write initial
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* null bytes and record the position at which to start
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* writing the significant bytes. In this case, the execution
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* trace of this function does not depend on the value of the
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* number. */
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bytes_to_copy = stored_bytes;
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p = output + output_length - stored_bytes;
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memset(output, 0, output_length - stored_bytes);
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} else {
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/* The output buffer is smaller than the allocated size of X.
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* However X may fit if its leading bytes are zero. */
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bytes_to_copy = output_length;
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p = output;
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for (size_t i = bytes_to_copy; i < stored_bytes; i++) {
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if (GET_BYTE(X, i) != 0) {
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return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
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}
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}
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}
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for (size_t i = 0; i < bytes_to_copy; i++) {
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p[bytes_to_copy - i - 1] = GET_BYTE(X, i);
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}
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return 0;
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}
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void mbedtls_mpi_core_shift_r(mbedtls_mpi_uint *X, size_t limbs,
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size_t count)
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{
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size_t i, v0, v1;
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mbedtls_mpi_uint r0 = 0, r1;
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v0 = count / biL;
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v1 = count & (biL - 1);
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if (v0 > limbs || (v0 == limbs && v1 > 0)) {
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memset(X, 0, limbs * ciL);
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return;
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}
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/*
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* shift by count / limb_size
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*/
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if (v0 > 0) {
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for (i = 0; i < limbs - v0; i++) {
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X[i] = X[i + v0];
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}
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for (; i < limbs; i++) {
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X[i] = 0;
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}
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}
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/*
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* shift by count % limb_size
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*/
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if (v1 > 0) {
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for (i = limbs; i > 0; i--) {
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r1 = X[i - 1] << (biL - v1);
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X[i - 1] >>= v1;
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X[i - 1] |= r0;
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r0 = r1;
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}
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}
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}
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void mbedtls_mpi_core_shift_l(mbedtls_mpi_uint *X, size_t limbs,
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size_t count)
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{
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size_t i, v0, v1;
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mbedtls_mpi_uint r0 = 0, r1;
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v0 = count / (biL);
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v1 = count & (biL - 1);
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/*
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* shift by count / limb_size
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*/
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if (v0 > 0) {
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for (i = limbs; i > v0; i--) {
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X[i - 1] = X[i - v0 - 1];
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}
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for (; i > 0; i--) {
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X[i - 1] = 0;
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}
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}
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/*
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* shift by count % limb_size
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*/
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if (v1 > 0) {
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for (i = v0; i < limbs; i++) {
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r1 = X[i] >> (biL - v1);
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X[i] <<= v1;
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X[i] |= r0;
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r0 = r1;
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}
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}
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}
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mbedtls_mpi_uint mbedtls_mpi_core_add(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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size_t limbs)
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{
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mbedtls_mpi_uint c = 0;
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for (size_t i = 0; i < limbs; i++) {
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mbedtls_mpi_uint t = c + A[i];
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c = (t < A[i]);
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t += B[i];
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c += (t < B[i]);
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X[i] = t;
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}
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return c;
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}
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mbedtls_mpi_uint mbedtls_mpi_core_add_if(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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size_t limbs,
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unsigned cond)
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{
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mbedtls_mpi_uint c = 0;
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mbedtls_ct_condition_t do_add = mbedtls_ct_bool(cond);
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for (size_t i = 0; i < limbs; i++) {
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mbedtls_mpi_uint add = mbedtls_ct_mpi_uint_if_else_0(do_add, A[i]);
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mbedtls_mpi_uint t = c + X[i];
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c = (t < X[i]);
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t += add;
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c += (t < add);
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X[i] = t;
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}
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return c;
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}
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mbedtls_mpi_uint mbedtls_mpi_core_sub(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *B,
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size_t limbs)
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{
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mbedtls_mpi_uint c = 0;
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for (size_t i = 0; i < limbs; i++) {
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mbedtls_mpi_uint z = (A[i] < c);
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mbedtls_mpi_uint t = A[i] - c;
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c = (t < B[i]) + z;
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X[i] = t - B[i];
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}
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return c;
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}
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mbedtls_mpi_uint mbedtls_mpi_core_mla(mbedtls_mpi_uint *d, size_t d_len,
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const mbedtls_mpi_uint *s, size_t s_len,
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mbedtls_mpi_uint b)
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{
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mbedtls_mpi_uint c = 0; /* carry */
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/*
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* It is a documented precondition of this function that d_len >= s_len.
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* If that's not the case, we swap these round: this turns what would be
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* a buffer overflow into an incorrect result.
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*/
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if (d_len < s_len) {
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s_len = d_len;
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}
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size_t excess_len = d_len - s_len;
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size_t steps_x8 = s_len / 8;
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size_t steps_x1 = s_len & 7;
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while (steps_x8--) {
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MULADDC_X8_INIT
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MULADDC_X8_CORE
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MULADDC_X8_STOP
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}
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while (steps_x1--) {
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MULADDC_X1_INIT
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MULADDC_X1_CORE
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MULADDC_X1_STOP
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}
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while (excess_len--) {
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*d += c;
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c = (*d < c);
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d++;
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}
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return c;
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}
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void mbedtls_mpi_core_mul(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A, size_t A_limbs,
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const mbedtls_mpi_uint *B, size_t B_limbs)
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{
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memset(X, 0, (A_limbs + B_limbs) * ciL);
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for (size_t i = 0; i < B_limbs; i++) {
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(void) mbedtls_mpi_core_mla(X + i, A_limbs + 1, A, A_limbs, B[i]);
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}
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|
}
|
|
|
|
/*
|
|
* Fast Montgomery initialization (thanks to Tom St Denis).
|
|
*/
|
|
mbedtls_mpi_uint mbedtls_mpi_core_montmul_init(const mbedtls_mpi_uint *N)
|
|
{
|
|
mbedtls_mpi_uint x = N[0];
|
|
|
|
x += ((N[0] + 2) & 4) << 1;
|
|
|
|
for (unsigned int i = biL; i >= 8; i /= 2) {
|
|
x *= (2 - (N[0] * x));
|
|
}
|
|
|
|
return ~x + 1;
|
|
}
|
|
|
|
void mbedtls_mpi_core_montmul(mbedtls_mpi_uint *X,
|
|
const mbedtls_mpi_uint *A,
|
|
const mbedtls_mpi_uint *B,
|
|
size_t B_limbs,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t AN_limbs,
|
|
mbedtls_mpi_uint mm,
|
|
mbedtls_mpi_uint *T)
|
|
{
|
|
memset(T, 0, (2 * AN_limbs + 1) * ciL);
|
|
|
|
for (size_t i = 0; i < AN_limbs; i++) {
|
|
/* T = (T + u0*B + u1*N) / 2^biL */
|
|
mbedtls_mpi_uint u0 = A[i];
|
|
mbedtls_mpi_uint u1 = (T[0] + u0 * B[0]) * mm;
|
|
|
|
(void) mbedtls_mpi_core_mla(T, AN_limbs + 2, B, B_limbs, u0);
|
|
(void) mbedtls_mpi_core_mla(T, AN_limbs + 2, N, AN_limbs, u1);
|
|
|
|
T++;
|
|
}
|
|
|
|
/*
|
|
* The result we want is (T >= N) ? T - N : T.
|
|
*
|
|
* For better constant-time properties in this function, we always do the
|
|
* subtraction, with the result in X.
|
|
*
|
|
* We also look to see if there was any carry in the final additions in the
|
|
* loop above.
|
|
*/
|
|
|
|
mbedtls_mpi_uint carry = T[AN_limbs];
|
|
mbedtls_mpi_uint borrow = mbedtls_mpi_core_sub(X, T, N, AN_limbs);
|
|
|
|
/*
|
|
* Using R as the Montgomery radix (auxiliary modulus) i.e. 2^(biL*AN_limbs):
|
|
*
|
|
* T can be in one of 3 ranges:
|
|
*
|
|
* 1) T < N : (carry, borrow) = (0, 1): we want T
|
|
* 2) N <= T < R : (carry, borrow) = (0, 0): we want X
|
|
* 3) T >= R : (carry, borrow) = (1, 1): we want X
|
|
*
|
|
* and (carry, borrow) = (1, 0) can't happen.
|
|
*
|
|
* So the correct return value is already in X if (carry ^ borrow) = 0,
|
|
* but is in (the lower AN_limbs limbs of) T if (carry ^ borrow) = 1.
|
|
*/
|
|
mbedtls_ct_memcpy_if(mbedtls_ct_bool(carry ^ borrow),
|
|
(unsigned char *) X,
|
|
(unsigned char *) T,
|
|
NULL,
|
|
AN_limbs * sizeof(mbedtls_mpi_uint));
|
|
}
|
|
|
|
int mbedtls_mpi_core_get_mont_r2_unsafe(mbedtls_mpi *X,
|
|
const mbedtls_mpi *N)
|
|
{
|
|
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
|
|
|
|
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 1));
|
|
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(X, N->n * 2 * biL));
|
|
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(X, X, N));
|
|
MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(X, N->n));
|
|
|
|
cleanup:
|
|
return ret;
|
|
}
|
|
|
|
MBEDTLS_STATIC_TESTABLE
|
|
void mbedtls_mpi_core_ct_uint_table_lookup(mbedtls_mpi_uint *dest,
|
|
const mbedtls_mpi_uint *table,
|
|
size_t limbs,
|
|
size_t count,
|
|
size_t index)
|
|
{
|
|
for (size_t i = 0; i < count; i++, table += limbs) {
|
|
mbedtls_ct_condition_t assign = mbedtls_ct_uint_eq(i, index);
|
|
mbedtls_mpi_core_cond_assign(dest, table, limbs, assign);
|
|
}
|
|
}
|
|
|
|
/* Fill X with n_bytes random bytes.
|
|
* X must already have room for those bytes.
|
|
* The ordering of the bytes returned from the RNG is suitable for
|
|
* deterministic ECDSA (see RFC 6979 §3.3 and the specification of
|
|
* mbedtls_mpi_core_random()).
|
|
*/
|
|
int mbedtls_mpi_core_fill_random(
|
|
mbedtls_mpi_uint *X, size_t X_limbs,
|
|
size_t n_bytes,
|
|
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
|
|
{
|
|
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
|
|
const size_t limbs = CHARS_TO_LIMBS(n_bytes);
|
|
const size_t overhead = (limbs * ciL) - n_bytes;
|
|
|
|
if (X_limbs < limbs) {
|
|
return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
|
|
}
|
|
|
|
memset(X, 0, overhead);
|
|
memset((unsigned char *) X + limbs * ciL, 0, (X_limbs - limbs) * ciL);
|
|
MBEDTLS_MPI_CHK(f_rng(p_rng, (unsigned char *) X + overhead, n_bytes));
|
|
mbedtls_mpi_core_bigendian_to_host(X, limbs);
|
|
|
|
cleanup:
|
|
return ret;
|
|
}
|
|
|
|
int mbedtls_mpi_core_random(mbedtls_mpi_uint *X,
|
|
mbedtls_mpi_uint min,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t limbs,
|
|
int (*f_rng)(void *, unsigned char *, size_t),
|
|
void *p_rng)
|
|
{
|
|
mbedtls_ct_condition_t ge_lower = MBEDTLS_CT_TRUE, lt_upper = MBEDTLS_CT_FALSE;
|
|
size_t n_bits = mbedtls_mpi_core_bitlen(N, limbs);
|
|
size_t n_bytes = (n_bits + 7) / 8;
|
|
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
|
|
|
|
/*
|
|
* When min == 0, each try has at worst a probability 1/2 of failing
|
|
* (the msb has a probability 1/2 of being 0, and then the result will
|
|
* be < N), so after 30 tries failure probability is a most 2**(-30).
|
|
*
|
|
* When N is just below a power of 2, as is the case when generating
|
|
* a random scalar on most elliptic curves, 1 try is enough with
|
|
* overwhelming probability. When N is just above a power of 2,
|
|
* as when generating a random scalar on secp224k1, each try has
|
|
* a probability of failing that is almost 1/2.
|
|
*
|
|
* The probabilities are almost the same if min is nonzero but negligible
|
|
* compared to N. This is always the case when N is crypto-sized, but
|
|
* it's convenient to support small N for testing purposes. When N
|
|
* is small, use a higher repeat count, otherwise the probability of
|
|
* failure is macroscopic.
|
|
*/
|
|
int count = (n_bytes > 4 ? 30 : 250);
|
|
|
|
/*
|
|
* Match the procedure given in RFC 6979 §3.3 (deterministic ECDSA)
|
|
* when f_rng is a suitably parametrized instance of HMAC_DRBG:
|
|
* - use the same byte ordering;
|
|
* - keep the leftmost n_bits bits of the generated octet string;
|
|
* - try until result is in the desired range.
|
|
* This also avoids any bias, which is especially important for ECDSA.
|
|
*/
|
|
do {
|
|
MBEDTLS_MPI_CHK(mbedtls_mpi_core_fill_random(X, limbs,
|
|
n_bytes,
|
|
f_rng, p_rng));
|
|
mbedtls_mpi_core_shift_r(X, limbs, 8 * n_bytes - n_bits);
|
|
|
|
if (--count == 0) {
|
|
ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
|
|
goto cleanup;
|
|
}
|
|
|
|
ge_lower = mbedtls_mpi_core_uint_le_mpi(min, X, limbs);
|
|
lt_upper = mbedtls_mpi_core_lt_ct(X, N, limbs);
|
|
} while (mbedtls_ct_bool_and(ge_lower, lt_upper) == MBEDTLS_CT_FALSE);
|
|
|
|
cleanup:
|
|
return ret;
|
|
}
|
|
|
|
static size_t exp_mod_get_window_size(size_t Ebits)
|
|
{
|
|
#if MBEDTLS_MPI_WINDOW_SIZE >= 6
|
|
return (Ebits > 671) ? 6 : (Ebits > 239) ? 5 : (Ebits > 79) ? 4 : 1;
|
|
#elif MBEDTLS_MPI_WINDOW_SIZE == 5
|
|
return (Ebits > 239) ? 5 : (Ebits > 79) ? 4 : 1;
|
|
#elif MBEDTLS_MPI_WINDOW_SIZE > 1
|
|
return (Ebits > 79) ? MBEDTLS_MPI_WINDOW_SIZE : 1;
|
|
#else
|
|
(void) Ebits;
|
|
return 1;
|
|
#endif
|
|
}
|
|
|
|
size_t mbedtls_mpi_core_exp_mod_working_limbs(size_t AN_limbs, size_t E_limbs)
|
|
{
|
|
const size_t wsize = exp_mod_get_window_size(E_limbs * biL);
|
|
const size_t welem = ((size_t) 1) << wsize;
|
|
|
|
/* How big does each part of the working memory pool need to be? */
|
|
const size_t table_limbs = welem * AN_limbs;
|
|
const size_t select_limbs = AN_limbs;
|
|
const size_t temp_limbs = 2 * AN_limbs + 1;
|
|
|
|
return table_limbs + select_limbs + temp_limbs;
|
|
}
|
|
|
|
static void exp_mod_precompute_window(const mbedtls_mpi_uint *A,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t AN_limbs,
|
|
mbedtls_mpi_uint mm,
|
|
const mbedtls_mpi_uint *RR,
|
|
size_t welem,
|
|
mbedtls_mpi_uint *Wtable,
|
|
mbedtls_mpi_uint *temp)
|
|
{
|
|
/* W[0] = 1 (in Montgomery presentation) */
|
|
memset(Wtable, 0, AN_limbs * ciL);
|
|
Wtable[0] = 1;
|
|
mbedtls_mpi_core_montmul(Wtable, Wtable, RR, AN_limbs, N, AN_limbs, mm, temp);
|
|
|
|
/* W[1] = A (already in Montgomery presentation) */
|
|
mbedtls_mpi_uint *W1 = Wtable + AN_limbs;
|
|
memcpy(W1, A, AN_limbs * ciL);
|
|
|
|
/* W[i+1] = W[i] * W[1], i >= 2 */
|
|
mbedtls_mpi_uint *Wprev = W1;
|
|
for (size_t i = 2; i < welem; i++) {
|
|
mbedtls_mpi_uint *Wcur = Wprev + AN_limbs;
|
|
mbedtls_mpi_core_montmul(Wcur, Wprev, W1, AN_limbs, N, AN_limbs, mm, temp);
|
|
Wprev = Wcur;
|
|
}
|
|
}
|
|
|
|
#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
|
|
// Set to a default that is neither MBEDTLS_MPI_IS_PUBLIC nor MBEDTLS_MPI_IS_SECRET
|
|
int mbedtls_mpi_optionally_safe_codepath = MBEDTLS_MPI_IS_PUBLIC + MBEDTLS_MPI_IS_SECRET + 1;
|
|
#endif
|
|
|
|
/*
|
|
* This function calculates the indices of the exponent where the exponentiation algorithm should
|
|
* start processing.
|
|
*
|
|
* Warning! If the parameter E_public has MBEDTLS_MPI_IS_PUBLIC as its value,
|
|
* this function is not constant time with respect to the exponent (parameter E).
|
|
*/
|
|
static inline void exp_mod_calc_first_bit_optionally_safe(const mbedtls_mpi_uint *E,
|
|
size_t E_limbs,
|
|
int E_public,
|
|
size_t *E_limb_index,
|
|
size_t *E_bit_index)
|
|
{
|
|
if (E_public == MBEDTLS_MPI_IS_PUBLIC) {
|
|
/*
|
|
* Skip leading zero bits.
|
|
*/
|
|
size_t E_bits = mbedtls_mpi_core_bitlen(E, E_limbs);
|
|
if (E_bits == 0) {
|
|
/*
|
|
* If E is 0 mbedtls_mpi_core_bitlen() returns 0. Even if that is the case, we will want
|
|
* to represent it as a single 0 bit and as such the bitlength will be 1.
|
|
*/
|
|
E_bits = 1;
|
|
}
|
|
|
|
*E_limb_index = E_bits / biL;
|
|
*E_bit_index = E_bits % biL;
|
|
|
|
#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
|
|
mbedtls_mpi_optionally_safe_codepath = MBEDTLS_MPI_IS_PUBLIC;
|
|
#endif
|
|
} else {
|
|
/*
|
|
* Here we need to be constant time with respect to E and can't do anything better than
|
|
* start at the first allocated bit.
|
|
*/
|
|
*E_limb_index = E_limbs;
|
|
*E_bit_index = 0;
|
|
#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
|
|
// Only mark the codepath safe if there wasn't an unsafe codepath before
|
|
if (mbedtls_mpi_optionally_safe_codepath != MBEDTLS_MPI_IS_PUBLIC) {
|
|
mbedtls_mpi_optionally_safe_codepath = MBEDTLS_MPI_IS_SECRET;
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Warning! If the parameter window_public has MBEDTLS_MPI_IS_PUBLIC as its value, this function is
|
|
* not constant time with respect to the window parameter and consequently the exponent of the
|
|
* exponentiation (parameter E of mbedtls_mpi_core_exp_mod_optionally_safe).
|
|
*/
|
|
static inline void exp_mod_table_lookup_optionally_safe(mbedtls_mpi_uint *Wselect,
|
|
mbedtls_mpi_uint *Wtable,
|
|
size_t AN_limbs, size_t welem,
|
|
mbedtls_mpi_uint window,
|
|
int window_public)
|
|
{
|
|
if (window_public == MBEDTLS_MPI_IS_PUBLIC) {
|
|
memcpy(Wselect, Wtable + window * AN_limbs, AN_limbs * ciL);
|
|
#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
|
|
mbedtls_mpi_optionally_safe_codepath = MBEDTLS_MPI_IS_PUBLIC;
|
|
#endif
|
|
} else {
|
|
/* Select Wtable[window] without leaking window through
|
|
* memory access patterns. */
|
|
mbedtls_mpi_core_ct_uint_table_lookup(Wselect, Wtable,
|
|
AN_limbs, welem, window);
|
|
#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
|
|
// Only mark the codepath safe if there wasn't an unsafe codepath before
|
|
if (mbedtls_mpi_optionally_safe_codepath != MBEDTLS_MPI_IS_PUBLIC) {
|
|
mbedtls_mpi_optionally_safe_codepath = MBEDTLS_MPI_IS_SECRET;
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
|
|
/* Exponentiation: X := A^E mod N.
|
|
*
|
|
* Warning! If the parameter E_public has MBEDTLS_MPI_IS_PUBLIC as its value,
|
|
* this function is not constant time with respect to the exponent (parameter E).
|
|
*
|
|
* A must already be in Montgomery form.
|
|
*
|
|
* As in other bignum functions, assume that AN_limbs and E_limbs are nonzero.
|
|
*
|
|
* RR must contain 2^{2*biL} mod N.
|
|
*
|
|
* The algorithm is a variant of Left-to-right k-ary exponentiation: HAC 14.82
|
|
* (The difference is that the body in our loop processes a single bit instead
|
|
* of a full window.)
|
|
*/
|
|
static void mbedtls_mpi_core_exp_mod_optionally_safe(mbedtls_mpi_uint *X,
|
|
const mbedtls_mpi_uint *A,
|
|
const mbedtls_mpi_uint *N,
|
|
size_t AN_limbs,
|
|
const mbedtls_mpi_uint *E,
|
|
size_t E_limbs,
|
|
int E_public,
|
|
const mbedtls_mpi_uint *RR,
|
|
mbedtls_mpi_uint *T)
|
|
{
|
|
/* We'll process the bits of E from most significant
|
|
* (limb_index=E_limbs-1, E_bit_index=biL-1) to least significant
|
|
* (limb_index=0, E_bit_index=0). */
|
|
size_t E_limb_index;
|
|
size_t E_bit_index;
|
|
exp_mod_calc_first_bit_optionally_safe(E, E_limbs, E_public,
|
|
&E_limb_index, &E_bit_index);
|
|
|
|
const size_t wsize = exp_mod_get_window_size(E_limb_index * biL);
|
|
const size_t welem = ((size_t) 1) << wsize;
|
|
|
|
/* This is how we will use the temporary storage T, which must have space
|
|
* for table_limbs, select_limbs and (2 * AN_limbs + 1) for montmul. */
|
|
const size_t table_limbs = welem * AN_limbs;
|
|
const size_t select_limbs = AN_limbs;
|
|
|
|
/* Pointers to specific parts of the temporary working memory pool */
|
|
mbedtls_mpi_uint *const Wtable = T;
|
|
mbedtls_mpi_uint *const Wselect = Wtable + table_limbs;
|
|
mbedtls_mpi_uint *const temp = Wselect + select_limbs;
|
|
|
|
/*
|
|
* Window precomputation
|
|
*/
|
|
|
|
const mbedtls_mpi_uint mm = mbedtls_mpi_core_montmul_init(N);
|
|
|
|
/* Set Wtable[i] = A^i (in Montgomery representation) */
|
|
exp_mod_precompute_window(A, N, AN_limbs,
|
|
mm, RR,
|
|
welem, Wtable, temp);
|
|
|
|
/*
|
|
* Fixed window exponentiation
|
|
*/
|
|
|
|
/* X = 1 (in Montgomery presentation) initially */
|
|
memcpy(X, Wtable, AN_limbs * ciL);
|
|
|
|
/* At any given time, window contains window_bits bits from E.
|
|
* window_bits can go up to wsize. */
|
|
size_t window_bits = 0;
|
|
mbedtls_mpi_uint window = 0;
|
|
|
|
do {
|
|
/* Square */
|
|
mbedtls_mpi_core_montmul(X, X, X, AN_limbs, N, AN_limbs, mm, temp);
|
|
|
|
/* Move to the next bit of the exponent */
|
|
if (E_bit_index == 0) {
|
|
--E_limb_index;
|
|
E_bit_index = biL - 1;
|
|
} else {
|
|
--E_bit_index;
|
|
}
|
|
/* Insert next exponent bit into window */
|
|
++window_bits;
|
|
window <<= 1;
|
|
window |= (E[E_limb_index] >> E_bit_index) & 1;
|
|
|
|
/* Clear window if it's full. Also clear the window at the end,
|
|
* when we've finished processing the exponent. */
|
|
if (window_bits == wsize ||
|
|
(E_bit_index == 0 && E_limb_index == 0)) {
|
|
|
|
exp_mod_table_lookup_optionally_safe(Wselect, Wtable, AN_limbs, welem,
|
|
window, E_public);
|
|
/* Multiply X by the selected element. */
|
|
mbedtls_mpi_core_montmul(X, X, Wselect, AN_limbs, N, AN_limbs, mm,
|
|
temp);
|
|
window = 0;
|
|
window_bits = 0;
|
|
}
|
|
} while (!(E_bit_index == 0 && E_limb_index == 0));
|
|
}
|
|
|
|
void mbedtls_mpi_core_exp_mod(mbedtls_mpi_uint *X,
|
|
const mbedtls_mpi_uint *A,
|
|
const mbedtls_mpi_uint *N, size_t AN_limbs,
|
|
const mbedtls_mpi_uint *E, size_t E_limbs,
|
|
const mbedtls_mpi_uint *RR,
|
|
mbedtls_mpi_uint *T)
|
|
{
|
|
mbedtls_mpi_core_exp_mod_optionally_safe(X,
|
|
A,
|
|
N,
|
|
AN_limbs,
|
|
E,
|
|
E_limbs,
|
|
MBEDTLS_MPI_IS_SECRET,
|
|
RR,
|
|
T);
|
|
}
|
|
|
|
void mbedtls_mpi_core_exp_mod_unsafe(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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const mbedtls_mpi_uint *N, size_t AN_limbs,
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const mbedtls_mpi_uint *E, size_t E_limbs,
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const mbedtls_mpi_uint *RR,
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mbedtls_mpi_uint *T)
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{
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mbedtls_mpi_core_exp_mod_optionally_safe(X,
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A,
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N,
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AN_limbs,
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E,
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E_limbs,
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MBEDTLS_MPI_IS_PUBLIC,
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RR,
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T);
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}
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mbedtls_mpi_uint mbedtls_mpi_core_sub_int(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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mbedtls_mpi_uint c, /* doubles as carry */
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size_t limbs)
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{
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for (size_t i = 0; i < limbs; i++) {
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mbedtls_mpi_uint s = A[i];
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mbedtls_mpi_uint t = s - c;
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c = (t > s);
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X[i] = t;
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}
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|
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return c;
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}
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mbedtls_ct_condition_t mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
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size_t limbs)
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|
{
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volatile const mbedtls_mpi_uint *force_read_A = A;
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mbedtls_mpi_uint bits = 0;
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|
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for (size_t i = 0; i < limbs; i++) {
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bits |= force_read_A[i];
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}
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|
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return mbedtls_ct_bool(bits);
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}
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void mbedtls_mpi_core_to_mont_rep(mbedtls_mpi_uint *X,
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const mbedtls_mpi_uint *A,
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|
const mbedtls_mpi_uint *N,
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|
size_t AN_limbs,
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|
mbedtls_mpi_uint mm,
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|
const mbedtls_mpi_uint *rr,
|
|
mbedtls_mpi_uint *T)
|
|
{
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mbedtls_mpi_core_montmul(X, A, rr, AN_limbs, N, AN_limbs, mm, T);
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}
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|
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void mbedtls_mpi_core_from_mont_rep(mbedtls_mpi_uint *X,
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|
const mbedtls_mpi_uint *A,
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|
const mbedtls_mpi_uint *N,
|
|
size_t AN_limbs,
|
|
mbedtls_mpi_uint mm,
|
|
mbedtls_mpi_uint *T)
|
|
{
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const mbedtls_mpi_uint Rinv = 1; /* 1/R in Mont. rep => 1 */
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|
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mbedtls_mpi_core_montmul(X, A, &Rinv, 1, N, AN_limbs, mm, T);
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}
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|
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#endif /* MBEDTLS_BIGNUM_C */
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