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mbedtls/library/bignum.c
Dave Rodgman e3c05853d6 Header updates 
Signed-off-by: Dave Rodgman <dave.rodgman@arm.com>
2023-11-03 12:21:36 +00:00

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/*
* Multi-precision integer library
*
* Copyright The Mbed TLS Contributors
* SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
*/
/*
* 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 "bignum_core.h"
#include "bn_mul.h"
#include "mbedtls/platform_util.h"
#include "mbedtls/error.h"
#include "constant_time_internal.h"
#include <limits.h>
#include <string.h>
#include "mbedtls/platform.h"
#define MPI_VALIDATE_RET(cond) \
MBEDTLS_INTERNAL_VALIDATE_RET(cond, MBEDTLS_ERR_MPI_BAD_INPUT_DATA)
#define MPI_VALIDATE(cond) \
MBEDTLS_INTERNAL_VALIDATE(cond)
/*
* Compare signed values in constant time
*/
int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X,
const mbedtls_mpi *Y,
unsigned *ret)
{
mbedtls_ct_condition_t different_sign, X_is_negative, Y_is_negative, result;
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 N_is_negative to MBEDTLS_CT_FALSE if N >= 0, MBEDTLS_CT_TRUE if N < 0.
* We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0.
*/
X_is_negative = mbedtls_ct_bool((X->s & 2) >> 1);
Y_is_negative = mbedtls_ct_bool((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).
*/
different_sign = mbedtls_ct_bool_ne(X_is_negative, Y_is_negative); // true if different sign
result = mbedtls_ct_bool_and(different_sign, X_is_negative);
/*
* Assuming signs are the same, compare X and Y. We switch the comparison
* order if they are negative so that we get the right result, regardles of
* sign.
*/
/* This array is used to conditionally swap the pointers in const time */
void * const p[2] = { X->p, Y->p };
size_t i = mbedtls_ct_size_if_else_0(X_is_negative, 1);
mbedtls_ct_condition_t lt = mbedtls_mpi_core_lt_ct(p[i], p[i ^ 1], X->n);
/*
* Store in result iff the signs are the same (i.e., iff different_sign == false). If
* the signs differ, result has already been set, so we don't change it.
*/
result = mbedtls_ct_bool_or(result,
mbedtls_ct_bool_and(mbedtls_ct_bool_not(different_sign), lt));
*ret = mbedtls_ct_uint_if_else_0(result, 1);
return 0;
}
/*
* 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.)
*/
#if defined(_MSC_VER) && defined(_M_ARM64) && (_MSC_FULL_VER < 193131103)
/*
* MSVC miscompiles this function if it's inlined prior to Visual Studio 2022 version 17.1. See:
* https://developercommunity.visualstudio.com/t/c-compiler-miscompiles-part-of-mbedtls-library-on/1646989
*/
__declspec(noinline)
#endif
int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X,
const mbedtls_mpi *Y,
unsigned char assign)
{
int ret = 0;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(Y != NULL);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n));
{
mbedtls_ct_condition_t do_assign = mbedtls_ct_bool(assign);
X->s = (int) mbedtls_ct_uint_if(do_assign, Y->s, X->s);
mbedtls_mpi_core_cond_assign(X->p, Y->p, Y->n, do_assign);
mbedtls_ct_condition_t do_not_assign = mbedtls_ct_bool_not(do_assign);
for (size_t i = Y->n; i < X->n; i++) {
X->p[i] = mbedtls_ct_mpi_uint_if_else_0(do_not_assign, X->p[i]);
}
}
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 would 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 = 0;
int s;
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(Y != NULL);
if (X == Y) {
return 0;
}
mbedtls_ct_condition_t do_swap = mbedtls_ct_bool(swap);
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n));
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Y, X->n));
s = X->s;
X->s = (int) mbedtls_ct_uint_if(do_swap, Y->s, X->s);
Y->s = (int) mbedtls_ct_uint_if(do_swap, s, Y->s);
mbedtls_mpi_core_cond_swap(X->p, Y->p, X->n, do_swap);
cleanup:
return ret;
}
/* Implementation that should never be optimized out by the compiler */
#define mbedtls_mpi_zeroize_and_free(v, n) mbedtls_zeroize_and_free(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_and_free(X->p, X->n);
}
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_and_free(X->p, X->n);
}
/* nblimbs fits in n because we ensure that MBEDTLS_MPI_MAX_LIMBS
* fits, and we've checked that nblimbs <= MBEDTLS_MPI_MAX_LIMBS. */
X->n = (unsigned short) 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_and_free(X->p, X->n);
}
/* i fits in n because we ensure that MBEDTLS_MPI_MAX_LIMBS
* fits, and we've checked that i <= nblimbs <= MBEDTLS_MPI_MAX_LIMBS. */
X->n = (unsigned short) i;
X->p = p;
return 0;
}
/* Resize X to have exactly n limbs and set it to 0. */
static int mbedtls_mpi_resize_clear(mbedtls_mpi *X, size_t limbs)
{
if (limbs == 0) {
mbedtls_mpi_free(X);
return 0;
} else if (X->n == limbs) {
memset(X->p, 0, limbs * ciL);
X->s = 1;
return 0;
} else {
mbedtls_mpi_free(X);
return mbedtls_mpi_grow(X, limbs);
}
}
/*
* Copy the contents of Y into X.
*
* This function is not constant-time. Leading zeros in Y may be removed.
*
* Ensure that X does not shrink. This is not guaranteed by the public API,
* but some code in the bignum module relies on this property, for example
* in mbedtls_mpi_exp_mod().
*/
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) {
if (X->n != 0) {
X->s = 1;
memset(X->p, 0, X->n * ciL);
}
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));
}
static inline mbedtls_mpi_uint mpi_sint_abs(mbedtls_mpi_sint z)
{
if (z >= 0) {
return z;
}
/* Take care to handle the most negative value (-2^(biL-1)) correctly.
* A naive -z would have undefined behavior.
* Write this in a way that makes popular compilers happy (GCC, Clang,
* MSVC). */
return (mbedtls_mpi_uint) 0 - (mbedtls_mpi_uint) z;
}
/* Convert x to a sign, i.e. to 1, if x is positive, or -1, if x is negative.
* This looks awkward but generates smaller code than (x < 0 ? -1 : 1) */
#define TO_SIGN(x) ((mbedtls_mpi_sint) (((mbedtls_mpi_uint) x) >> (biL - 1)) * -2 + 1)
/*
* 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] = mpi_sint_abs(z);
X->s = TO_SIGN(z);
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;
}
/*
* 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;
MBEDTLS_INTERNAL_VALIDATE_RET(X != NULL, 0);
#if defined(__has_builtin)
#if (MBEDTLS_MPI_UINT_MAX == UINT_MAX) && __has_builtin(__builtin_ctz)
#define mbedtls_mpi_uint_ctz __builtin_ctz
#elif (MBEDTLS_MPI_UINT_MAX == ULONG_MAX) && __has_builtin(__builtin_ctzl)
#define mbedtls_mpi_uint_ctz __builtin_ctzl
#elif (MBEDTLS_MPI_UINT_MAX == ULLONG_MAX) && __has_builtin(__builtin_ctzll)
#define mbedtls_mpi_uint_ctz __builtin_ctzll
#endif
#endif
#if defined(mbedtls_mpi_uint_ctz)
for (i = 0; i < X->n; i++) {
if (X->p[i] != 0) {
return i * biL + mbedtls_mpi_uint_ctz(X->p[i]);
}
}
#else
size_t count = 0;
for (i = 0; i < X->n; i++) {
for (size_t j = 0; j < biL; j++, count++) {
if (((X->p[i] >> j) & 1) != 0) {
return count;
}
}
}
#endif
return 0;
}
/*
* Return the number of bits
*/
size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X)
{
return mbedtls_mpi_core_bitlen(X->p, X->n);
}
/*
* 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;
int sign = 1;
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);
if (s[0] == 0) {
mbedtls_mpi_free(X);
return 0;
}
if (s[0] == '-') {
++s;
sign = -1;
}
slen = strlen(s);
if (radix == 16) {
if (slen > SIZE_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++) {
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++) {
MBEDTLS_MPI_CHK(mpi_get_digit(&d, radix, s[i]));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T, X, radix));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, &T, d));
}
}
if (sign < 0 && mbedtls_mpi_bitlen(X) != 0) {
X->s = -1;
}
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 */
/*
* Import X from unsigned binary data, little endian
*
* This function is guaranteed to return an MPI with exactly the necessary
* number of limbs (in particular, it does not skip 0s in the input).
*/
int mbedtls_mpi_read_binary_le(mbedtls_mpi *X,
const unsigned char *buf, size_t buflen)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
const size_t limbs = CHARS_TO_LIMBS(buflen);
/* Ensure that target MPI has exactly the necessary number of limbs */
MBEDTLS_MPI_CHK(mbedtls_mpi_resize_clear(X, limbs));
MBEDTLS_MPI_CHK(mbedtls_mpi_core_read_le(X->p, X->n, buf, buflen));
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
*
* This function is guaranteed to return an MPI with exactly the necessary
* number of limbs (in particular, it does not skip 0s in the input).
*/
int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
const size_t limbs = CHARS_TO_LIMBS(buflen);
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(buflen == 0 || buf != NULL);
/* Ensure that target MPI has exactly the necessary number of limbs */
MBEDTLS_MPI_CHK(mbedtls_mpi_resize_clear(X, limbs));
MBEDTLS_MPI_CHK(mbedtls_mpi_core_read_be(X->p, X->n, buf, buflen));
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)
{
return mbedtls_mpi_core_write_le(X->p, X->n, buf, buflen);
}
/*
* Export X into unsigned binary data, big endian
*/
int mbedtls_mpi_write_binary(const mbedtls_mpi *X,
unsigned char *buf, size_t buflen)
{
return mbedtls_mpi_core_write_be(X->p, X->n, buf, buflen);
}
/*
* 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;
MPI_VALIDATE_RET(X != NULL);
i = mbedtls_mpi_bitlen(X) + count;
if (X->n * biL < i) {
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, BITS_TO_LIMBS(i)));
}
ret = 0;
mbedtls_mpi_core_shift_l(X->p, X->n, count);
cleanup:
return ret;
}
/*
* Right-shift: X >>= count
*/
int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count)
{
MPI_VALIDATE_RET(X != NULL);
if (X->n != 0) {
mbedtls_mpi_core_shift_r(X->p, X->n, count);
}
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 == j == 0, i.e. abs(X) == abs(Y),
* we end up returning 0 at the end of the function. */
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;
}
/*
* 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 = mpi_sint_abs(z);
Y.s = TO_SIGN(z);
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 j;
mbedtls_mpi_uint *p;
mbedtls_mpi_uint c;
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 must 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;
}
}
/* Exit early to avoid undefined behavior on NULL+0 when X->n == 0
* and B is 0 (of any size). */
if (j == 0) {
return 0;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j));
/* j is the number of non-zero limbs of B. Add those to X. */
p = X->p;
c = mbedtls_mpi_core_add(p, p, B->p, j);
p += j;
/* Now propagate any carry */
while (c != 0) {
if (j >= X->n) {
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j + 1));
p = X->p + j;
}
*p += c; c = (*p < c); j++; p++;
}
cleanup:
return ret;
}
/*
* 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)
{
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);
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;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, A->n));
/* Set the high limbs of X to match A. Don't touch the lower limbs
* because X might be aliased to B, and we must not overwrite the
* significant digits of B. */
if (A->n > n && A != X) {
memcpy(X->p + n, A->p + n, (A->n - n) * ciL);
}
if (X->n > A->n) {
memset(X->p + A->n, 0, (X->n - A->n) * ciL);
}
carry = mbedtls_mpi_core_sub(X->p, A->p, B->p, n);
if (carry != 0) {
/* Propagate the carry through the rest of X. */
carry = mbedtls_mpi_core_sub_int(X->p + n, X->p + n, carry, X->n - n);
/* If we have further carry/borrow, the result is negative. */
if (carry != 0) {
ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
goto cleanup;
}
}
/* X should always be positive as a result of unsigned subtractions. */
X->s = 1;
cleanup:
return ret;
}
/* Common function for signed addition and subtraction.
* Calculate A + B * flip_B where flip_B is 1 or -1.
*/
static int add_sub_mpi(mbedtls_mpi *X,
const mbedtls_mpi *A, const mbedtls_mpi *B,
int flip_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 * flip_B < 0) {
int cmp = mbedtls_mpi_cmp_abs(A, B);
if (cmp >= 0) {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, A, B));
/* If |A| = |B|, the result is 0 and we must set the sign bit
* to +1 regardless of which of A or B was negative. Otherwise,
* since |A| > |B|, the sign is the sign of A. */
X->s = cmp == 0 ? 1 : s;
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, B, A));
/* Since |A| < |B|, the sign is the opposite of 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_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
return add_sub_mpi(X, A, B, 1);
}
/*
* Signed subtraction: X = A - B
*/
int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
return add_sub_mpi(X, A, B, -1);
}
/*
* 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] = mpi_sint_abs(b);
B.s = TO_SIGN(b);
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] = mpi_sint_abs(b);
B.s = TO_SIGN(b);
B.n = 1;
B.p = p;
return mbedtls_mpi_sub_mpi(X, A, &B);
}
/*
* 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;
int result_is_zero = 0;
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;
}
}
if (i == 0) {
result_is_zero = 1;
}
for (j = B->n; j > 0; j--) {
if (B->p[j - 1] != 0) {
break;
}
}
if (j == 0) {
result_is_zero = 1;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i + j));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));
mbedtls_mpi_core_mul(X->p, A->p, i, B->p, j);
/* If the result is 0, we don't shortcut the operation, which reduces
* but does not eliminate side channels leaking the zero-ness. We do
* need to take care to set the sign bit properly since the library does
* not fully support an MPI object with a value of 0 and s == -1. */
if (result_is_zero) {
X->s = 1;
} else {
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)
{
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(A != NULL);
size_t n = A->n;
while (n > 0 && A->p[n - 1] == 0) {
--n;
}
/* The general method below doesn't work if b==0. */
if (b == 0 || n == 0) {
return mbedtls_mpi_lset(X, 0);
}
/* Calculate A*b as A + A*(b-1) to take advantage of mbedtls_mpi_core_mla */
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
/* In general, A * b requires 1 limb more than b. If
* A->p[n - 1] * b / b == A->p[n - 1], then A * b fits in the same
* number of limbs as A and the call to grow() is not required since
* copy() will take care of the growth if needed. However, experimentally,
* making the call to grow() unconditional causes slightly fewer
* calls to calloc() in ECP code, presumably because it reuses the
* same mpi for a while and this way the mpi is more likely to directly
* grow to its final size.
*
* Note that calculating A*b as 0 + A*b doesn't work as-is because
* A,X can be the same. */
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, n + 1));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A));
mbedtls_mpi_core_mla(X->p, X->n, A->p, n, b - 1);
cleanup:
return ret;
}
/*
* 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 = ~(mbedtls_mpi_uint) 0u;
}
return ~(mbedtls_mpi_uint) 0u;
}
#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_mpi_core_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, A->n + 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] = ~(mbedtls_mpi_uint) 0u;
} 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] = mpi_sint_abs(b);
B.s = TO_SIGN(b);
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 || A->n == 0) {
*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;
}
static void mpi_montg_init(mbedtls_mpi_uint *mm, const mbedtls_mpi *N)
{
*mm = mbedtls_mpi_core_montmul_init(N->p);
}
/** 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 modulus. \p 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 1
* (T->n >= 2 * N->n + 1).
* Its initial content is unused and
* its final content is indeterminate.
* It does not get reallocated.
*/
static void mpi_montmul(mbedtls_mpi *A, const mbedtls_mpi *B,
const mbedtls_mpi *N, mbedtls_mpi_uint mm,
mbedtls_mpi *T)
{
mbedtls_mpi_core_montmul(A->p, A->p, B->p, B->n, N->p, N->n, mm, T->p);
}
/*
* 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, mbedtls_mpi *T)
{
mbedtls_mpi_uint z = 1;
mbedtls_mpi U;
U.n = 1;
U.s = 1;
U.p = &z;
mpi_montmul(A, &U, N, mm, T);
}
/**
* Select an MPI from a table without leaking the index.
*
* This is functionally equivalent to mbedtls_mpi_copy(R, T[idx]) except it
* reads the entire table in order to avoid leaking the value of idx to an
* attacker able to observe memory access patterns.
*
* \param[out] R Where to write the selected MPI.
* \param[in] T The table to read from.
* \param[in] T_size The number of elements in the table.
* \param[in] idx The index of the element to select;
* this must satisfy 0 <= idx < T_size.
*
* \return \c 0 on success, or a negative error code.
*/
static int mpi_select(mbedtls_mpi *R, const mbedtls_mpi *T, size_t T_size, size_t idx)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
for (size_t i = 0; i < T_size; i++) {
MBEDTLS_MPI_CHK(mbedtls_mpi_safe_cond_assign(R, &T[i],
(unsigned char) mbedtls_ct_uint_eq(i, idx)));
}
cleanup:
return ret;
}
/*
* 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 *prec_RR)
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t window_bitsize;
size_t i, j, nblimbs;
size_t bufsize, nbits;
size_t exponent_bits_in_window = 0;
mbedtls_mpi_uint ei, mm, state;
mbedtls_mpi RR, T, W[(size_t) 1 << MBEDTLS_MPI_WINDOW_SIZE], WW, 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);
mbedtls_mpi_init(&WW);
memset(W, 0, sizeof(W));
i = mbedtls_mpi_bitlen(E);
window_bitsize = (i > 671) ? 6 : (i > 239) ? 5 :
(i > 79) ? 4 : (i > 23) ? 3 : 1;
#if (MBEDTLS_MPI_WINDOW_SIZE < 6)
if (window_bitsize > MBEDTLS_MPI_WINDOW_SIZE) {
window_bitsize = MBEDTLS_MPI_WINDOW_SIZE;
}
#endif
const size_t w_table_used_size = (size_t) 1 << window_bitsize;
/*
* This function is not constant-trace: its memory accesses depend on the
* exponent value. To defend against timing attacks, callers (such as RSA
* and DHM) should use exponent blinding. However this is not enough if the
* adversary can find the exponent in a single trace, so this function
* takes extra precautions against adversaries who can observe memory
* access patterns.
*
* This function performs a series of multiplications by table elements and
* squarings, and we want the prevent the adversary from finding out which
* table element was used, and from distinguishing between multiplications
* and squarings. Firstly, when multiplying by an element of the window
* W[i], we do a constant-trace table lookup to obfuscate i. This leaves
* squarings as having a different memory access patterns from other
* multiplications. So secondly, we put the accumulator in the table as
* well, and also do a constant-trace table lookup to multiply by the
* accumulator which is W[x_index].
*
* This way, all multiplications take the form of a lookup-and-multiply.
* The number of lookup-and-multiply operations inside each iteration of
* the main loop still depends on the bits of the exponent, but since the
* other operations in the loop don't have an easily recognizable memory
* trace, an adversary is unlikely to be able to observe the exact
* patterns.
*
* An adversary may still be able to recover the exponent if they can
* observe both memory accesses and branches. However, branch prediction
* exploitation typically requires many traces of execution over the same
* data, which is defeated by randomized blinding.
*/
const size_t x_index = 0;
mbedtls_mpi_init(&W[x_index]);
j = N->n + 1;
/* All W[i] including the accumulator must have at least N->n limbs for
* the mpi_montmul() and mpi_montred() calls later. Here we ensure that
* W[1] and the accumulator W[x_index] are large enough. later we'll grow
* other W[i] to the same length. They must not be shrunk midway through
* this function!
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[x_index], 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 (prec_RR == NULL || prec_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 (prec_RR != NULL) {
memcpy(prec_RR, &RR, sizeof(mbedtls_mpi));
}
} else {
memcpy(&RR, prec_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));
/* This should be a no-op because W[1] is already that large before
* mbedtls_mpi_mod_mpi(), but it's necessary to avoid an overflow
* in mpi_montmul() below, so let's make sure. */
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[1], N->n + 1));
} else {
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[1], A));
}
/* Note that this is safe because W[1] always has at least N->n limbs
* (it grew above and was preserved by mbedtls_mpi_copy()). */
mpi_montmul(&W[1], &RR, N, mm, &T);
/*
* W[x_index] = R^2 * R^-1 mod N = R mod N
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[x_index], &RR));
mpi_montred(&W[x_index], N, mm, &T);
if (window_bitsize > 1) {
/*
* W[i] = W[1] ^ i
*
* The first bit of the sliding window is always 1 and therefore we
* only need to store the second half of the table.
*
* (There are two special elements in the table: W[0] for the
* accumulator/result and W[1] for A in Montgomery form. Both of these
* are already set at this point.)
*/
j = w_table_used_size / 2;
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 < window_bitsize - 1; i++) {
mpi_montmul(&W[j], &W[j], N, mm, &T);
}
/*
* W[i] = W[i - 1] * W[1]
*/
for (i = j + 1; i < w_table_used_size; 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;
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 W[x_index]
*/
MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size, x_index));
mpi_montmul(&W[x_index], &WW, N, mm, &T);
continue;
}
/*
* add ei to current window
*/
state = 2;
nbits++;
exponent_bits_in_window |= (ei << (window_bitsize - nbits));
if (nbits == window_bitsize) {
/*
* W[x_index] = W[x_index]^window_bitsize R^-1 mod N
*/
for (i = 0; i < window_bitsize; i++) {
MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size,
x_index));
mpi_montmul(&W[x_index], &WW, N, mm, &T);
}
/*
* W[x_index] = W[x_index] * W[exponent_bits_in_window] R^-1 mod N
*/
MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size,
exponent_bits_in_window));
mpi_montmul(&W[x_index], &WW, N, mm, &T);
state--;
nbits = 0;
exponent_bits_in_window = 0;
}
}
/*
* process the remaining bits
*/
for (i = 0; i < nbits; i++) {
MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size, x_index));
mpi_montmul(&W[x_index], &WW, N, mm, &T);
exponent_bits_in_window <<= 1;
if ((exponent_bits_in_window & ((size_t) 1 << window_bitsize)) != 0) {
MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size, 1));
mpi_montmul(&W[x_index], &WW, N, mm, &T);
}
}
/*
* W[x_index] = A^E * R * R^-1 mod N = A^E mod N
*/
mpi_montred(&W[x_index], N, mm, &T);
if (neg && E->n != 0 && (E->p[0] & 1) != 0) {
W[x_index].s = -1;
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&W[x_index], N, &W[x_index]));
}
/*
* Load the result in the output variable.
*/
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &W[x_index]));
cleanup:
/* The first bit of the sliding window is always 1 and therefore the first
* half of the table was unused. */
for (i = w_table_used_size/2; i < w_table_used_size; i++) {
mbedtls_mpi_free(&W[i]);
}
mbedtls_mpi_free(&W[x_index]);
mbedtls_mpi_free(&W[1]);
mbedtls_mpi_free(&T);
mbedtls_mpi_free(&Apos);
mbedtls_mpi_free(&WW);
if (prec_RR == NULL || prec_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);
/* The loop below gives the correct result when A==0 but not when B==0.
* So have a special case for B==0. Leverage the fact that we just
* calculated the lsb and lsb(B)==0 iff B is odd or 0 to make the test
* slightly more efficient than cmp_int(). */
if (lzt == 0 && mbedtls_mpi_get_bit(&TB, 0) == 0) {
ret = mbedtls_mpi_copy(G, A);
goto cleanup;
}
if (lzt < lz) {
lz = lzt;
}
TA.s = TB.s = 1;
/* We mostly follow the procedure described in HAC 14.54, but with some
* minor differences:
* - Sequences of multiplications or divisions by 2 are grouped into a
* single shift operation.
* - The procedure in HAC assumes that 0 < TB <= TA.
* - The condition TB <= TA is not actually necessary for correctness.
* TA and TB have symmetric roles except for the loop termination
* condition, and the shifts at the beginning of the loop body
* remove any significance from the ordering of TA vs TB before
* the shifts.
* - If TA = 0, the loop goes through 0 iterations and the result is
* correctly TB.
* - The case TB = 0 was short-circuited above.
*
* For the correctness proof below, decompose the original values of
* A and B as
* A = sa * 2^a * A' with A'=0 or A' odd, and sa = +-1
* B = sb * 2^b * B' with B'=0 or B' odd, and sb = +-1
* Then gcd(A, B) = 2^{min(a,b)} * gcd(A',B'),
* and gcd(A',B') is odd or 0.
*
* At the beginning, we have TA = |A| and TB = |B| so gcd(A,B) = gcd(TA,TB).
* The code maintains the following invariant:
* gcd(A,B) = 2^k * gcd(TA,TB) for some k (I)
*/
/* Proof that the loop terminates:
* At each iteration, either the right-shift by 1 is made on a nonzero
* value and the nonnegative integer bitlen(TA) + bitlen(TB) decreases
* by at least 1, or the right-shift by 1 is made on zero and then
* TA becomes 0 which ends the loop (TB cannot be 0 if it is right-shifted
* since in that case TB is calculated from TB-TA with the condition TB>TA).
*/
while (mbedtls_mpi_cmp_int(&TA, 0) != 0) {
/* Divisions by 2 preserve the invariant (I). */
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, mbedtls_mpi_lsb(&TA)));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, mbedtls_mpi_lsb(&TB)));
/* Set either TA or TB to |TA-TB|/2. Since TA and TB are both odd,
* TA-TB is even so the division by 2 has an integer result.
* Invariant (I) is preserved since any odd divisor of both TA and TB
* also divides |TA-TB|/2, and any odd divisor of both TA and |TA-TB|/2
* also divides TB, and any odd divisor of both TB and |TA-TB|/2 also
* divides TA.
*/
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));
}
/* Note that one of TA or TB is still odd. */
}
/* By invariant (I), gcd(A,B) = 2^k * gcd(TA,TB) for some k.
* At the loop exit, TA = 0, so gcd(TA,TB) = TB.
* - If there was at least one loop iteration, then one of TA or TB is odd,
* and TA = 0, so TB is odd and gcd(TA,TB) = gcd(A',B'). In this case,
* lz = min(a,b) so gcd(A,B) = 2^lz * TB.
* - If there was no loop iteration, then A was 0, and gcd(A,B) = B.
* In this case, lz = 0 and B = TB so gcd(A,B) = B = 2^lz * TB as well.
*/
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.
* The bytes returned from the RNG are used in a specific order which
* is suitable for deterministic ECDSA (see the specification of
* mbedtls_mpi_random() and the implementation in mbedtls_mpi_fill_random()).
*/
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;
const size_t limbs = CHARS_TO_LIMBS(size);
MPI_VALIDATE_RET(X != NULL);
MPI_VALIDATE_RET(f_rng != NULL);
/* Ensure that target MPI has exactly the necessary number of limbs */
MBEDTLS_MPI_CHK(mbedtls_mpi_resize_clear(X, limbs));
if (size == 0) {
return 0;
}
ret = mbedtls_mpi_core_fill_random(X->p, X->n, size, f_rng, p_rng);
cleanup:
return ret;
}
int mbedtls_mpi_random(mbedtls_mpi *X,
mbedtls_mpi_sint min,
const mbedtls_mpi *N,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng)
{
if (min < 0) {
return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
}
if (mbedtls_mpi_cmp_int(N, min) <= 0) {
return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
}
/* Ensure that target MPI has exactly the same number of limbs
* as the upper bound, even if the upper bound has leading zeros.
* This is necessary for mbedtls_mpi_core_random. */
int ret = mbedtls_mpi_resize_clear(X, N->n);
if (ret != 0) {
return ret;
}
return mbedtls_mpi_core_random(X->p, min, N->p, X->n, f_rng, p_rng);
}
/*
* 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)
/* Gaps between primes, starting at 3. https://oeis.org/A001223 */
static const unsigned char small_prime_gaps[] = {
2, 2, 4, 2, 4, 2, 4, 6,
2, 6, 4, 2, 4, 6, 6, 2,
6, 4, 2, 6, 4, 6, 8, 4,
2, 4, 2, 4, 14, 4, 6, 2,
10, 2, 6, 6, 4, 6, 6, 2,
10, 2, 4, 2, 12, 12, 4, 2,
4, 6, 2, 10, 6, 6, 6, 2,
6, 4, 2, 10, 14, 4, 2, 4,
14, 6, 10, 2, 4, 6, 8, 6,
6, 4, 6, 8, 4, 8, 10, 2,
10, 2, 6, 4, 6, 8, 4, 2,
4, 12, 8, 4, 8, 4, 6, 12,
2, 18, 6, 10, 6, 6, 2, 6,
10, 6, 6, 2, 6, 6, 4, 2,
12, 10, 2, 4, 6, 6, 2, 12,
4, 6, 8, 10, 8, 10, 8, 6,
6, 4, 8, 6, 4, 8, 4, 14,
10, 12, 2, 10, 2, 4, 2, 10,
14, 4, 2, 4, 14, 4, 2, 4,
20, 4, 8, 10, 8, 4, 6, 6,
14, 4, 6, 6, 8, 6, /*reaches 997*/
0 /* the last entry is effectively unused */
};
/*
* 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;
unsigned p = 3; /* The first odd prime */
if ((X->p[0] & 1) == 0) {
return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
}
for (i = 0; i < sizeof(small_prime_gaps); p += small_prime_gaps[i], i++) {
MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, p));
if (r == 0) {
if (mbedtls_mpi_cmp_int(X, p) == 0) {
return 1;
} else {
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);
}
/*
* 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 {
/*
* A 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 */
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