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Diffstat (limited to 'externals/mbedtls/library/bignum.c')
| -rw-r--r-- | externals/mbedtls/library/bignum.c | 2956 |
1 files changed, 0 insertions, 2956 deletions
diff --git a/externals/mbedtls/library/bignum.c b/externals/mbedtls/library/bignum.c deleted file mode 100644 index bd352e1bbb..0000000000 --- a/externals/mbedtls/library/bignum.c +++ /dev/null @@ -1,2956 +0,0 @@ -/* - * Multi-precision integer library - * - * Copyright The Mbed TLS Contributors - * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later - * - * This file is provided under the Apache License 2.0, or the - * GNU General Public License v2.0 or later. - * - * ********** - * Apache License 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. - * - * ********** - * - * ********** - * GNU General Public License v2.0 or later: - * - * This program is free software; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation; either version 2 of the License, or - * (at your option) any later version. - * - * This program is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU General Public License for more details. - * - * You should have received a copy of the GNU General Public License along - * with this program; if not, write to the Free Software Foundation, Inc., - * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. - * - * ********** - */ - -/* - * 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 - * - */ - -#if !defined(MBEDTLS_CONFIG_FILE) -#include "mbedtls/config.h" -#else -#include MBEDTLS_CONFIG_FILE -#endif - -#if defined(MBEDTLS_BIGNUM_C) - -#include "mbedtls/bignum.h" -#include "mbedtls/bn_mul.h" -#include "mbedtls/platform_util.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; - 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; - 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] == '-' ) - { - ++s; - sign = -1; - } - - 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++ ) - { - 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_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; - 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, big endian - */ -int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen ) -{ - int ret; - 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: - - return( ret ); -} - -/* - * 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; - 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; - 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; - 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; - 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; - size_t i, n, t, k; - mbedtls_mpi X, Y, Z, T1, T2; - 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 ); mbedtls_mpi_init( &T2 ); - - 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 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T2, 3 ) ); - - 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); - } - - 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] ) ); - - MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T2, 0 ) ); - 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]; - } - 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_mpi_free( &T2 ); - - 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; - 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; - 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; - size_t lz, lzt; - mbedtls_mpi TG, TA, TB; - - MPI_VALIDATE_RET( G != NULL ); - MPI_VALIDATE_RET( A != NULL ); - MPI_VALIDATE_RET( B != NULL ); - - mbedtls_mpi_init( &TG ); 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( &TG ); 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; - 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_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_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", 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 */ |