/*
* Multi-precision integer library
*
* Copyright The Mbed TLS Contributors
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the "License"); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/*
* The following sources were referenced in the design of this Multi-precision
* Integer library:
*
* [1] Handbook of Applied Cryptography - 1997
* Menezes, van Oorschot and Vanstone
*
* [2] Multi-Precision Math
* Tom St Denis
* https://github.com/libtom/libtommath/blob/develop/tommath.pdf
*
* [3] GNU Multi-Precision Arithmetic Library
* https://gmplib.org/manual/index.html
*
*/
#include "common.h"
#if defined(MBEDTLS_BIGNUM_C)
#include "mbedtls/bignum.h"
#include "mbedtls/bn_mul.h"
#include "mbedtls/platform_util.h"
#include "mbedtls/error.h"
#include <string.h>
#if defined(MBEDTLS_PLATFORM_C)
#include "mbedtls/platform.h"
#else
#include <stdio.h>
#include <stdlib.h>
#define mbedtls_printf printf
#define mbedtls_calloc calloc
#define mbedtls_free free
#endif
#define MPI_VALIDATE_RET( cond ) \
MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_MPI_BAD_INPUT_DATA )
#define MPI_VALIDATE( cond ) \
MBEDTLS_INTERNAL_VALIDATE( cond )
#define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */
#define biL (ciL << 3) /* bits in limb */
#define biH (ciL << 2) /* half limb size */
#define MPI_SIZE_T_MAX ( (size_t) -1 ) /* SIZE_T_MAX is not standard */
/*
* Convert between bits/chars and number of limbs
* Divide first in order to avoid potential overflows
*/
#define BITS_TO_LIMBS(i) ( (i) / biL + ( (i) % biL != 0 ) )
#define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) )
/* Implementation that should never be optimized out by the compiler */
static void mbedtls_mpi_zeroize(mbedtls_mpi_uint *v, size_t n) {
mbedtls_platform_zeroize(v, ciL * n);
}
/*
* Initialize one MPI
*/
void mbedtls_mpi_init(mbedtls_mpi *X) {
MPI_VALIDATE(X != NULL);
X->s = 1;
X->n = 0;
X->p = NULL;
}
/*
* Unallocate one MPI
*/
void mbedtls_mpi_free(mbedtls_mpi *X) {
if (X == NULL)
return;
if (X->p != NULL) {
mbedtls_mpi_zeroize(X->p, X->n);
mbedtls_free(X->p);
}
X->s = 1;
X->n = 0;
X->p = NULL;
}
/*
* Enlarge to the specified number of limbs
*/
int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs) {
mbedtls_mpi_uint *p;
MPI_VALIDATE_RET(X != NULL);
if (nblimbs > MBEDTLS_MPI_MAX_LIMBS)
return (MBEDTLS_ERR_MPI_ALLOC_FAILED);
if (X->n < nblimbs) {
if ((p = (mbedtls_mpi_uint *)mbedtls_calloc(nblimbs, ciL)) == NULL)
return (MBEDTLS_ERR_MPI_ALLOC_FAILED);
if (X->p != NULL) {
memcpy(p, X->p, X->n * ciL);
mbedtls_mpi_zeroize(X->p, X->n);
mbedtls_free(X->p);
}
X->n = nblimbs;
X->p = p;
}
return (0);
}
/*
* Resize down as much as possible,
* while keeping at least the specified number of limbs
*/
int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs) {
mbedtls_mpi_uint *p;
size_t i;
MPI_VALIDATE_RET(X != NULL);
if (nblimbs > MBEDTLS_MPI_MAX_LIMBS)
return (MBEDTLS_ERR_MPI_ALLOC_FAILED);
/* Actually resize up if there are currently fewer than nblimbs limbs. */
if (X->n <= nblimbs)
return (mbedtls_mpi_grow(X, nblimbs));
/* After this point, then X->n > nblimbs and in particular X->n > 0. */
for (i = X->n - 1; i > 0; i--)
if (X->p[i] != 0)
break;
i++;
if (i < nblimbs)
i = nblimbs;
if ((p = (mbedtls_mpi_uint *)mbedtls_calloc(i, ciL)) == NULL)
return (MBEDTLS_ERR_MPI_ALLOC_FAILED);
if (X->p != NULL) {
memcpy(p, X->p, i * ciL);
mbedtls_mpi_zeroize(X->p, X->n);
mbedtls_free(X->p);
}
X->n = i;
X->p = p;
return (0);
}
/*
* Copy the contents of Y into X
*/
int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y) {
int ret = 0;
size_t i;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(Y != NULL);
if (X == Y)
return (0);
if (Y->n == 0) {
mbedtls_mpi_free(X);
return (0);
}
for (i = Y->n - 1; i > 0; i--)
if (Y->p[i] != 0)
break;
i++;
X->s = Y->s;
if (X->n < i) {
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i));
} else {
memset(X->p + i, 0, (X->n - i) * ciL);
}
memcpy(X->p, Y->p, i * ciL);
cleanup:
return (ret);
}
/*
* Swap the contents of X and Y
*/
void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y) {
mbedtls_mpi T;
MPI_VALIDATE(X != NULL);
MPI_VALIDATE(Y != NULL);
memcpy(&T, X, sizeof(mbedtls_mpi));
memcpy(X, Y, sizeof(mbedtls_mpi));
memcpy(Y, &T, sizeof(mbedtls_mpi));
}
/*
* Conditionally assign dest = src, without leaking information
* about whether the assignment was made or not.
* dest and src must be arrays of limbs of size n.
* assign must be 0 or 1.
*/
static void mpi_safe_cond_assign(size_t n,
mbedtls_mpi_uint *dest,
const mbedtls_mpi_uint *src,
unsigned char assign) {
size_t i;
for (i = 0; i < n; i++)
dest[i] = dest[i] * (1 - assign) + src[i] * assign;
}
/*
* Conditionally assign X = Y, without leaking information
* about whether the assignment was made or not.
* (Leaking information about the respective sizes of X and Y is ok however.)
*/
int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign) {
int ret = 0;
size_t i;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(Y != NULL);
/* make sure assign is 0 or 1 in a time-constant manner */
assign = (assign | (unsigned char) - assign) >> 7;
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n));
X->s = X->s * (1 - assign) + Y->s * assign;
mpi_safe_cond_assign(Y->n, X->p, Y->p, assign);
for (i = Y->n; i < X->n; i++)
X->p[i] *= (1 - assign);
cleanup:
return (ret);
}
/*
* Conditionally swap X and Y, without leaking information
* about whether the swap was made or not.
* Here it is not ok to simply swap the pointers, which whould lead to
* different memory access patterns when X and Y are used afterwards.
*/
int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap) {
int ret, s;
size_t i;
mbedtls_mpi_uint tmp;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(Y != NULL);
if (X == Y)
return (0);
/* make sure swap is 0 or 1 in a time-constant manner */
swap = (swap | (unsigned char) - swap) >> 7;
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n));
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Y, X->n));
s = X->s;
X->s = X->s * (1 - swap) + Y->s * swap;
Y->s = Y->s * (1 - swap) + s * swap;
for (i = 0; i < X->n; i++) {
tmp = X->p[i];
X->p[i] = X->p[i] * (1 - swap) + Y->p[i] * swap;
Y->p[i] = Y->p[i] * (1 - swap) + tmp * swap;
}
cleanup:
return (ret);
}
/*
* Set value from integer
*/
int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MPI_VALIDATE_RET(X != NULL);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, 1));
memset(X->p, 0, X->n * ciL);
X->p[0] = (z < 0) ? -z : z;
X->s = (z < 0) ? -1 : 1;
cleanup:
return (ret);
}
/*
* Get a specific bit
*/
int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos) {
MPI_VALIDATE_RET(X != NULL);
if (X->n * biL <= pos)
return (0);
return ((X->p[pos / biL] >> (pos % biL)) & 0x01);
}
/* Get a specific byte, without range checks. */
#define GET_BYTE( X, i ) \
( ( ( X )->p[( i ) / ciL] >> ( ( ( i ) % ciL ) * 8 ) ) & 0xff )
/*
* Set a bit to a specific value of 0 or 1
*/
int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val) {
int ret = 0;
size_t off = pos / biL;
size_t idx = pos % biL;
MPI_VALIDATE_RET(X != NULL);
if (val != 0 && val != 1)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
if (X->n * biL <= pos) {
if (val == 0)
return (0);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, off + 1));
}
X->p[off] &= ~((mbedtls_mpi_uint) 0x01 << idx);
X->p[off] |= (mbedtls_mpi_uint) val << idx;
cleanup:
return (ret);
}
/*
* Return the number of less significant zero-bits
*/
size_t mbedtls_mpi_lsb(const mbedtls_mpi *X) {
size_t i, j, count = 0;
MBEDTLS_INTERNAL_VALIDATE_RET(X != NULL, 0);
for (i = 0; i < X->n; i++)
for (j = 0; j < biL; j++, count++)
if (((X->p[i] >> j) & 1) != 0)
return (count);
return (0);
}
/*
* Count leading zero bits in a given integer
*/
static size_t mbedtls_clz(const mbedtls_mpi_uint x) {
size_t j;
mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);
for (j = 0; j < biL; j++) {
if (x & mask) break;
mask >>= 1;
}
return j;
}
/*
* Return the number of bits
*/
size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X) {
size_t i, j;
if (X->n == 0)
return (0);
for (i = X->n - 1; i > 0; i--)
if (X->p[i] != 0)
break;
j = biL - mbedtls_clz(X->p[i]);
return ((i * biL) + j);
}
/*
* Return the total size in bytes
*/
size_t mbedtls_mpi_size(const mbedtls_mpi *X) {
return ((mbedtls_mpi_bitlen(X) + 7) >> 3);
}
/*
* Convert an ASCII character to digit value
*/
static int mpi_get_digit(mbedtls_mpi_uint *d, int radix, char c) {
*d = 255;
if (c >= 0x30 && c <= 0x39) *d = c - 0x30;
if (c >= 0x41 && c <= 0x46) *d = c - 0x37;
if (c >= 0x61 && c <= 0x66) *d = c - 0x57;
if (*d >= (mbedtls_mpi_uint) radix)
return (MBEDTLS_ERR_MPI_INVALID_CHARACTER);
return (0);
}
/*
* Import from an ASCII string
*/
int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i, j, slen, n;
mbedtls_mpi_uint d;
mbedtls_mpi T;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(s != NULL);
if (radix < 2 || radix > 16)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
mbedtls_mpi_init(&T);
slen = strlen(s);
if (radix == 16) {
if (slen > MPI_SIZE_T_MAX >> 2)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
n = BITS_TO_LIMBS(slen << 2);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, n));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));
for (i = slen, j = 0; i > 0; i--, j++) {
if (i == 1 && s[i - 1] == '-') {
X->s = -1;
break;
}
MBEDTLS_MPI_CHK(mpi_get_digit(&d, radix, s[i - 1]));
X->p[j / (2 * ciL)] |= d << ((j % (2 * ciL)) << 2);
}
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));
for (i = 0; i < slen; i++) {
if (i == 0 && s[i] == '-') {
X->s = -1;
continue;
}
MBEDTLS_MPI_CHK(mpi_get_digit(&d, radix, s[i]));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T, X, radix));
if (X->s == 1) {
MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, &T, d));
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(X, &T, d));
}
}
}
cleanup:
mbedtls_mpi_free(&T);
return (ret);
}
/*
* Helper to write the digits high-order first.
*/
static int mpi_write_hlp(mbedtls_mpi *X, int radix,
char **p, const size_t buflen) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi_uint r;
size_t length = 0;
char *p_end = *p + buflen;
do {
if (length >= buflen) {
return (MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL);
}
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, radix));
MBEDTLS_MPI_CHK(mbedtls_mpi_div_int(X, NULL, X, radix));
/*
* Write the residue in the current position, as an ASCII character.
*/
if (r < 0xA)
*(--p_end) = (char)('0' + r);
else
*(--p_end) = (char)('A' + (r - 0xA));
length++;
} while (mbedtls_mpi_cmp_int(X, 0) != 0);
memmove(*p, p_end, length);
*p += length;
cleanup:
return (ret);
}
/*
* Export into an ASCII string
*/
int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix,
char *buf, size_t buflen, size_t *olen) {
int ret = 0;
size_t n;
char *p;
mbedtls_mpi T;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(olen != NULL);
MPI_VALIDATE_RET(buflen == 0 || buf != NULL);
if (radix < 2 || radix > 16)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
n = mbedtls_mpi_bitlen(X); /* Number of bits necessary to present `n`. */
if (radix >= 4) n >>= 1; /* Number of 4-adic digits necessary to present
* `n`. If radix > 4, this might be a strict
* overapproximation of the number of
* radix-adic digits needed to present `n`. */
if (radix >= 16) n >>= 1; /* Number of hexadecimal digits necessary to
* present `n`. */
n += 1; /* Terminating null byte */
n += 1; /* Compensate for the divisions above, which round down `n`
* in case it's not even. */
n += 1; /* Potential '-'-sign. */
n += (n & 1); /* Make n even to have enough space for hexadecimal writing,
* which always uses an even number of hex-digits. */
if (buflen < n) {
*olen = n;
return (MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL);
}
p = buf;
mbedtls_mpi_init(&T);
if (X->s == -1) {
*p++ = '-';
buflen--;
}
if (radix == 16) {
int c;
size_t i, j, k;
for (i = X->n, k = 0; i > 0; i--) {
for (j = ciL; j > 0; j--) {
c = (X->p[i - 1] >> ((j - 1) << 3)) & 0xFF;
if (c == 0 && k == 0 && (i + j) != 2)
continue;
*(p++) = "0123456789ABCDEF" [c / 16];
*(p++) = "0123456789ABCDEF" [c % 16];
k = 1;
}
}
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T, X));
if (T.s == -1)
T.s = 1;
MBEDTLS_MPI_CHK(mpi_write_hlp(&T, radix, &p, buflen));
}
*p++ = '\0';
*olen = p - buf;
cleanup:
mbedtls_mpi_free(&T);
return (ret);
}
#if defined(MBEDTLS_FS_IO)
/*
* Read X from an opened file
*/
int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin) {
mbedtls_mpi_uint d;
size_t slen;
char *p;
/*
* Buffer should have space for (short) label and decimal formatted MPI,
* newline characters and '\0'
*/
char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(fin != NULL);
if (radix < 2 || radix > 16)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
memset(s, 0, sizeof(s));
if (fgets(s, sizeof(s) - 1, fin) == NULL)
return (MBEDTLS_ERR_MPI_FILE_IO_ERROR);
slen = strlen(s);
if (slen == sizeof(s) - 2)
return (MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL);
if (slen > 0 && s[slen - 1] == '\n') { slen--; s[slen] = '\0'; }
if (slen > 0 && s[slen - 1] == '\r') { slen--; s[slen] = '\0'; }
p = s + slen;
while (p-- > s)
if (mpi_get_digit(&d, radix, *p) != 0)
break;
return (mbedtls_mpi_read_string(X, radix, p + 1));
}
/*
* Write X into an opened file (or stdout if fout == NULL)
*/
int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X, int radix, FILE *fout) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t n, slen, plen;
/*
* Buffer should have space for (short) label and decimal formatted MPI,
* newline characters and '\0'
*/
char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
MPI_VALIDATE_RET(X != NULL);
if (radix < 2 || radix > 16)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
memset(s, 0, sizeof(s));
MBEDTLS_MPI_CHK(mbedtls_mpi_write_string(X, radix, s, sizeof(s) - 2, &n));
if (p == NULL) p = "";
plen = strlen(p);
slen = strlen(s);
s[slen++] = '\r';
s[slen++] = '\n';
if (fout != NULL) {
if (fwrite(p, 1, plen, fout) != plen ||
fwrite(s, 1, slen, fout) != slen)
return (MBEDTLS_ERR_MPI_FILE_IO_ERROR);
} else
mbedtls_printf("%s%s", p, s);
cleanup:
return (ret);
}
#endif /* MBEDTLS_FS_IO */
/* Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
* into the storage form used by mbedtls_mpi. */
static mbedtls_mpi_uint mpi_uint_bigendian_to_host_c(mbedtls_mpi_uint x) {
uint8_t i;
unsigned char *x_ptr;
mbedtls_mpi_uint tmp = 0;
for (i = 0, x_ptr = (unsigned char *) &x; i < ciL; i++, x_ptr++) {
tmp <<= CHAR_BIT;
tmp |= (mbedtls_mpi_uint) * x_ptr;
}
return (tmp);
}
static mbedtls_mpi_uint mpi_uint_bigendian_to_host(mbedtls_mpi_uint x) {
#if defined(__BYTE_ORDER__)
/* Nothing to do on bigendian systems. */
#if ( __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ )
return (x);
#endif /* __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ */
#if ( __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ )
/* For GCC and Clang, have builtins for byte swapping. */
#if defined(__GNUC__) && defined(__GNUC_PREREQ)
#if __GNUC_PREREQ(4,3)
#define have_bswap
#endif
#endif
#if defined(__clang__) && defined(__has_builtin)
#if __has_builtin(__builtin_bswap32) && \
__has_builtin(__builtin_bswap64)
#define have_bswap
#endif
#endif
#if defined(have_bswap)
/* The compiler is hopefully able to statically evaluate this! */
switch (sizeof(mbedtls_mpi_uint)) {
case 4:
return (__builtin_bswap32(x));
case 8:
return (__builtin_bswap64(x));
}
#endif
#endif /* __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ */
#endif /* __BYTE_ORDER__ */
/* Fall back to C-based reordering if we don't know the byte order
* or we couldn't use a compiler-specific builtin. */
return (mpi_uint_bigendian_to_host_c(x));
}
static void mpi_bigendian_to_host(mbedtls_mpi_uint *const p, size_t limbs) {
mbedtls_mpi_uint *cur_limb_left;
mbedtls_mpi_uint *cur_limb_right;
if (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 = p, cur_limb_right = p + (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_uint_bigendian_to_host(*cur_limb_left);
*cur_limb_left = mpi_uint_bigendian_to_host(*cur_limb_right);
*cur_limb_right = tmp;
}
}
/*
* Import X from unsigned binary data, little endian
*/
int mbedtls_mpi_read_binary_le(mbedtls_mpi *X,
const unsigned char *buf, size_t buflen) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i;
size_t const limbs = CHARS_TO_LIMBS(buflen);
/* Ensure that target MPI has exactly the necessary number of limbs */
if (X->n != limbs) {
mbedtls_mpi_free(X);
mbedtls_mpi_init(X);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, limbs));
}
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));
for (i = 0; i < buflen; i++)
X->p[i / ciL] |= ((mbedtls_mpi_uint) buf[i]) << ((i % ciL) << 3);
cleanup:
/*
* This function is also used to import keys. However, wiping the buffers
* upon failure is not necessary because failure only can happen before any
* input is copied.
*/
return (ret);
}
/*
* Import X from unsigned binary data, big endian
*/
int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf, size_t buflen) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t const limbs = CHARS_TO_LIMBS(buflen);
size_t const overhead = (limbs * ciL) - buflen;
unsigned char *Xp;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(buflen == 0 || buf != NULL);
/* Ensure that target MPI has exactly the necessary number of limbs */
if (X->n != limbs) {
mbedtls_mpi_free(X);
mbedtls_mpi_init(X);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, limbs));
}
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));
/* Avoid calling `memcpy` with NULL source argument,
* even if buflen is 0. */
if (buf != NULL) {
Xp = (unsigned char *) X->p;
memcpy(Xp + overhead, buf, buflen);
mpi_bigendian_to_host(X->p, limbs);
}
cleanup:
/*
* This function is also used to import keys. However, wiping the buffers
* upon failure is not necessary because failure only can happen before any
* input is copied.
*/
return (ret);
}
/*
* Export X into unsigned binary data, little endian
*/
int mbedtls_mpi_write_binary_le(const mbedtls_mpi *X,
unsigned char *buf, size_t buflen) {
size_t stored_bytes = X->n * ciL;
size_t bytes_to_copy;
size_t i;
if (stored_bytes < buflen) {
bytes_to_copy = stored_bytes;
} else {
bytes_to_copy = buflen;
/* The output buffer is smaller than the allocated size of X.
* However X may fit if its leading bytes are zero. */
for (i = bytes_to_copy; i < stored_bytes; i++) {
if (GET_BYTE(X, i) != 0)
return (MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL);
}
}
for (i = 0; i < bytes_to_copy; i++)
buf[i] = GET_BYTE(X, i);
if (stored_bytes < buflen) {
/* Write trailing 0 bytes */
memset(buf + stored_bytes, 0, buflen - stored_bytes);
}
return (0);
}
/*
* Export X into unsigned binary data, big endian
*/
int mbedtls_mpi_write_binary(const mbedtls_mpi *X,
unsigned char *buf, size_t buflen) {
size_t stored_bytes;
size_t bytes_to_copy;
unsigned char *p;
size_t i;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(buflen == 0 || buf != NULL);
stored_bytes = X->n * ciL;
if (stored_bytes < buflen) {
/* 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 = buf + buflen - stored_bytes;
memset(buf, 0, buflen - 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 = buflen;
p = buf;
for (i = bytes_to_copy; i < stored_bytes; i++) {
if (GET_BYTE(X, i) != 0)
return (MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL);
}
}
for (i = 0; i < bytes_to_copy; i++)
p[bytes_to_copy - i - 1] = GET_BYTE(X, i);
return (0);
}
/*
* Left-shift: X <<= count
*/
int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i, v0, t1;
mbedtls_mpi_uint r0 = 0, r1;
MPI_VALIDATE_RET(X != NULL);
v0 = count / (biL);
t1 = count & (biL - 1);
i = mbedtls_mpi_bitlen(X) + count;
if (X->n * biL < i)
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, BITS_TO_LIMBS(i)));
ret = 0;
/*
* shift by count / limb_size
*/
if (v0 > 0) {
for (i = X->n; i > v0; i--)
X->p[i - 1] = X->p[i - v0 - 1];
for (; i > 0; i--)
X->p[i - 1] = 0;
}
/*
* shift by count % limb_size
*/
if (t1 > 0) {
for (i = v0; i < X->n; i++) {
r1 = X->p[i] >> (biL - t1);
X->p[i] <<= t1;
X->p[i] |= r0;
r0 = r1;
}
}
cleanup:
return (ret);
}
/*
* Right-shift: X >>= count
*/
int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count) {
size_t i, v0, v1;
mbedtls_mpi_uint r0 = 0, r1;
MPI_VALIDATE_RET(X != NULL);
v0 = count / biL;
v1 = count & (biL - 1);
if (v0 > X->n || (v0 == X->n && v1 > 0))
return mbedtls_mpi_lset(X, 0);
/*
* shift by count / limb_size
*/
if (v0 > 0) {
for (i = 0; i < X->n - v0; i++)
X->p[i] = X->p[i + v0];
for (; i < X->n; i++)
X->p[i] = 0;
}
/*
* shift by count % limb_size
*/
if (v1 > 0) {
for (i = X->n; i > 0; i--) {
r1 = X->p[i - 1] << (biL - v1);
X->p[i - 1] >>= v1;
X->p[i - 1] |= r0;
r0 = r1;
}
}
return (0);
}
/*
* Compare unsigned values
*/
int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y) {
size_t i, j;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(Y != NULL);
for (i = X->n; i > 0; i--)
if (X->p[i - 1] != 0)
break;
for (j = Y->n; j > 0; j--)
if (Y->p[j - 1] != 0)
break;
if (i == 0 && j == 0)
return (0);
if (i > j) return (1);
if (j > i) return (-1);
for (; i > 0; i--) {
if (X->p[i - 1] > Y->p[i - 1]) return (1);
if (X->p[i - 1] < Y->p[i - 1]) return (-1);
}
return (0);
}
/*
* Compare signed values
*/
int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y) {
size_t i, j;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(Y != NULL);
for (i = X->n; i > 0; i--)
if (X->p[i - 1] != 0)
break;
for (j = Y->n; j > 0; j--)
if (Y->p[j - 1] != 0)
break;
if (i == 0 && j == 0)
return (0);
if (i > j) return (X->s);
if (j > i) return (-Y->s);
if (X->s > 0 && Y->s < 0) return (1);
if (Y->s > 0 && X->s < 0) return (-1);
for (; i > 0; i--) {
if (X->p[i - 1] > Y->p[i - 1]) return (X->s);
if (X->p[i - 1] < Y->p[i - 1]) return (-X->s);
}
return (0);
}
/** Decide if an integer is less than the other, without branches.
*
* \param x First integer.
* \param y Second integer.
*
* \return 1 if \p x is less than \p y, 0 otherwise
*/
static unsigned ct_lt_mpi_uint(const mbedtls_mpi_uint x,
const mbedtls_mpi_uint y) {
mbedtls_mpi_uint ret;
mbedtls_mpi_uint cond;
/*
* Check if the most significant bits (MSB) of the operands are different.
*/
cond = (x ^ y);
/*
* If the MSB are the same then the difference x-y will be negative (and
* have its MSB set to 1 during conversion to unsigned) if and only if x<y.
*/
ret = (x - y) & ~cond;
/*
* If the MSB are different, then the operand with the MSB of 1 is the
* bigger. (That is if y has MSB of 1, then x<y is true and it is false if
* the MSB of y is 0.)
*/
ret |= y & cond;
ret = ret >> (biL - 1);
return (unsigned) ret;
}
/*
* Compare signed values in constant time
*/
int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, const mbedtls_mpi *Y,
unsigned *ret) {
size_t i;
/* The value of any of these variables is either 0 or 1 at all times. */
unsigned cond, done, X_is_negative, Y_is_negative;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(Y != NULL);
MPI_VALIDATE_RET(ret != NULL);
if (X->n != Y->n)
return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
/*
* Set sign_N to 1 if N >= 0, 0 if N < 0.
* We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0.
*/
X_is_negative = (X->s & 2) >> 1;
Y_is_negative = (Y->s & 2) >> 1;
/*
* If the signs are different, then the positive operand is the bigger.
* That is if X is negative (X_is_negative == 1), then X < Y is true and it
* is false if X is positive (X_is_negative == 0).
*/
cond = (X_is_negative ^ Y_is_negative);
*ret = cond & X_is_negative;
/*
* This is a constant-time function. We might have the result, but we still
* need to go through the loop. Record if we have the result already.
*/
done = cond;
for (i = X->n; i > 0; i--) {
/*
* If Y->p[i - 1] < X->p[i - 1] then X < Y is true if and only if both
* X and Y are negative.
*
* Again even if we can make a decision, we just mark the result and
* the fact that we are done and continue looping.
*/
cond = ct_lt_mpi_uint(Y->p[i - 1], X->p[i - 1]);
*ret |= cond & (1 - done) & X_is_negative;
done |= cond;
/*
* If X->p[i - 1] < Y->p[i - 1] then X < Y is true if and only if both
* X and Y are positive.
*
* Again even if we can make a decision, we just mark the result and
* the fact that we are done and continue looping.
*/
cond = ct_lt_mpi_uint(X->p[i - 1], Y->p[i - 1]);
*ret |= cond & (1 - done) & (1 - X_is_negative);
done |= cond;
}
return (0);
}
/*
* Compare signed values
*/
int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z) {
mbedtls_mpi Y;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET(X != NULL);
*p = (z < 0) ? -z : z;
Y.s = (z < 0) ? -1 : 1;
Y.n = 1;
Y.p = p;
return (mbedtls_mpi_cmp_mpi(X, &Y));
}
/*
* Unsigned addition: X = |A| + |B| (HAC 14.7)
*/
int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i, j;
mbedtls_mpi_uint *o, *p, c, tmp;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(B != NULL);
if (X == B) {
const mbedtls_mpi *T = A;
A = X;
B = T;
}
if (X != A)
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A));
/*
* X should always be positive as a result of unsigned additions.
*/
X->s = 1;
for (j = B->n; j > 0; j--)
if (B->p[j - 1] != 0)
break;
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j));
o = B->p;
p = X->p;
c = 0;
/*
* tmp is used because it might happen that p == o
*/
for (i = 0; i < j; i++, o++, p++) {
tmp = *o;
*p += c;
c = (*p < c);
*p += tmp;
c += (*p < tmp);
}
while (c != 0) {
if (i >= X->n) {
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i + 1));
p = X->p + i;
}
*p += c;
c = (*p < c);
i++;
p++;
}
cleanup:
return (ret);
}
/**
* Helper for mbedtls_mpi subtraction.
*
* Calculate d - s where d and s have the same size.
* This function operates modulo (2^ciL)^n and returns the carry
* (1 if there was a wraparound, i.e. if `d < s`, and 0 otherwise).
*
* \param n Number of limbs of \p d and \p s.
* \param[in,out] d On input, the left operand.
* On output, the result of the subtraction:
* \param[in] s The right operand.
*
* \return 1 if `d < s`.
* 0 if `d >= s`.
*/
static mbedtls_mpi_uint mpi_sub_hlp(size_t n,
mbedtls_mpi_uint *d,
const mbedtls_mpi_uint *s) {
size_t i;
mbedtls_mpi_uint c, z;
for (i = c = 0; i < n; i++, s++, d++) {
z = (*d < c);
*d -= c;
c = (*d < *s) + z;
*d -= *s;
}
return (c);
}
/*
* Unsigned subtraction: X = |A| - |B| (HAC 14.9, 14.10)
*/
int mbedtls_mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) {
mbedtls_mpi TB;
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t n;
mbedtls_mpi_uint carry;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(B != NULL);
mbedtls_mpi_init(&TB);
if (X == B) {
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, B));
B = &TB;
}
if (X != A)
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A));
/*
* X should always be positive as a result of unsigned subtractions.
*/
X->s = 1;
ret = 0;
for (n = B->n; n > 0; n--)
if (B->p[n - 1] != 0)
break;
if (n > A->n) {
/* B >= (2^ciL)^n > A */
ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
goto cleanup;
}
carry = mpi_sub_hlp(n, X->p, B->p);
if (carry != 0) {
/* Propagate the carry to the first nonzero limb of X. */
for (; n < X->n && X->p[n] == 0; n++)
--X->p[n];
/* If we ran out of space for the carry, it means that the result
* is negative. */
if (n == X->n) {
ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
goto cleanup;
}
--X->p[n];
}
cleanup:
mbedtls_mpi_free(&TB);
return (ret);
}
/*
* Signed addition: X = A + B
*/
int mbedtls_mpi_add_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) {
int ret, s;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(B != NULL);
s = A->s;
if (A->s * B->s < 0) {
if (mbedtls_mpi_cmp_abs(A, B) >= 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, A, B));
X->s = s;
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, B, A));
X->s = -s;
}
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_add_abs(X, A, B));
X->s = s;
}
cleanup:
return (ret);
}
/*
* Signed subtraction: X = A - B
*/
int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) {
int ret, s;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(B != NULL);
s = A->s;
if (A->s * B->s > 0) {
if (mbedtls_mpi_cmp_abs(A, B) >= 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, A, B));
X->s = s;
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, B, A));
X->s = -s;
}
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_add_abs(X, A, B));
X->s = s;
}
cleanup:
return (ret);
}
/*
* Signed addition: X = A + b
*/
int mbedtls_mpi_add_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b) {
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
p[0] = (b < 0) ? -b : b;
_B.s = (b < 0) ? -1 : 1;
_B.n = 1;
_B.p = p;
return (mbedtls_mpi_add_mpi(X, A, &_B));
}
/*
* Signed subtraction: X = A - b
*/
int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b) {
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
p[0] = (b < 0) ? -b : b;
_B.s = (b < 0) ? -1 : 1;
_B.n = 1;
_B.p = p;
return (mbedtls_mpi_sub_mpi(X, A, &_B));
}
/*
* Helper for mbedtls_mpi multiplication
*/
static
#if defined(__APPLE__) && defined(__arm__)
/*
* Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
* appears to need this to prevent bad ARM code generation at -O3.
*/
__attribute__((noinline))
#endif
void mpi_mul_hlp(size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b) {
mbedtls_mpi_uint c = 0, t = 0;
#if defined(MULADDC_HUIT)
for (; i >= 8; i -= 8) {
MULADDC_INIT
MULADDC_HUIT
MULADDC_STOP
}
for (; i > 0; i--) {
MULADDC_INIT
MULADDC_CORE
MULADDC_STOP
}
#else /* MULADDC_HUIT */
for (; i >= 16; i -= 16) {
MULADDC_INIT
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_STOP
}
for (; i >= 8; i -= 8) {
MULADDC_INIT
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_STOP
}
for (; i > 0; i--) {
MULADDC_INIT
MULADDC_CORE
MULADDC_STOP
}
#endif /* MULADDC_HUIT */
t++;
do {
*d += c;
c = (*d < c);
d++;
} while (c != 0);
}
/*
* Baseline multiplication: X = A * B (HAC 14.12)
*/
int mbedtls_mpi_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i, j;
mbedtls_mpi TA, TB;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(B != NULL);
mbedtls_mpi_init(&TA);
mbedtls_mpi_init(&TB);
if (X == A) { MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TA, A)); A = &TA; }
if (X == B) { MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, B)); B = &TB; }
for (i = A->n; i > 0; i--)
if (A->p[i - 1] != 0)
break;
for (j = B->n; j > 0; j--)
if (B->p[j - 1] != 0)
break;
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i + j));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));
for (; j > 0; j--)
mpi_mul_hlp(i, A->p, X->p + j - 1, B->p[j - 1]);
X->s = A->s * B->s;
cleanup:
mbedtls_mpi_free(&TB);
mbedtls_mpi_free(&TA);
return (ret);
}
/*
* Baseline multiplication: X = A * b
*/
int mbedtls_mpi_mul_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b) {
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
_B.s = 1;
_B.n = 1;
_B.p = p;
p[0] = b;
return (mbedtls_mpi_mul_mpi(X, A, &_B));
}
/*
* Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and
* mbedtls_mpi_uint divisor, d
*/
static mbedtls_mpi_uint mbedtls_int_div_int(mbedtls_mpi_uint u1,
mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r) {
#if defined(MBEDTLS_HAVE_UDBL)
mbedtls_t_udbl dividend, quotient;
#else
const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH;
const mbedtls_mpi_uint uint_halfword_mask = ((mbedtls_mpi_uint) 1 << biH) - 1;
mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient;
mbedtls_mpi_uint u0_msw, u0_lsw;
size_t s;
#endif
/*
* Check for overflow
*/
if (0 == d || u1 >= d) {
if (r != NULL) *r = ~0;
return (~0);
}
#if defined(MBEDTLS_HAVE_UDBL)
dividend = (mbedtls_t_udbl) u1 << biL;
dividend |= (mbedtls_t_udbl) u0;
quotient = dividend / d;
if (quotient > ((mbedtls_t_udbl) 1 << biL) - 1)
quotient = ((mbedtls_t_udbl) 1 << biL) - 1;
if (r != NULL)
*r = (mbedtls_mpi_uint)(dividend - (quotient * d));
return (mbedtls_mpi_uint) quotient;
#else
/*
* Algorithm D, Section 4.3.1 - The Art of Computer Programming
* Vol. 2 - Seminumerical Algorithms, Knuth
*/
/*
* Normalize the divisor, d, and dividend, u0, u1
*/
s = mbedtls_clz(d);
d = d << s;
u1 = u1 << s;
u1 |= (u0 >> (biL - s)) & (-(mbedtls_mpi_sint)s >> (biL - 1));
u0 = u0 << s;
d1 = d >> biH;
d0 = d & uint_halfword_mask;
u0_msw = u0 >> biH;
u0_lsw = u0 & uint_halfword_mask;
/*
* Find the first quotient and remainder
*/
q1 = u1 / d1;
r0 = u1 - d1 * q1;
while (q1 >= radix || (q1 * d0 > radix * r0 + u0_msw)) {
q1 -= 1;
r0 += d1;
if (r0 >= radix) break;
}
rAX = (u1 * radix) + (u0_msw - q1 * d);
q0 = rAX / d1;
r0 = rAX - q0 * d1;
while (q0 >= radix || (q0 * d0 > radix * r0 + u0_lsw)) {
q0 -= 1;
r0 += d1;
if (r0 >= radix) break;
}
if (r != NULL)
*r = (rAX * radix + u0_lsw - q0 * d) >> s;
quotient = q1 * radix + q0;
return quotient;
#endif
}
/*
* Division by mbedtls_mpi: A = Q * B + R (HAC 14.20)
*/
int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
const mbedtls_mpi *B) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i, n, t, k;
mbedtls_mpi X, Y, Z, T1, T2;
mbedtls_mpi_uint TP2[3];
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(B != NULL);
if (mbedtls_mpi_cmp_int(B, 0) == 0)
return (MBEDTLS_ERR_MPI_DIVISION_BY_ZERO);
mbedtls_mpi_init(&X);
mbedtls_mpi_init(&Y);
mbedtls_mpi_init(&Z);
mbedtls_mpi_init(&T1);
/*
* Avoid dynamic memory allocations for constant-size T2.
*
* T2 is used for comparison only and the 3 limbs are assigned explicitly,
* so nobody increase the size of the MPI and we're safe to use an on-stack
* buffer.
*/
T2.s = 1;
T2.n = sizeof(TP2) / sizeof(*TP2);
T2.p = TP2;
if (mbedtls_mpi_cmp_abs(A, B) < 0) {
if (Q != NULL) MBEDTLS_MPI_CHK(mbedtls_mpi_lset(Q, 0));
if (R != NULL) MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, A));
return (0);
}
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&X, A));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Y, B));
X.s = Y.s = 1;
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&Z, A->n + 2));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&Z, 0));
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T1, 2));
k = mbedtls_mpi_bitlen(&Y) % biL;
if (k < biL - 1) {
k = biL - 1 - k;
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&X, k));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&Y, k));
} else k = 0;
n = X.n - 1;
t = Y.n - 1;
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&Y, biL * (n - t)));
while (mbedtls_mpi_cmp_mpi(&X, &Y) >= 0) {
Z.p[n - t]++;
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&X, &X, &Y));
}
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&Y, biL * (n - t)));
for (i = n; i > t ; i--) {
if (X.p[i] >= Y.p[t])
Z.p[i - t - 1] = ~0;
else {
Z.p[i - t - 1] = mbedtls_int_div_int(X.p[i], X.p[i - 1],
Y.p[t], NULL);
}
T2.p[0] = (i < 2) ? 0 : X.p[i - 2];
T2.p[1] = (i < 1) ? 0 : X.p[i - 1];
T2.p[2] = X.p[i];
Z.p[i - t - 1]++;
do {
Z.p[i - t - 1]--;
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&T1, 0));
T1.p[0] = (t < 1) ? 0 : Y.p[t - 1];
T1.p[1] = Y.p[t];
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T1, &T1, Z.p[i - t - 1]));
} while (mbedtls_mpi_cmp_mpi(&T1, &T2) > 0);
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T1, &Y, Z.p[i - t - 1]));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&T1, biL * (i - t - 1)));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&X, &X, &T1));
if (mbedtls_mpi_cmp_int(&X, 0) < 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T1, &Y));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&T1, biL * (i - t - 1)));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&X, &X, &T1));
Z.p[i - t - 1]--;
}
}
if (Q != NULL) {
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(Q, &Z));
Q->s = A->s * B->s;
}
if (R != NULL) {
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&X, k));
X.s = A->s;
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, &X));
if (mbedtls_mpi_cmp_int(R, 0) == 0)
R->s = 1;
}
cleanup:
mbedtls_mpi_free(&X);
mbedtls_mpi_free(&Y);
mbedtls_mpi_free(&Z);
mbedtls_mpi_free(&T1);
mbedtls_platform_zeroize(TP2, sizeof(TP2));
return (ret);
}
/*
* Division by int: A = Q * b + R
*/
int mbedtls_mpi_div_int(mbedtls_mpi *Q, mbedtls_mpi *R,
const mbedtls_mpi *A,
mbedtls_mpi_sint b) {
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET(A != NULL);
p[0] = (b < 0) ? -b : b;
_B.s = (b < 0) ? -1 : 1;
_B.n = 1;
_B.p = p;
return (mbedtls_mpi_div_mpi(Q, R, A, &_B));
}
/*
* Modulo: R = A mod B
*/
int mbedtls_mpi_mod_mpi(mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MPI_VALIDATE_RET(R != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(B != NULL);
if (mbedtls_mpi_cmp_int(B, 0) < 0)
return (MBEDTLS_ERR_MPI_NEGATIVE_VALUE);
MBEDTLS_MPI_CHK(mbedtls_mpi_div_mpi(NULL, R, A, B));
while (mbedtls_mpi_cmp_int(R, 0) < 0)
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(R, R, B));
while (mbedtls_mpi_cmp_mpi(R, B) >= 0)
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(R, R, B));
cleanup:
return (ret);
}
/*
* Modulo: r = A mod b
*/
int mbedtls_mpi_mod_int(mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b) {
size_t i;
mbedtls_mpi_uint x, y, z;
MPI_VALIDATE_RET(r != NULL);
MPI_VALIDATE_RET(A != NULL);
if (b == 0)
return (MBEDTLS_ERR_MPI_DIVISION_BY_ZERO);
if (b < 0)
return (MBEDTLS_ERR_MPI_NEGATIVE_VALUE);
/*
* handle trivial cases
*/
if (b == 1) {
*r = 0;
return (0);
}
if (b == 2) {
*r = A->p[0] & 1;
return (0);
}
/*
* general case
*/
for (i = A->n, y = 0; i > 0; i--) {
x = A->p[i - 1];
y = (y << biH) | (x >> biH);
z = y / b;
y -= z * b;
x <<= biH;
y = (y << biH) | (x >> biH);
z = y / b;
y -= z * b;
}
/*
* If A is negative, then the current y represents a negative value.
* Flipping it to the positive side.
*/
if (A->s < 0 && y != 0)
y = b - y;
*r = y;
return (0);
}
/*
* Fast Montgomery initialization (thanks to Tom St Denis)
*/
static void mpi_montg_init(mbedtls_mpi_uint *mm, const mbedtls_mpi *N) {
mbedtls_mpi_uint x, m0 = N->p[0];
unsigned int i;
x = m0;
x += ((m0 + 2) & 4) << 1;
for (i = biL; i >= 8; i /= 2)
x *= (2 - (m0 * x));
*mm = ~x + 1;
}
/** Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
*
* \param[in,out] A One of the numbers to multiply.
* It must have at least as many limbs as N
* (A->n >= N->n), and any limbs beyond n are ignored.
* On successful completion, A contains the result of
* the multiplication A * B * R^-1 mod N where
* R = (2^ciL)^n.
* \param[in] B One of the numbers to multiply.
* It must be nonzero and must not have more limbs than N
* (B->n <= N->n).
* \param[in] N The modulo. N must be odd.
* \param mm The value calculated by `mpi_montg_init(&mm, N)`.
* This is -N^-1 mod 2^ciL.
* \param[in,out] T A bignum for temporary storage.
* It must be at least twice the limb size of N plus 2
* (T->n >= 2 * (N->n + 1)).
* Its initial content is unused and
* its final content is indeterminate.
* Note that unlike the usual convention in the library
* for `const mbedtls_mpi*`, the content of T can change.
*/
static void mpi_montmul(mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
const mbedtls_mpi *T) {
size_t i, n, m;
mbedtls_mpi_uint u0, u1, *d;
memset(T->p, 0, T->n * ciL);
d = T->p;
n = N->n;
m = (B->n < n) ? B->n : n;
for (i = 0; i < n; i++) {
/*
* T = (T + u0*B + u1*N) / 2^biL
*/
u0 = A->p[i];
u1 = (d[0] + u0 * B->p[0]) * mm;
mpi_mul_hlp(m, B->p, d, u0);
mpi_mul_hlp(n, N->p, d, u1);
*d++ = u0;
d[n + 1] = 0;
}
/* At this point, d is either the desired result or the desired result
* plus N. We now potentially subtract N, avoiding leaking whether the
* subtraction is performed through side channels. */
/* Copy the n least significant limbs of d to A, so that
* A = d if d < N (recall that N has n limbs). */
memcpy(A->p, d, n * ciL);
/* If d >= N then we want to set A to d - N. To prevent timing attacks,
* do the calculation without using conditional tests. */
/* Set d to d0 + (2^biL)^n - N where d0 is the current value of d. */
d[n] += 1;
d[n] -= mpi_sub_hlp(n, d, N->p);
/* If d0 < N then d < (2^biL)^n
* so d[n] == 0 and we want to keep A as it is.
* If d0 >= N then d >= (2^biL)^n, and d <= (2^biL)^n + N < 2 * (2^biL)^n
* so d[n] == 1 and we want to set A to the result of the subtraction
* which is d - (2^biL)^n, i.e. the n least significant limbs of d.
* This exactly corresponds to a conditional assignment. */
mpi_safe_cond_assign(n, A->p, d, (unsigned char) d[n]);
}
/*
* Montgomery reduction: A = A * R^-1 mod N
*
* See mpi_montmul() regarding constraints and guarantees on the parameters.
*/
static void mpi_montred(mbedtls_mpi *A, const mbedtls_mpi *N,
mbedtls_mpi_uint mm, const mbedtls_mpi *T) {
mbedtls_mpi_uint z = 1;
mbedtls_mpi U;
U.n = U.s = (int) z;
U.p = &z;
mpi_montmul(A, &U, N, mm, T);
}
/*
* Sliding-window exponentiation: X = A^E mod N (HAC 14.85)
*/
int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *E, const mbedtls_mpi *N,
mbedtls_mpi *_RR) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t wbits, wsize, one = 1;
size_t i, j, nblimbs;
size_t bufsize, nbits;
mbedtls_mpi_uint ei, mm, state;
mbedtls_mpi RR, T, W[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
int neg;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(E != NULL);
MPI_VALIDATE_RET(N != NULL);
if (mbedtls_mpi_cmp_int(N, 0) <= 0 || (N->p[0] & 1) == 0)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
if (mbedtls_mpi_cmp_int(E, 0) < 0)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
if (mbedtls_mpi_bitlen(E) > MBEDTLS_MPI_MAX_BITS ||
mbedtls_mpi_bitlen(N) > MBEDTLS_MPI_MAX_BITS)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
/*
* Init temps and window size
*/
mpi_montg_init(&mm, N);
mbedtls_mpi_init(&RR);
mbedtls_mpi_init(&T);
mbedtls_mpi_init(&Apos);
memset(W, 0, sizeof(W));
i = mbedtls_mpi_bitlen(E);
wsize = (i > 671) ? 6 : (i > 239) ? 5 :
(i > 79) ? 4 : (i > 23) ? 3 : 1;
#if( MBEDTLS_MPI_WINDOW_SIZE < 6 )
if (wsize > MBEDTLS_MPI_WINDOW_SIZE)
wsize = MBEDTLS_MPI_WINDOW_SIZE;
#endif
j = N->n + 1;
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j));
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[1], j));
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T, j * 2));
/*
* Compensate for negative A (and correct at the end)
*/
neg = (A->s == -1);
if (neg) {
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Apos, A));
Apos.s = 1;
A = &Apos;
}
/*
* If 1st call, pre-compute R^2 mod N
*/
if (_RR == NULL || _RR->p == NULL) {
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&RR, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&RR, N->n * 2 * biL));
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&RR, &RR, N));
if (_RR != NULL)
memcpy(_RR, &RR, sizeof(mbedtls_mpi));
} else
memcpy(&RR, _RR, sizeof(mbedtls_mpi));
/*
* W[1] = A * R^2 * R^-1 mod N = A * R mod N
*/
if (mbedtls_mpi_cmp_mpi(A, N) >= 0)
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&W[1], A, N));
else
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[1], A));
mpi_montmul(&W[1], &RR, N, mm, &T);
/*
* X = R^2 * R^-1 mod N = R mod N
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &RR));
mpi_montred(X, N, mm, &T);
if (wsize > 1) {
/*
* W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
*/
j = one << (wsize - 1);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[j], N->n + 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[j], &W[1]));
for (i = 0; i < wsize - 1; i++)
mpi_montmul(&W[j], &W[j], N, mm, &T);
/*
* W[i] = W[i - 1] * W[1]
*/
for (i = j + 1; i < (one << wsize); i++) {
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[i], N->n + 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[i], &W[i - 1]));
mpi_montmul(&W[i], &W[1], N, mm, &T);
}
}
nblimbs = E->n;
bufsize = 0;
nbits = 0;
wbits = 0;
state = 0;
while (1) {
if (bufsize == 0) {
if (nblimbs == 0)
break;
nblimbs--;
bufsize = sizeof(mbedtls_mpi_uint) << 3;
}
bufsize--;
ei = (E->p[nblimbs] >> bufsize) & 1;
/*
* skip leading 0s
*/
if (ei == 0 && state == 0)
continue;
if (ei == 0 && state == 1) {
/*
* out of window, square X
*/
mpi_montmul(X, X, N, mm, &T);
continue;
}
/*
* add ei to current window
*/
state = 2;
nbits++;
wbits |= (ei << (wsize - nbits));
if (nbits == wsize) {
/*
* X = X^wsize R^-1 mod N
*/
for (i = 0; i < wsize; i++)
mpi_montmul(X, X, N, mm, &T);
/*
* X = X * W[wbits] R^-1 mod N
*/
mpi_montmul(X, &W[wbits], N, mm, &T);
state--;
nbits = 0;
wbits = 0;
}
}
/*
* process the remaining bits
*/
for (i = 0; i < nbits; i++) {
mpi_montmul(X, X, N, mm, &T);
wbits <<= 1;
if ((wbits & (one << wsize)) != 0)
mpi_montmul(X, &W[1], N, mm, &T);
}
/*
* X = A^E * R * R^-1 mod N = A^E mod N
*/
mpi_montred(X, N, mm, &T);
if (neg && E->n != 0 && (E->p[0] & 1) != 0) {
X->s = -1;
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, N, X));
}
cleanup:
for (i = (one << (wsize - 1)); i < (one << wsize); i++)
mbedtls_mpi_free(&W[i]);
mbedtls_mpi_free(&W[1]);
mbedtls_mpi_free(&T);
mbedtls_mpi_free(&Apos);
if (_RR == NULL || _RR->p == NULL)
mbedtls_mpi_free(&RR);
return (ret);
}
/*
* Greatest common divisor: G = gcd(A, B) (HAC 14.54)
*/
int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t lz, lzt;
mbedtls_mpi TA, TB;
MPI_VALIDATE_RET(G != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(B != NULL);
mbedtls_mpi_init(&TA);
mbedtls_mpi_init(&TB);
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TA, A));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, B));
lz = mbedtls_mpi_lsb(&TA);
lzt = mbedtls_mpi_lsb(&TB);
if (lzt < lz)
lz = lzt;
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, lz));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, lz));
TA.s = TB.s = 1;
while (mbedtls_mpi_cmp_int(&TA, 0) != 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, mbedtls_mpi_lsb(&TA)));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, mbedtls_mpi_lsb(&TB)));
if (mbedtls_mpi_cmp_mpi(&TA, &TB) >= 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&TA, &TA, &TB));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, 1));
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&TB, &TB, &TA));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, 1));
}
}
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&TB, lz));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(G, &TB));
cleanup:
mbedtls_mpi_free(&TA);
mbedtls_mpi_free(&TB);
return (ret);
}
/*
* Fill X with size bytes of random.
*
* Use a temporary bytes representation to make sure the result is the same
* regardless of the platform endianness (useful when f_rng is actually
* deterministic, eg for tests).
*/
int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t const limbs = CHARS_TO_LIMBS(size);
size_t const overhead = (limbs * ciL) - size;
unsigned char *Xp;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(f_rng != NULL);
/* Ensure that target MPI has exactly the necessary number of limbs */
if (X->n != limbs) {
mbedtls_mpi_free(X);
mbedtls_mpi_init(X);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, limbs));
}
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));
Xp = (unsigned char *) X->p;
MBEDTLS_MPI_CHK(f_rng(p_rng, Xp + overhead, size));
mpi_bigendian_to_host(X->p, limbs);
cleanup:
return (ret);
}
/*
* Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64)
*/
int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
MPI_VALIDATE_RET(N != NULL);
if (mbedtls_mpi_cmp_int(N, 1) <= 0)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
mbedtls_mpi_init(&TA);
mbedtls_mpi_init(&TU);
mbedtls_mpi_init(&U1);
mbedtls_mpi_init(&U2);
mbedtls_mpi_init(&G);
mbedtls_mpi_init(&TB);
mbedtls_mpi_init(&TV);
mbedtls_mpi_init(&V1);
mbedtls_mpi_init(&V2);
MBEDTLS_MPI_CHK(mbedtls_mpi_gcd(&G, A, N));
if (mbedtls_mpi_cmp_int(&G, 1) != 0) {
ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
goto cleanup;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&TA, A, N));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TU, &TA));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, N));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TV, N));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&U1, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&U2, 0));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&V1, 0));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&V2, 1));
do {
while ((TU.p[0] & 1) == 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TU, 1));
if ((U1.p[0] & 1) != 0 || (U2.p[0] & 1) != 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&U1, &U1, &TB));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U2, &U2, &TA));
}
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&U1, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&U2, 1));
}
while ((TV.p[0] & 1) == 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TV, 1));
if ((V1.p[0] & 1) != 0 || (V2.p[0] & 1) != 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&V1, &V1, &TB));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V2, &V2, &TA));
}
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&V1, 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&V2, 1));
}
if (mbedtls_mpi_cmp_mpi(&TU, &TV) >= 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&TU, &TU, &TV));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U1, &U1, &V1));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U2, &U2, &V2));
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&TV, &TV, &TU));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V1, &V1, &U1));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V2, &V2, &U2));
}
} while (mbedtls_mpi_cmp_int(&TU, 0) != 0);
while (mbedtls_mpi_cmp_int(&V1, 0) < 0)
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&V1, &V1, N));
while (mbedtls_mpi_cmp_mpi(&V1, N) >= 0)
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V1, &V1, N));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &V1));
cleanup:
mbedtls_mpi_free(&TA);
mbedtls_mpi_free(&TU);
mbedtls_mpi_free(&U1);
mbedtls_mpi_free(&U2);
mbedtls_mpi_free(&G);
mbedtls_mpi_free(&TB);
mbedtls_mpi_free(&TV);
mbedtls_mpi_free(&V1);
mbedtls_mpi_free(&V2);
return (ret);
}
#if defined(MBEDTLS_GENPRIME)
static const int small_prime[] = {
3, 5, 7, 11, 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97,
101, 103, 107, 109, 113, 127, 131, 137,
139, 149, 151, 157, 163, 167, 173, 179,
181, 191, 193, 197, 199, 211, 223, 227,
229, 233, 239, 241, 251, 257, 263, 269,
271, 277, 281, 283, 293, 307, 311, 313,
317, 331, 337, 347, 349, 353, 359, 367,
373, 379, 383, 389, 397, 401, 409, 419,
421, 431, 433, 439, 443, 449, 457, 461,
463, 467, 479, 487, 491, 499, 503, 509,
521, 523, 541, 547, 557, 563, 569, 571,
577, 587, 593, 599, 601, 607, 613, 617,
619, 631, 641, 643, 647, 653, 659, 661,
673, 677, 683, 691, 701, 709, 719, 727,
733, 739, 743, 751, 757, 761, 769, 773,
787, 797, 809, 811, 821, 823, 827, 829,
839, 853, 857, 859, 863, 877, 881, 883,
887, 907, 911, 919, 929, 937, 941, 947,
953, 967, 971, 977, 983, 991, 997, -103
};
/*
* Small divisors test (X must be positive)
*
* Return values:
* 0: no small factor (possible prime, more tests needed)
* 1: certain prime
* MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
* other negative: error
*/
static int mpi_check_small_factors(const mbedtls_mpi *X) {
int ret = 0;
size_t i;
mbedtls_mpi_uint r;
if ((X->p[0] & 1) == 0)
return (MBEDTLS_ERR_MPI_NOT_ACCEPTABLE);
for (i = 0; small_prime[i] > 0; i++) {
if (mbedtls_mpi_cmp_int(X, small_prime[i]) <= 0)
return (1);
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, small_prime[i]));
if (r == 0)
return (MBEDTLS_ERR_MPI_NOT_ACCEPTABLE);
}
cleanup:
return (ret);
}
/*
* Miller-Rabin pseudo-primality test (HAC 4.24)
*/
static int mpi_miller_rabin(const mbedtls_mpi *X, size_t rounds,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng) {
int ret, count;
size_t i, j, k, s;
mbedtls_mpi W, R, T, A, RR;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(f_rng != NULL);
mbedtls_mpi_init(&W);
mbedtls_mpi_init(&R);
mbedtls_mpi_init(&T);
mbedtls_mpi_init(&A);
mbedtls_mpi_init(&RR);
/*
* W = |X| - 1
* R = W >> lsb( W )
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(&W, X, 1));
s = mbedtls_mpi_lsb(&W);
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R, &W));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&R, s));
for (i = 0; i < rounds; i++) {
/*
* pick a random A, 1 < A < |X| - 1
*/
count = 0;
do {
MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(&A, X->n * ciL, f_rng, p_rng));
j = mbedtls_mpi_bitlen(&A);
k = mbedtls_mpi_bitlen(&W);
if (j > k) {
A.p[A.n - 1] &= ((mbedtls_mpi_uint) 1 << (k - (A.n - 1) * biL - 1)) - 1;
}
if (count++ > 30) {
ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
goto cleanup;
}
} while (mbedtls_mpi_cmp_mpi(&A, &W) >= 0 ||
mbedtls_mpi_cmp_int(&A, 1) <= 0);
/*
* A = A^R mod |X|
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(&A, &A, &R, X, &RR));
if (mbedtls_mpi_cmp_mpi(&A, &W) == 0 ||
mbedtls_mpi_cmp_int(&A, 1) == 0)
continue;
j = 1;
while (j < s && mbedtls_mpi_cmp_mpi(&A, &W) != 0) {
/*
* A = A * A mod |X|
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&T, &A, &A));
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&A, &T, X));
if (mbedtls_mpi_cmp_int(&A, 1) == 0)
break;
j++;
}
/*
* not prime if A != |X| - 1 or A == 1
*/
if (mbedtls_mpi_cmp_mpi(&A, &W) != 0 ||
mbedtls_mpi_cmp_int(&A, 1) == 0) {
ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
break;
}
}
cleanup:
mbedtls_mpi_free(&W);
mbedtls_mpi_free(&R);
mbedtls_mpi_free(&T);
mbedtls_mpi_free(&A);
mbedtls_mpi_free(&RR);
return (ret);
}
/*
* Pseudo-primality test: small factors, then Miller-Rabin
*/
int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng) {
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi XX;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(f_rng != NULL);
XX.s = 1;
XX.n = X->n;
XX.p = X->p;
if (mbedtls_mpi_cmp_int(&XX, 0) == 0 ||
mbedtls_mpi_cmp_int(&XX, 1) == 0)
return (MBEDTLS_ERR_MPI_NOT_ACCEPTABLE);
if (mbedtls_mpi_cmp_int(&XX, 2) == 0)
return (0);
if ((ret = mpi_check_small_factors(&XX)) != 0) {
if (ret == 1)
return (0);
return (ret);
}
return (mpi_miller_rabin(&XX, rounds, f_rng, p_rng));
}
#if !defined(MBEDTLS_DEPRECATED_REMOVED)
/*
* Pseudo-primality test, error probability 2^-80
*/
int mbedtls_mpi_is_prime(const mbedtls_mpi *X,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng) {
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(f_rng != NULL);
/*
* In the past our key generation aimed for an error rate of at most
* 2^-80. Since this function is deprecated, aim for the same certainty
* here as well.
*/
return (mbedtls_mpi_is_prime_ext(X, 40, f_rng, p_rng));
}
#endif
/*
* Prime number generation
*
* To generate an RSA key in a way recommended by FIPS 186-4, both primes must
* be either 1024 bits or 1536 bits long, and flags must contain
* MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR.
*/
int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng) {
#ifdef MBEDTLS_HAVE_INT64
// ceil(2^63.5)
#define CEIL_MAXUINT_DIV_SQRT2 0xb504f333f9de6485ULL
#else
// ceil(2^31.5)
#define CEIL_MAXUINT_DIV_SQRT2 0xb504f334U
#endif
int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
size_t k, n;
int rounds;
mbedtls_mpi_uint r;
mbedtls_mpi Y;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(f_rng != NULL);
if (nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS)
return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
mbedtls_mpi_init(&Y);
n = BITS_TO_LIMBS(nbits);
if ((flags & MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR) == 0) {
/*
* 2^-80 error probability, number of rounds chosen per HAC, table 4.4
*/
rounds = ((nbits >= 1300) ? 2 : (nbits >= 850) ? 3 :
(nbits >= 650) ? 4 : (nbits >= 350) ? 8 :
(nbits >= 250) ? 12 : (nbits >= 150) ? 18 : 27);
} else {
/*
* 2^-100 error probability, number of rounds computed based on HAC,
* fact 4.48
*/
rounds = ((nbits >= 1450) ? 4 : (nbits >= 1150) ? 5 :
(nbits >= 1000) ? 6 : (nbits >= 850) ? 7 :
(nbits >= 750) ? 8 : (nbits >= 500) ? 13 :
(nbits >= 250) ? 28 : (nbits >= 150) ? 40 : 51);
}
while (1) {
MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(X, n * ciL, f_rng, p_rng));
/* make sure generated number is at least (nbits-1)+0.5 bits (FIPS 186-4 §B.3.3 steps 4.4, 5.5) */
if (X->p[n - 1] < CEIL_MAXUINT_DIV_SQRT2) continue;
k = n * biL;
if (k > nbits) MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(X, k - nbits));
X->p[0] |= 1;
if ((flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH) == 0) {
ret = mbedtls_mpi_is_prime_ext(X, rounds, f_rng, p_rng);
if (ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE)
goto cleanup;
} else {
/*
* An necessary condition for Y and X = 2Y + 1 to be prime
* is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
* Make sure it is satisfied, while keeping X = 3 mod 4
*/
X->p[0] |= 2;
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, 3));
if (r == 0)
MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 8));
else if (r == 1)
MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 4));
/* Set Y = (X-1) / 2, which is X / 2 because X is odd */
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Y, X));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&Y, 1));
while (1) {
/*
* First, check small factors for X and Y
* before doing Miller-Rabin on any of them
*/
if ((ret = mpi_check_small_factors(X)) == 0 &&
(ret = mpi_check_small_factors(&Y)) == 0 &&
(ret = mpi_miller_rabin(X, rounds, f_rng, p_rng))
== 0 &&
(ret = mpi_miller_rabin(&Y, rounds, f_rng, p_rng))
== 0)
goto cleanup;
if (ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE)
goto cleanup;
/*
* Next candidates. We want to preserve Y = (X-1) / 2 and
* Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3)
* so up Y by 6 and X by 12.
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 12));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&Y, &Y, 6));
}
}
}
cleanup:
mbedtls_mpi_free(&Y);
return (ret);
}
#endif /* MBEDTLS_GENPRIME */
#if defined(MBEDTLS_SELF_TEST)
#define GCD_PAIR_COUNT 3
static const int gcd_pairs[GCD_PAIR_COUNT][3] = {
{ 693, 609, 21 },
{ 1764, 868, 28 },
{ 768454923, 542167814, 1 }
};
/*
* Checkup routine
*/
int mbedtls_mpi_self_test(int verbose) {
int ret, i;
mbedtls_mpi A, E, N, X, Y, U, V;
mbedtls_mpi_init(&A);
mbedtls_mpi_init(&E);
mbedtls_mpi_init(&N);
mbedtls_mpi_init(&X);
mbedtls_mpi_init(&Y);
mbedtls_mpi_init(&U);
mbedtls_mpi_init(&V);
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&A, 16,
"EFE021C2645FD1DC586E69184AF4A31E" \
"D5F53E93B5F123FA41680867BA110131" \
"944FE7952E2517337780CB0DB80E61AA" \
"E7C8DDC6C5C6AADEB34EB38A2F40D5E6"));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&E, 16,
"B2E7EFD37075B9F03FF989C7C5051C20" \
"34D2A323810251127E7BF8625A4F49A5" \
"F3E27F4DA8BD59C47D6DAABA4C8127BD" \
"5B5C25763222FEFCCFC38B832366C29E"));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&N, 16,
"0066A198186C18C10B2F5ED9B522752A" \
"9830B69916E535C8F047518A889A43A5" \
"94B6BED27A168D31D4A52F88925AA8F5"));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&X, &A, &N));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16,
"602AB7ECA597A3D6B56FF9829A5E8B85" \
"9E857EA95A03512E2BAE7391688D264A" \
"A5663B0341DB9CCFD2C4C5F421FEC814" \
"8001B72E848A38CAE1C65F78E56ABDEF" \
"E12D3C039B8A02D6BE593F0BBBDA56F1" \
"ECF677152EF804370C1A305CAF3B5BF1" \
"30879B56C61DE584A0F53A2447A51E"));
if (verbose != 0)
mbedtls_printf(" MPI test #1 (mul_mpi): ");
if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) {
if (verbose != 0)
mbedtls_printf("failed\n");
ret = 1;
goto cleanup;
}
if (verbose != 0)
mbedtls_printf("passed\n");
MBEDTLS_MPI_CHK(mbedtls_mpi_div_mpi(&X, &Y, &A, &N));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16,
"256567336059E52CAE22925474705F39A94"));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&V, 16,
"6613F26162223DF488E9CD48CC132C7A" \
"0AC93C701B001B092E4E5B9F73BCD27B" \
"9EE50D0657C77F374E903CDFA4C642"));
if (verbose != 0)
mbedtls_printf(" MPI test #2 (div_mpi): ");
if (mbedtls_mpi_cmp_mpi(&X, &U) != 0 ||
mbedtls_mpi_cmp_mpi(&Y, &V) != 0) {
if (verbose != 0)
mbedtls_printf("failed\n");
ret = 1;
goto cleanup;
}
if (verbose != 0)
mbedtls_printf("passed\n");
MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(&X, &A, &E, &N, NULL));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16,
"36E139AEA55215609D2816998ED020BB" \
"BD96C37890F65171D948E9BC7CBAA4D9" \
"325D24D6A3C12710F10A09FA08AB87"));
if (verbose != 0)
mbedtls_printf(" MPI test #3 (exp_mod): ");
if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) {
if (verbose != 0)
mbedtls_printf("failed\n");
ret = 1;
goto cleanup;
}
if (verbose != 0)
mbedtls_printf("passed\n");
MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&X, &A, &N));
MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16,
"003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
"C3DBA76456363A10869622EAC2DD84EC" \
"C5B8A74DAC4D09E03B5E0BE779F2DF61"));
if (verbose != 0)
mbedtls_printf(" MPI test #4 (inv_mod): ");
if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) {
if (verbose != 0)
mbedtls_printf("failed\n");
ret = 1;
goto cleanup;
}
if (verbose != 0)
mbedtls_printf("passed\n");
if (verbose != 0)
mbedtls_printf(" MPI test #5 (simple gcd): ");
for (i = 0; i < GCD_PAIR_COUNT; i++) {
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&X, gcd_pairs[i][0]));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&Y, gcd_pairs[i][1]));
MBEDTLS_MPI_CHK(mbedtls_mpi_gcd(&A, &X, &Y));
if (mbedtls_mpi_cmp_int(&A, gcd_pairs[i][2]) != 0) {
if (verbose != 0)
mbedtls_printf("failed at %d\n", i);
ret = 1;
goto cleanup;
}
}
if (verbose != 0)
mbedtls_printf("passed\n");
cleanup:
if (ret != 0 && verbose != 0)
mbedtls_printf("Unexpected error, return code = %08X\n", (unsigned int) ret);
mbedtls_mpi_free(&A);
mbedtls_mpi_free(&E);
mbedtls_mpi_free(&N);
mbedtls_mpi_free(&X);
mbedtls_mpi_free(&Y);
mbedtls_mpi_free(&U);
mbedtls_mpi_free(&V);
if (verbose != 0)
mbedtls_printf("\n");
return (ret);
}
#endif /* MBEDTLS_SELF_TEST */
#endif /* MBEDTLS_BIGNUM_C */