/* | |
* Multi-precision integer library | |
* | |
* Copyright (C) 2006-2015, ARM Limited, All Rights Reserved | |
* SPDX-License-Identifier: Apache-2.0 | |
* | |
* Licensed under the Apache License, Version 2.0 (the "License"); you may | |
* not use this file except in compliance with the License. | |
* You may obtain a copy of the License at | |
* | |
* http://www.apache.org/licenses/LICENSE-2.0 | |
* | |
* Unless required by applicable law or agreed to in writing, software | |
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT | |
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
* See the License for the specific language governing permissions and | |
* limitations under the License. | |
* | |
* This file is part of mbed TLS (https://tls.mbed.org) | |
*/ | |
/* | |
* 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 in this case */ | |
if( X->n <= nblimbs ) | |
return( mbedtls_mpi_grow( X, nblimbs ) ); | |
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->p == NULL ) | |
{ | |
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 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; | |
for( i = 0; i < Y->n; i++ ) | |
X->p[i] = X->p[i] * ( 1 - assign ) + Y->p[i] * assign; | |
for( ; 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; | |
mbedtls_mpi_uint d; | |
mbedtls_mpi T; | |
MPI_VALIDATE_RET( X != NULL ); | |
MPI_VALIDATE_RET( s != NULL ); | |
if( radix < 2 || radix > 16 ) | |
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); | |
mbedtls_mpi_init( &T ); | |
slen = strlen( s ); | |
if( radix == 16 ) | |
{ | |
if( slen > MPI_SIZE_T_MAX >> 2 ) | |
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); | |
n = BITS_TO_LIMBS( slen << 2 ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); | |
for( i = slen, j = 0; i > 0; i--, j++ ) | |
{ | |
if( i == 1 && s[i - 1] == '-' ) | |
{ | |
X->s = -1; | |
break; | |
} | |
MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) ); | |
X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 ); | |
} | |
} | |
else | |
{ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); | |
for( i = 0; i < slen; i++ ) | |
{ | |
if( i == 0 && s[i] == '-' ) | |
{ | |
X->s = -1; | |
continue; | |
} | |
MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) ); | |
if( X->s == 1 ) | |
{ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) ); | |
} | |
else | |
{ | |
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, &T, d ) ); | |
} | |
} | |
} | |
cleanup: | |
mbedtls_mpi_free( &T ); | |
return( ret ); | |
} | |
/* | |
* Helper to write the digits high-order first. | |
*/ | |
static int mpi_write_hlp( mbedtls_mpi *X, int radix, | |
char **p, const size_t buflen ) | |
{ | |
int ret; | |
mbedtls_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; | |
mbedtls_mpi_uint tmp = 0; | |
/* This works regardless of the endianness. */ | |
for( i = 0; i < ciL; i++, x >>= 8 ) | |
tmp |= ( x & 0xFF ) << ( ( ciL - 1 - i ) << 3 ); | |
return( tmp ); | |
} | |
static mbedtls_mpi_uint mpi_uint_bigendian_to_host( mbedtls_mpi_uint x ) | |
{ | |
#if defined(__BYTE_ORDER__) | |
/* Nothing to do on bigendian systems. */ | |
#if ( __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ ) | |
return( x ); | |
#endif /* __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ */ | |
#if ( __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ ) | |
/* For GCC and Clang, have builtins for byte swapping. */ | |
#if defined(__GNUC__) && defined(__GNUC_PREREQ) | |
#if __GNUC_PREREQ(4,3) | |
#define have_bswap | |
#endif | |
#endif | |
#if defined(__clang__) && defined(__has_builtin) | |
#if __has_builtin(__builtin_bswap32) && \ | |
__has_builtin(__builtin_bswap64) | |
#define have_bswap | |
#endif | |
#endif | |
#if defined(have_bswap) | |
/* The compiler is hopefully able to statically evaluate this! */ | |
switch( sizeof(mbedtls_mpi_uint) ) | |
{ | |
case 4: | |
return( __builtin_bswap32(x) ); | |
case 8: | |
return( __builtin_bswap64(x) ); | |
} | |
#endif | |
#endif /* __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ */ | |
#endif /* __BYTE_ORDER__ */ | |
/* Fall back to C-based reordering if we don't know the byte order | |
* or we couldn't use a compiler-specific builtin. */ | |
return( mpi_uint_bigendian_to_host_c( x ) ); | |
} | |
static void mpi_bigendian_to_host( mbedtls_mpi_uint * const p, size_t limbs ) | |
{ | |
mbedtls_mpi_uint *cur_limb_left; | |
mbedtls_mpi_uint *cur_limb_right; | |
if( limbs == 0 ) | |
return; | |
/* | |
* Traverse limbs and | |
* - adapt byte-order in each limb | |
* - swap the limbs themselves. | |
* For that, simultaneously traverse the limbs from left to right | |
* and from right to left, as long as the left index is not bigger | |
* than the right index (it's not a problem if limbs is odd and the | |
* indices coincide in the last iteration). | |
*/ | |
for( cur_limb_left = p, cur_limb_right = p + ( limbs - 1 ); | |
cur_limb_left <= cur_limb_right; | |
cur_limb_left++, cur_limb_right-- ) | |
{ | |
mbedtls_mpi_uint tmp; | |
/* Note that if cur_limb_left == cur_limb_right, | |
* this code effectively swaps the bytes only once. */ | |
tmp = mpi_uint_bigendian_to_host( *cur_limb_left ); | |
*cur_limb_left = mpi_uint_bigendian_to_host( *cur_limb_right ); | |
*cur_limb_right = tmp; | |
} | |
} | |
/* | |
* Import X from unsigned binary data, little endian | |
*/ | |
int mbedtls_mpi_read_binary_le( mbedtls_mpi *X, | |
const unsigned char *buf, size_t buflen ) | |
{ | |
int ret; | |
size_t i; | |
size_t const limbs = CHARS_TO_LIMBS( buflen ); | |
/* Ensure that target MPI has exactly the necessary number of limbs */ | |
if( X->n != limbs ) | |
{ | |
mbedtls_mpi_free( X ); | |
mbedtls_mpi_init( X ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) ); | |
} | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); | |
for( i = 0; i < buflen; i++ ) | |
X->p[i / ciL] |= ((mbedtls_mpi_uint) buf[i]) << ((i % ciL) << 3); | |
cleanup: | |
/* | |
* This function is also used to import keys. However, wiping the buffers | |
* upon failure is not necessary because failure only can happen before any | |
* input is copied. | |
*/ | |
return( ret ); | |
} | |
/* | |
* Import X from unsigned binary data, big endian | |
*/ | |
int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen ) | |
{ | |
int ret; | |
size_t const limbs = CHARS_TO_LIMBS( buflen ); | |
size_t const overhead = ( limbs * ciL ) - buflen; | |
unsigned char *Xp; | |
MPI_VALIDATE_RET( X != NULL ); | |
MPI_VALIDATE_RET( buflen == 0 || buf != NULL ); | |
/* Ensure that target MPI has exactly the necessary number of limbs */ | |
if( X->n != limbs ) | |
{ | |
mbedtls_mpi_free( X ); | |
mbedtls_mpi_init( X ); | |
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) ); | |
} | |
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); | |
/* Avoid calling `memcpy` with NULL source argument, | |
* even if buflen is 0. */ | |
if( buf != NULL ) | |
{ | |
Xp = (unsigned char*) X->p; | |
memcpy( Xp + overhead, buf, buflen ); | |
mpi_bigendian_to_host( X->p, limbs ); | |
} | |
cleanup: | |
/* | |
* This function is also used to import keys. However, wiping the buffers | |
* upon failure is not necessary because failure only can happen before any | |
* input is copied. | |
*/ | |
return( ret ); | |
} | |
/* | |
* Export X into unsigned binary data, little endian | |
*/ | |
int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X, | |
unsigned char *buf, size_t buflen ) | |
{ | |
size_t stored_bytes = X->n * ciL; | |
size_t bytes_to_copy; | |
size_t i; | |
if( stored_bytes < buflen ) | |
{ | |
bytes_to_copy = stored_bytes; | |
} | |
else | |
{ | |
bytes_to_copy = buflen; | |
/* The output buffer is smaller than the allocated size of X. | |
* However X may fit if its leading bytes are zero. */ | |
for( i = bytes_to_copy; i < stored_bytes; i++ ) | |
{ | |
if( GET_BYTE( X, i ) != 0 ) | |
return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); | |
} | |
} | |
for( i = 0; i < bytes_to_copy; i++ ) | |
buf[i] = GET_BYTE( X, i ); | |
if( stored_bytes < buflen ) | |
{ | |
/* Write trailing 0 bytes */ | |
memset( buf + stored_bytes, 0, buflen - stored_bytes ); | |
} | |
return( 0 ); | |
} | |
/* | |
* Export X into unsigned binary data, big endian | |
*/ | |
int mbedtls_mpi_write_binary( const mbedtls_mpi *X, | |
unsigned char *buf, size_t buflen ) | |
{ | |
size_t stored_bytes; | |
size_t bytes_to_copy; | |
unsigned char *p; | |
size_t i; | |
MPI_VALIDATE_RET( X != NULL ); | |
MPI_VALIDATE_RET( buflen == 0 || buf != NULL ); | |
stored_bytes = X->n * ciL; | |
if( stored_bytes < buflen ) | |
{ | |
/* There is enough space in the output buffer. Write initial | |
* null bytes and record the position at which to start | |
* writing the significant bytes. In this case, the execution | |
* trace of this function does not depend on the value of the | |
* number. */ | |
bytes_to_copy = stored_bytes; | |
p = buf + buflen - stored_bytes; | |
memset( buf, 0, buflen - stored_bytes ); | |
} | |
else | |
{ | |
/* The output buffer is smaller than the allocated size of X. | |
* However X may fit if its leading bytes are zero. */ | |
bytes_to_copy = buflen; | |
p = buf; | |
for( i = bytes_to_copy; i < stored_bytes; i++ ) | |
{ | |
if( GET_BYTE( X, i ) != 0 ) | |
return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); | |
} | |
} | |
for( i = 0; i < bytes_to_copy; i++ ) | |
p[bytes_to_copy - i - 1] = GET_BYTE( X, i ); | |
return( 0 ); | |
} | |
/* | |
* Left-shift: X <<= count | |
*/ | |
int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count ) | |
{ | |
int ret; | |
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 ); | |
} | |
/* | |
* 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 | |
*/ | |
static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d ) | |
{ | |
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; | |
} | |
while( c != 0 ) | |
{ | |
z = ( *d < c ); *d -= c; | |
c = z; d++; | |
} | |
} | |
/* | |
* Unsigned subtraction: X = |A| - |B| (HAC 14.9) | |
*/ | |
int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) | |
{ | |
mbedtls_mpi TB; | |
int ret; | |
size_t n; | |
MPI_VALIDATE_RET( X != NULL ); | |
MPI_VALIDATE_RET( A != NULL ); | |
MPI_VALIDATE_RET( B != NULL ); | |
if( mbedtls_mpi_cmp_abs( A, B ) < 0 ) | |
return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE ); | |
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; | |
mpi_sub_hlp( n, B->p, X->p ); | |
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) | |
*/ | |
static int 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; | |
if( T->n < N->n + 1 || T->p == NULL ) | |
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); | |
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; | |
} | |
memcpy( A->p, d, ( n + 1 ) * ciL ); | |
if( mbedtls_mpi_cmp_abs( A, N ) >= 0 ) | |
mpi_sub_hlp( n, N->p, A->p ); | |
else | |
/* prevent timing attacks */ | |
mpi_sub_hlp( n, A->p, T->p ); | |
return( 0 ); | |
} | |
/* | |
* Montgomery reduction: A = A * R^-1 mod N | |
*/ | |
static int 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; | |
return( 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[ 2 << 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 ); | |
/* | |
* 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 ) ); | |
MBEDTLS_MPI_CHK( 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 ) ); | |
MBEDTLS_MPI_CHK( 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++ ) | |
MBEDTLS_MPI_CHK( 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] ) ); | |
MBEDTLS_MPI_CHK( 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 | |
*/ | |
MBEDTLS_MPI_CHK( 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++ ) | |
MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) ); | |
/* | |
* X = X * W[wbits] R^-1 mod N | |
*/ | |
MBEDTLS_MPI_CHK( mpi_montmul( X, &W[wbits], N, mm, &T ) ); | |
state--; | |
nbits = 0; | |
wbits = 0; | |
} | |
} | |
/* | |
* process the remaining bits | |
*/ | |
for( i = 0; i < nbits; i++ ) | |
{ | |
MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) ); | |
wbits <<= 1; | |
if( ( wbits & ( one << wsize ) ) != 0 ) | |
MBEDTLS_MPI_CHK( mpi_montmul( X, &W[1], N, mm, &T ) ); | |
} | |
/* | |
* X = A^E * R * R^-1 mod N = A^E mod N | |
*/ | |
MBEDTLS_MPI_CHK( 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; | |
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 ) ); | |
i = mbedtls_mpi_bitlen( X ); | |
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) { | |
return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; | |
} | |
} 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 */ |