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godot/thirdparty/mbedtls/library/bignum_core.c

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/*
* Core bignum functions
*
* Copyright The Mbed TLS Contributors
* SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
*/
#include "common.h"
#if defined(MBEDTLS_BIGNUM_C)
#include <string.h>
#include "mbedtls/error.h"
#include "mbedtls/platform_util.h"
#include "constant_time_internal.h"
#include "mbedtls/platform.h"
#include "bignum_core.h"
#include "bn_mul.h"
#include "constant_time_internal.h"
size_t mbedtls_mpi_core_clz(mbedtls_mpi_uint a)
{
#if defined(__has_builtin)
#if (MBEDTLS_MPI_UINT_MAX == UINT_MAX) && __has_builtin(__builtin_clz)
#define core_clz __builtin_clz
#elif (MBEDTLS_MPI_UINT_MAX == ULONG_MAX) && __has_builtin(__builtin_clzl)
#define core_clz __builtin_clzl
#elif (MBEDTLS_MPI_UINT_MAX == ULLONG_MAX) && __has_builtin(__builtin_clzll)
#define core_clz __builtin_clzll
#endif
#endif
#if defined(core_clz)
return (size_t) core_clz(a);
#else
size_t j;
mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);
for (j = 0; j < biL; j++) {
if (a & mask) {
break;
}
mask >>= 1;
}
return j;
#endif
}
size_t mbedtls_mpi_core_bitlen(const mbedtls_mpi_uint *A, size_t A_limbs)
{
int i;
size_t j;
for (i = ((int) A_limbs) - 1; i >= 0; i--) {
if (A[i] != 0) {
j = biL - mbedtls_mpi_core_clz(A[i]);
return (i * biL) + j;
}
}
return 0;
}
static mbedtls_mpi_uint mpi_bigendian_to_host(mbedtls_mpi_uint a)
{
if (MBEDTLS_IS_BIG_ENDIAN) {
/* Nothing to do on bigendian systems. */
return a;
} else {
#if defined(MBEDTLS_HAVE_INT32)
return (mbedtls_mpi_uint) MBEDTLS_BSWAP32(a);
#elif defined(MBEDTLS_HAVE_INT64)
return (mbedtls_mpi_uint) MBEDTLS_BSWAP64(a);
#endif
}
}
void mbedtls_mpi_core_bigendian_to_host(mbedtls_mpi_uint *A,
size_t A_limbs)
{
mbedtls_mpi_uint *cur_limb_left;
mbedtls_mpi_uint *cur_limb_right;
if (A_limbs == 0) {
return;
}
/*
* Traverse limbs and
* - adapt byte-order in each limb
* - swap the limbs themselves.
* For that, simultaneously traverse the limbs from left to right
* and from right to left, as long as the left index is not bigger
* than the right index (it's not a problem if limbs is odd and the
* indices coincide in the last iteration).
*/
for (cur_limb_left = A, cur_limb_right = A + (A_limbs - 1);
cur_limb_left <= cur_limb_right;
cur_limb_left++, cur_limb_right--) {
mbedtls_mpi_uint tmp;
/* Note that if cur_limb_left == cur_limb_right,
* this code effectively swaps the bytes only once. */
tmp = mpi_bigendian_to_host(*cur_limb_left);
*cur_limb_left = mpi_bigendian_to_host(*cur_limb_right);
*cur_limb_right = tmp;
}
}
/* Whether min <= A, in constant time.
* A_limbs must be at least 1. */
mbedtls_ct_condition_t mbedtls_mpi_core_uint_le_mpi(mbedtls_mpi_uint min,
const mbedtls_mpi_uint *A,
size_t A_limbs)
{
/* min <= least significant limb? */
mbedtls_ct_condition_t min_le_lsl = mbedtls_ct_uint_ge(A[0], min);
/* limbs other than the least significant one are all zero? */
mbedtls_ct_condition_t msll_mask = MBEDTLS_CT_FALSE;
for (size_t i = 1; i < A_limbs; i++) {
msll_mask = mbedtls_ct_bool_or(msll_mask, mbedtls_ct_bool(A[i]));
}
/* min <= A iff the lowest limb of A is >= min or the other limbs
* are not all zero. */
return mbedtls_ct_bool_or(msll_mask, min_le_lsl);
}
mbedtls_ct_condition_t mbedtls_mpi_core_lt_ct(const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *B,
size_t limbs)
{
mbedtls_ct_condition_t ret = MBEDTLS_CT_FALSE, cond = MBEDTLS_CT_FALSE, done = MBEDTLS_CT_FALSE;
for (size_t i = limbs; i > 0; i--) {
/*
* If B[i - 1] < A[i - 1] then A < B is false and the result must
* remain 0.
*
* Again even if we can make a decision, we just mark the result and
* the fact that we are done and continue looping.
*/
cond = mbedtls_ct_uint_lt(B[i - 1], A[i - 1]);
done = mbedtls_ct_bool_or(done, cond);
/*
* If A[i - 1] < B[i - 1] then A < B is true.
*
* Again even if we can make a decision, we just mark the result and
* the fact that we are done and continue looping.
*/
cond = mbedtls_ct_uint_lt(A[i - 1], B[i - 1]);
ret = mbedtls_ct_bool_or(ret, mbedtls_ct_bool_and(cond, mbedtls_ct_bool_not(done)));
done = mbedtls_ct_bool_or(done, cond);
}
/*
* If all the limbs were equal, then the numbers are equal, A < B is false
* and leaving the result 0 is correct.
*/
return ret;
}
void mbedtls_mpi_core_cond_assign(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
size_t limbs,
mbedtls_ct_condition_t assign)
{
if (X == A) {
return;
}
/* This function is very performance-sensitive for RSA. For this reason
* we have the loop below, instead of calling mbedtls_ct_memcpy_if
* (this is more optimal since here we don't have to handle the case where
* we copy awkwardly sized data).
*/
for (size_t i = 0; i < limbs; i++) {
X[i] = mbedtls_ct_mpi_uint_if(assign, A[i], X[i]);
}
}
void mbedtls_mpi_core_cond_swap(mbedtls_mpi_uint *X,
mbedtls_mpi_uint *Y,
size_t limbs,
mbedtls_ct_condition_t swap)
{
if (X == Y) {
return;
}
for (size_t i = 0; i < limbs; i++) {
mbedtls_mpi_uint tmp = X[i];
X[i] = mbedtls_ct_mpi_uint_if(swap, Y[i], X[i]);
Y[i] = mbedtls_ct_mpi_uint_if(swap, tmp, Y[i]);
}
}
int mbedtls_mpi_core_read_le(mbedtls_mpi_uint *X,
size_t X_limbs,
const unsigned char *input,
size_t input_length)
{
const size_t limbs = CHARS_TO_LIMBS(input_length);
if (X_limbs < limbs) {
return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
}
if (X != NULL) {
memset(X, 0, X_limbs * ciL);
for (size_t i = 0; i < input_length; i++) {
size_t offset = ((i % ciL) << 3);
X[i / ciL] |= ((mbedtls_mpi_uint) input[i]) << offset;
}
}
return 0;
}
int mbedtls_mpi_core_read_be(mbedtls_mpi_uint *X,
size_t X_limbs,
const unsigned char *input,
size_t input_length)
{
const size_t limbs = CHARS_TO_LIMBS(input_length);
if (X_limbs < limbs) {
return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
}
/* If X_limbs is 0, input_length must also be 0 (from previous test).
* Nothing to do. */
if (X_limbs == 0) {
return 0;
}
memset(X, 0, X_limbs * ciL);
/* memcpy() with (NULL, 0) is undefined behaviour */
if (input_length != 0) {
size_t overhead = (X_limbs * ciL) - input_length;
unsigned char *Xp = (unsigned char *) X;
memcpy(Xp + overhead, input, input_length);
}
mbedtls_mpi_core_bigendian_to_host(X, X_limbs);
return 0;
}
int mbedtls_mpi_core_write_le(const mbedtls_mpi_uint *A,
size_t A_limbs,
unsigned char *output,
size_t output_length)
{
size_t stored_bytes = A_limbs * ciL;
size_t bytes_to_copy;
if (stored_bytes < output_length) {
bytes_to_copy = stored_bytes;
} else {
bytes_to_copy = output_length;
/* The output buffer is smaller than the allocated size of A.
* However A may fit if its leading bytes are zero. */
for (size_t i = bytes_to_copy; i < stored_bytes; i++) {
if (GET_BYTE(A, i) != 0) {
return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
}
}
}
for (size_t i = 0; i < bytes_to_copy; i++) {
output[i] = GET_BYTE(A, i);
}
if (stored_bytes < output_length) {
/* Write trailing 0 bytes */
memset(output + stored_bytes, 0, output_length - stored_bytes);
}
return 0;
}
int mbedtls_mpi_core_write_be(const mbedtls_mpi_uint *X,
size_t X_limbs,
unsigned char *output,
size_t output_length)
{
size_t stored_bytes;
size_t bytes_to_copy;
unsigned char *p;
stored_bytes = X_limbs * ciL;
if (stored_bytes < output_length) {
/* There is enough space in the output buffer. Write initial
* null bytes and record the position at which to start
* writing the significant bytes. In this case, the execution
* trace of this function does not depend on the value of the
* number. */
bytes_to_copy = stored_bytes;
p = output + output_length - stored_bytes;
memset(output, 0, output_length - stored_bytes);
} else {
/* The output buffer is smaller than the allocated size of X.
* However X may fit if its leading bytes are zero. */
bytes_to_copy = output_length;
p = output;
for (size_t i = bytes_to_copy; i < stored_bytes; i++) {
if (GET_BYTE(X, i) != 0) {
return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
}
}
}
for (size_t i = 0; i < bytes_to_copy; i++) {
p[bytes_to_copy - i - 1] = GET_BYTE(X, i);
}
return 0;
}
void mbedtls_mpi_core_shift_r(mbedtls_mpi_uint *X, size_t limbs,
size_t count)
{
size_t i, v0, v1;
mbedtls_mpi_uint r0 = 0, r1;
v0 = count / biL;
v1 = count & (biL - 1);
if (v0 > limbs || (v0 == limbs && v1 > 0)) {
memset(X, 0, limbs * ciL);
return;
}
/*
* shift by count / limb_size
*/
if (v0 > 0) {
for (i = 0; i < limbs - v0; i++) {
X[i] = X[i + v0];
}
for (; i < limbs; i++) {
X[i] = 0;
}
}
/*
* shift by count % limb_size
*/
if (v1 > 0) {
for (i = limbs; i > 0; i--) {
r1 = X[i - 1] << (biL - v1);
X[i - 1] >>= v1;
X[i - 1] |= r0;
r0 = r1;
}
}
}
void mbedtls_mpi_core_shift_l(mbedtls_mpi_uint *X, size_t limbs,
size_t count)
{
size_t i, v0, v1;
mbedtls_mpi_uint r0 = 0, r1;
v0 = count / (biL);
v1 = count & (biL - 1);
/*
* shift by count / limb_size
*/
if (v0 > 0) {
for (i = limbs; i > v0; i--) {
X[i - 1] = X[i - v0 - 1];
}
for (; i > 0; i--) {
X[i - 1] = 0;
}
}
/*
* shift by count % limb_size
*/
if (v1 > 0) {
for (i = v0; i < limbs; i++) {
r1 = X[i] >> (biL - v1);
X[i] <<= v1;
X[i] |= r0;
r0 = r1;
}
}
}
mbedtls_mpi_uint mbedtls_mpi_core_add(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *B,
size_t limbs)
{
mbedtls_mpi_uint c = 0;
for (size_t i = 0; i < limbs; i++) {
mbedtls_mpi_uint t = c + A[i];
c = (t < A[i]);
t += B[i];
c += (t < B[i]);
X[i] = t;
}
return c;
}
mbedtls_mpi_uint mbedtls_mpi_core_add_if(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
size_t limbs,
unsigned cond)
{
mbedtls_mpi_uint c = 0;
mbedtls_ct_condition_t do_add = mbedtls_ct_bool(cond);
for (size_t i = 0; i < limbs; i++) {
mbedtls_mpi_uint add = mbedtls_ct_mpi_uint_if_else_0(do_add, A[i]);
mbedtls_mpi_uint t = c + X[i];
c = (t < X[i]);
t += add;
c += (t < add);
X[i] = t;
}
return c;
}
mbedtls_mpi_uint mbedtls_mpi_core_sub(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *B,
size_t limbs)
{
mbedtls_mpi_uint c = 0;
for (size_t i = 0; i < limbs; i++) {
mbedtls_mpi_uint z = (A[i] < c);
mbedtls_mpi_uint t = A[i] - c;
c = (t < B[i]) + z;
X[i] = t - B[i];
}
return c;
}
mbedtls_mpi_uint mbedtls_mpi_core_mla(mbedtls_mpi_uint *d, size_t d_len,
const mbedtls_mpi_uint *s, size_t s_len,
mbedtls_mpi_uint b)
{
mbedtls_mpi_uint c = 0; /* carry */
/*
* It is a documented precondition of this function that d_len >= s_len.
* If that's not the case, we swap these round: this turns what would be
* a buffer overflow into an incorrect result.
*/
if (d_len < s_len) {
s_len = d_len;
}
size_t excess_len = d_len - s_len;
size_t steps_x8 = s_len / 8;
size_t steps_x1 = s_len & 7;
while (steps_x8--) {
MULADDC_X8_INIT
MULADDC_X8_CORE
MULADDC_X8_STOP
}
while (steps_x1--) {
MULADDC_X1_INIT
MULADDC_X1_CORE
MULADDC_X1_STOP
}
while (excess_len--) {
*d += c;
c = (*d < c);
d++;
}
return c;
}
void mbedtls_mpi_core_mul(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A, size_t A_limbs,
const mbedtls_mpi_uint *B, size_t B_limbs)
{
memset(X, 0, (A_limbs + B_limbs) * ciL);
for (size_t i = 0; i < B_limbs; i++) {
(void) mbedtls_mpi_core_mla(X + i, A_limbs + 1, A, A_limbs, B[i]);
}
}
/*
* 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;
}
}
/* Exponentiation: X := A^E mod N.
*
* 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.)
*/
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)
{
const size_t wsize = exp_mod_get_window_size(E_limbs * 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^(2^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);
/* 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 = E_limbs;
size_t E_bit_index = 0;
/* 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)) {
/* Select Wtable[window] without leaking window through
* memory access patterns. */
mbedtls_mpi_core_ct_uint_table_lookup(Wselect, Wtable,
AN_limbs, welem, window);
/* 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));
}
mbedtls_mpi_uint mbedtls_mpi_core_sub_int(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
mbedtls_mpi_uint c, /* doubles as carry */
size_t limbs)
{
for (size_t i = 0; i < limbs; i++) {
mbedtls_mpi_uint s = A[i];
mbedtls_mpi_uint t = s - c;
c = (t > s);
X[i] = t;
}
return c;
}
mbedtls_ct_condition_t mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
size_t limbs)
{
volatile const mbedtls_mpi_uint *force_read_A = A;
mbedtls_mpi_uint bits = 0;
for (size_t i = 0; i < limbs; i++) {
bits |= force_read_A[i];
}
return mbedtls_ct_bool(bits);
}
void mbedtls_mpi_core_to_mont_rep(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *N,
size_t AN_limbs,
mbedtls_mpi_uint mm,
const mbedtls_mpi_uint *rr,
mbedtls_mpi_uint *T)
{
mbedtls_mpi_core_montmul(X, A, rr, AN_limbs, N, AN_limbs, mm, T);
}
void mbedtls_mpi_core_from_mont_rep(mbedtls_mpi_uint *X,
const mbedtls_mpi_uint *A,
const mbedtls_mpi_uint *N,
size_t AN_limbs,
mbedtls_mpi_uint mm,
mbedtls_mpi_uint *T)
{
const mbedtls_mpi_uint Rinv = 1; /* 1/R in Mont. rep => 1 */
mbedtls_mpi_core_montmul(X, A, &Rinv, 1, N, AN_limbs, mm, T);
}
#endif /* MBEDTLS_BIGNUM_C */
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