diff options
Diffstat (limited to 'lib/mbedtls-2.27.0/library/bignum.c')
| -rw-r--r-- | lib/mbedtls-2.27.0/library/bignum.c | 3384 |
1 files changed, 3384 insertions, 0 deletions
diff --git a/lib/mbedtls-2.27.0/library/bignum.c b/lib/mbedtls-2.27.0/library/bignum.c new file mode 100644 index 0000000..20afa22 --- /dev/null +++ b/lib/mbedtls-2.27.0/library/bignum.c @@ -0,0 +1,3384 @@ +/* + * Multi-precision integer library + * + * Copyright The Mbed TLS Contributors + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the "License"); you may + * not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT + * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * The following sources were referenced in the design of this Multi-precision + * Integer library: + * + * [1] Handbook of Applied Cryptography - 1997 + * Menezes, van Oorschot and Vanstone + * + * [2] Multi-Precision Math + * Tom St Denis + * https://github.com/libtom/libtommath/blob/develop/tommath.pdf + * + * [3] GNU Multi-Precision Arithmetic Library + * https://gmplib.org/manual/index.html + * + */ + +#include "common.h" + +#if defined(MBEDTLS_BIGNUM_C) + +#include "mbedtls/bignum.h" +#include "mbedtls/bn_mul.h" +#include "mbedtls/platform_util.h" +#include "mbedtls/error.h" + +#include <string.h> + +#if defined(MBEDTLS_PLATFORM_C) +#include "mbedtls/platform.h" +#else +#include <stdio.h> +#include <stdlib.h> +#define mbedtls_printf printf +#define mbedtls_calloc calloc +#define mbedtls_free free +#endif + +#define MPI_VALIDATE_RET( cond ) \ + MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_MPI_BAD_INPUT_DATA ) +#define MPI_VALIDATE( cond ) \ + MBEDTLS_INTERNAL_VALIDATE( cond ) + +#define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */ +#define biL (ciL << 3) /* bits in limb */ +#define biH (ciL << 2) /* half limb size */ + +#define MPI_SIZE_T_MAX ( (size_t) -1 ) /* SIZE_T_MAX is not standard */ + +/* + * Convert between bits/chars and number of limbs + * Divide first in order to avoid potential overflows + */ +#define BITS_TO_LIMBS(i) ( (i) / biL + ( (i) % biL != 0 ) ) +#define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) ) + +/* Implementation that should never be optimized out by the compiler */ +static void mbedtls_mpi_zeroize( mbedtls_mpi_uint *v, size_t n ) +{ + mbedtls_platform_zeroize( v, ciL * n ); +} + +/* + * Initialize one MPI + */ +void mbedtls_mpi_init( mbedtls_mpi *X ) +{ + MPI_VALIDATE( X != NULL ); + + X->s = 1; + X->n = 0; + X->p = NULL; +} + +/* + * Unallocate one MPI + */ +void mbedtls_mpi_free( mbedtls_mpi *X ) +{ + if( X == NULL ) + return; + + if( X->p != NULL ) + { + mbedtls_mpi_zeroize( X->p, X->n ); + mbedtls_free( X->p ); + } + + X->s = 1; + X->n = 0; + X->p = NULL; +} + +/* + * Enlarge to the specified number of limbs + */ +int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs ) +{ + mbedtls_mpi_uint *p; + MPI_VALIDATE_RET( X != NULL ); + + if( nblimbs > MBEDTLS_MPI_MAX_LIMBS ) + return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); + + if( X->n < nblimbs ) + { + if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( nblimbs, ciL ) ) == NULL ) + return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); + + if( X->p != NULL ) + { + memcpy( p, X->p, X->n * ciL ); + mbedtls_mpi_zeroize( X->p, X->n ); + mbedtls_free( X->p ); + } + + X->n = nblimbs; + X->p = p; + } + + return( 0 ); +} + +/* + * Resize down as much as possible, + * while keeping at least the specified number of limbs + */ +int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs ) +{ + mbedtls_mpi_uint *p; + size_t i; + MPI_VALIDATE_RET( X != NULL ); + + if( nblimbs > MBEDTLS_MPI_MAX_LIMBS ) + return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); + + /* Actually resize up if there are currently fewer than nblimbs limbs. */ + if( X->n <= nblimbs ) + return( mbedtls_mpi_grow( X, nblimbs ) ); + /* After this point, then X->n > nblimbs and in particular X->n > 0. */ + + for( i = X->n - 1; i > 0; i-- ) + if( X->p[i] != 0 ) + break; + i++; + + if( i < nblimbs ) + i = nblimbs; + + if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( i, ciL ) ) == NULL ) + return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); + + if( X->p != NULL ) + { + memcpy( p, X->p, i * ciL ); + mbedtls_mpi_zeroize( X->p, X->n ); + mbedtls_free( X->p ); + } + + X->n = i; + X->p = p; + + return( 0 ); +} + +/* Resize X to have exactly n limbs and set it to 0. */ +static int mbedtls_mpi_resize_clear( mbedtls_mpi *X, size_t limbs ) +{ + if( limbs == 0 ) + { + mbedtls_mpi_free( X ); + return( 0 ); + } + else if( X->n == limbs ) + { + memset( X->p, 0, limbs * ciL ); + X->s = 1; + return( 0 ); + } + else + { + mbedtls_mpi_free( X ); + return( mbedtls_mpi_grow( X, limbs ) ); + } +} + +/* + * Copy the contents of Y into X. + * + * This function is not constant-time. Leading zeros in Y may be removed. + * + * Ensure that X does not shrink. This is not guaranteed by the public API, + * but some code in the bignum module relies on this property, for example + * in mbedtls_mpi_exp_mod(). + */ +int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y ) +{ + int ret = 0; + size_t i; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( Y != NULL ); + + if( X == Y ) + return( 0 ); + + if( Y->n == 0 ) + { + if( X->n != 0 ) + { + X->s = 1; + memset( X->p, 0, X->n * ciL ); + } + return( 0 ); + } + + for( i = Y->n - 1; i > 0; i-- ) + if( Y->p[i] != 0 ) + break; + i++; + + X->s = Y->s; + + if( X->n < i ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) ); + } + else + { + memset( X->p + i, 0, ( X->n - i ) * ciL ); + } + + memcpy( X->p, Y->p, i * ciL ); + +cleanup: + + return( ret ); +} + +/* + * Swap the contents of X and Y + */ +void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y ) +{ + mbedtls_mpi T; + MPI_VALIDATE( X != NULL ); + MPI_VALIDATE( Y != NULL ); + + memcpy( &T, X, sizeof( mbedtls_mpi ) ); + memcpy( X, Y, sizeof( mbedtls_mpi ) ); + memcpy( Y, &T, sizeof( mbedtls_mpi ) ); +} + +/** + * Select between two sign values in constant-time. + * + * This is functionally equivalent to second ? a : b but uses only bit + * operations in order to avoid branches. + * + * \param[in] a The first sign; must be either +1 or -1. + * \param[in] b The second sign; must be either +1 or -1. + * \param[in] second Must be either 1 (return b) or 0 (return a). + * + * \return The selected sign value. + */ +static int mpi_safe_cond_select_sign( int a, int b, unsigned char second ) +{ + /* In order to avoid questions about what we can reasonnably assume about + * the representations of signed integers, move everything to unsigned + * by taking advantage of the fact that a and b are either +1 or -1. */ + unsigned ua = a + 1; + unsigned ub = b + 1; + + /* second was 0 or 1, mask is 0 or 2 as are ua and ub */ + const unsigned mask = second << 1; + + /* select ua or ub */ + unsigned ur = ( ua & ~mask ) | ( ub & mask ); + + /* ur is now 0 or 2, convert back to -1 or +1 */ + return( (int) ur - 1 ); +} + +/* + * 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; + + /* MSVC has a warning about unary minus on unsigned integer types, + * but this is well-defined and precisely what we want to do here. */ +#if defined(_MSC_VER) +#pragma warning( push ) +#pragma warning( disable : 4146 ) +#endif + + /* all-bits 1 if assign is 1, all-bits 0 if assign is 0 */ + const mbedtls_mpi_uint mask = -assign; + +#if defined(_MSC_VER) +#pragma warning( pop ) +#endif + + for( i = 0; i < n; i++ ) + dest[i] = ( src[i] & mask ) | ( dest[i] & ~mask ); +} + +/* + * 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; + mbedtls_mpi_uint limb_mask; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( Y != NULL ); + + /* MSVC has a warning about unary minus on unsigned integer types, + * but this is well-defined and precisely what we want to do here. */ +#if defined(_MSC_VER) +#pragma warning( push ) +#pragma warning( disable : 4146 ) +#endif + + /* make sure assign is 0 or 1 in a time-constant manner */ + assign = (assign | (unsigned char)-assign) >> (sizeof( assign ) * 8 - 1); + /* all-bits 1 if assign is 1, all-bits 0 if assign is 0 */ + limb_mask = -assign; + +#if defined(_MSC_VER) +#pragma warning( pop ) +#endif + + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) ); + + X->s = mpi_safe_cond_select_sign( X->s, 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] &= ~limb_mask; + +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 limb_mask; + mbedtls_mpi_uint tmp; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( Y != NULL ); + + if( X == Y ) + return( 0 ); + + /* MSVC has a warning about unary minus on unsigned integer types, + * but this is well-defined and precisely what we want to do here. */ +#if defined(_MSC_VER) +#pragma warning( push ) +#pragma warning( disable : 4146 ) +#endif + + /* make sure swap is 0 or 1 in a time-constant manner */ + swap = (swap | (unsigned char)-swap) >> (sizeof( swap ) * 8 - 1); + /* all-bits 1 if swap is 1, all-bits 0 if swap is 0 */ + limb_mask = -swap; + +#if defined(_MSC_VER) +#pragma warning( pop ) +#endif + + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) ); + + s = X->s; + X->s = mpi_safe_cond_select_sign( X->s, Y->s, swap ); + Y->s = mpi_safe_cond_select_sign( Y->s, s, swap ); + + + for( i = 0; i < X->n; i++ ) + { + tmp = X->p[i]; + X->p[i] = ( X->p[i] & ~limb_mask ) | ( Y->p[i] & limb_mask ); + Y->p[i] = ( Y->p[i] & ~limb_mask ) | ( tmp & limb_mask ); + } + +cleanup: + return( ret ); +} + +/* + * Set value from integer + */ +int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + MPI_VALIDATE_RET( X != NULL ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) ); + memset( X->p, 0, X->n * ciL ); + + X->p[0] = ( z < 0 ) ? -z : z; + X->s = ( z < 0 ) ? -1 : 1; + +cleanup: + + return( ret ); +} + +/* + * Get a specific bit + */ +int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos ) +{ + MPI_VALIDATE_RET( X != NULL ); + + if( X->n * biL <= pos ) + return( 0 ); + + return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 ); +} + +/* Get a specific byte, without range checks. */ +#define GET_BYTE( X, i ) \ + ( ( ( X )->p[( i ) / ciL] >> ( ( ( i ) % ciL ) * 8 ) ) & 0xff ) + +/* + * Set a bit to a specific value of 0 or 1 + */ +int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val ) +{ + int ret = 0; + size_t off = pos / biL; + size_t idx = pos % biL; + MPI_VALIDATE_RET( X != NULL ); + + if( val != 0 && val != 1 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + if( X->n * biL <= pos ) + { + if( val == 0 ) + return( 0 ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, off + 1 ) ); + } + + X->p[off] &= ~( (mbedtls_mpi_uint) 0x01 << idx ); + X->p[off] |= (mbedtls_mpi_uint) val << idx; + +cleanup: + + return( ret ); +} + +/* + * Return the number of less significant zero-bits + */ +size_t mbedtls_mpi_lsb( const mbedtls_mpi *X ) +{ + size_t i, j, count = 0; + MBEDTLS_INTERNAL_VALIDATE_RET( X != NULL, 0 ); + + for( i = 0; i < X->n; i++ ) + for( j = 0; j < biL; j++, count++ ) + if( ( ( X->p[i] >> j ) & 1 ) != 0 ) + return( count ); + + return( 0 ); +} + +/* + * Count leading zero bits in a given integer + */ +static size_t mbedtls_clz( const mbedtls_mpi_uint x ) +{ + size_t j; + mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1); + + for( j = 0; j < biL; j++ ) + { + if( x & mask ) break; + + mask >>= 1; + } + + return j; +} + +/* + * Return the number of bits + */ +size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X ) +{ + size_t i, j; + + if( X->n == 0 ) + return( 0 ); + + for( i = X->n - 1; i > 0; i-- ) + if( X->p[i] != 0 ) + break; + + j = biL - mbedtls_clz( X->p[i] ); + + return( ( i * biL ) + j ); +} + +/* + * Return the total size in bytes + */ +size_t mbedtls_mpi_size( const mbedtls_mpi *X ) +{ + return( ( mbedtls_mpi_bitlen( X ) + 7 ) >> 3 ); +} + +/* + * Convert an ASCII character to digit value + */ +static int mpi_get_digit( mbedtls_mpi_uint *d, int radix, char c ) +{ + *d = 255; + + if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30; + if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37; + if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57; + + if( *d >= (mbedtls_mpi_uint) radix ) + return( MBEDTLS_ERR_MPI_INVALID_CHARACTER ); + + return( 0 ); +} + +/* + * Import from an ASCII string + */ +int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i, j, slen, n; + int sign = 1; + mbedtls_mpi_uint d; + mbedtls_mpi T; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( s != NULL ); + + if( radix < 2 || radix > 16 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + mbedtls_mpi_init( &T ); + + if( s[0] == 0 ) + { + mbedtls_mpi_free( X ); + return( 0 ); + } + + if( s[0] == '-' ) + { + ++s; + sign = -1; + } + + slen = strlen( s ); + + if( radix == 16 ) + { + if( slen > 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_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi_uint r; + size_t length = 0; + char *p_end = *p + buflen; + + do + { + if( length >= buflen ) + { + return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, radix ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_div_int( X, NULL, X, radix ) ); + /* + * Write the residue in the current position, as an ASCII character. + */ + if( r < 0xA ) + *(--p_end) = (char)( '0' + r ); + else + *(--p_end) = (char)( 'A' + ( r - 0xA ) ); + + length++; + } while( mbedtls_mpi_cmp_int( X, 0 ) != 0 ); + + memmove( *p, p_end, length ); + *p += length; + +cleanup: + + return( ret ); +} + +/* + * Export into an ASCII string + */ +int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix, + char *buf, size_t buflen, size_t *olen ) +{ + int ret = 0; + size_t n; + char *p; + mbedtls_mpi T; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( olen != NULL ); + MPI_VALIDATE_RET( buflen == 0 || buf != NULL ); + + if( radix < 2 || radix > 16 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + n = mbedtls_mpi_bitlen( X ); /* Number of bits necessary to present `n`. */ + if( radix >= 4 ) n >>= 1; /* Number of 4-adic digits necessary to present + * `n`. If radix > 4, this might be a strict + * overapproximation of the number of + * radix-adic digits needed to present `n`. */ + if( radix >= 16 ) n >>= 1; /* Number of hexadecimal digits necessary to + * present `n`. */ + + n += 1; /* Terminating null byte */ + n += 1; /* Compensate for the divisions above, which round down `n` + * in case it's not even. */ + n += 1; /* Potential '-'-sign. */ + n += ( n & 1 ); /* Make n even to have enough space for hexadecimal writing, + * which always uses an even number of hex-digits. */ + + if( buflen < n ) + { + *olen = n; + return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); + } + + p = buf; + mbedtls_mpi_init( &T ); + + if( X->s == -1 ) + { + *p++ = '-'; + buflen--; + } + + if( radix == 16 ) + { + int c; + size_t i, j, k; + + for( i = X->n, k = 0; i > 0; i-- ) + { + for( j = ciL; j > 0; j-- ) + { + c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF; + + if( c == 0 && k == 0 && ( i + j ) != 2 ) + continue; + + *(p++) = "0123456789ABCDEF" [c / 16]; + *(p++) = "0123456789ABCDEF" [c % 16]; + k = 1; + } + } + } + else + { + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T, X ) ); + + if( T.s == -1 ) + T.s = 1; + + MBEDTLS_MPI_CHK( mpi_write_hlp( &T, radix, &p, buflen ) ); + } + + *p++ = '\0'; + *olen = p - buf; + +cleanup: + + mbedtls_mpi_free( &T ); + + return( ret ); +} + +#if defined(MBEDTLS_FS_IO) +/* + * Read X from an opened file + */ +int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin ) +{ + mbedtls_mpi_uint d; + size_t slen; + char *p; + /* + * Buffer should have space for (short) label and decimal formatted MPI, + * newline characters and '\0' + */ + char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ]; + + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( fin != NULL ); + + if( radix < 2 || radix > 16 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + memset( s, 0, sizeof( s ) ); + if( fgets( s, sizeof( s ) - 1, fin ) == NULL ) + return( MBEDTLS_ERR_MPI_FILE_IO_ERROR ); + + slen = strlen( s ); + if( slen == sizeof( s ) - 2 ) + return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); + + if( slen > 0 && s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; } + if( slen > 0 && s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; } + + p = s + slen; + while( p-- > s ) + if( mpi_get_digit( &d, radix, *p ) != 0 ) + break; + + return( mbedtls_mpi_read_string( X, radix, p + 1 ) ); +} + +/* + * Write X into an opened file (or stdout if fout == NULL) + */ +int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t n, slen, plen; + /* + * Buffer should have space for (short) label and decimal formatted MPI, + * newline characters and '\0' + */ + char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ]; + MPI_VALIDATE_RET( X != NULL ); + + if( radix < 2 || radix > 16 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + memset( s, 0, sizeof( s ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_write_string( X, radix, s, sizeof( s ) - 2, &n ) ); + + if( p == NULL ) p = ""; + + plen = strlen( p ); + slen = strlen( s ); + s[slen++] = '\r'; + s[slen++] = '\n'; + + if( fout != NULL ) + { + if( fwrite( p, 1, plen, fout ) != plen || + fwrite( s, 1, slen, fout ) != slen ) + return( MBEDTLS_ERR_MPI_FILE_IO_ERROR ); + } + else + mbedtls_printf( "%s%s", p, s ); + +cleanup: + + return( ret ); +} +#endif /* MBEDTLS_FS_IO */ + + +/* Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint + * into the storage form used by mbedtls_mpi. */ + +static mbedtls_mpi_uint mpi_uint_bigendian_to_host_c( mbedtls_mpi_uint x ) +{ + uint8_t i; + unsigned char *x_ptr; + mbedtls_mpi_uint tmp = 0; + + for( i = 0, x_ptr = (unsigned char*) &x; i < ciL; i++, x_ptr++ ) + { + tmp <<= CHAR_BIT; + tmp |= (mbedtls_mpi_uint) *x_ptr; + } + + return( tmp ); +} + +static mbedtls_mpi_uint mpi_uint_bigendian_to_host( mbedtls_mpi_uint x ) +{ +#if defined(__BYTE_ORDER__) + +/* Nothing to do on bigendian systems. */ +#if ( __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ ) + return( x ); +#endif /* __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ */ + +#if ( __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ ) + +/* For GCC and Clang, have builtins for byte swapping. */ +#if defined(__GNUC__) && defined(__GNUC_PREREQ) +#if __GNUC_PREREQ(4,3) +#define have_bswap +#endif +#endif + +#if defined(__clang__) && defined(__has_builtin) +#if __has_builtin(__builtin_bswap32) && \ + __has_builtin(__builtin_bswap64) +#define have_bswap +#endif +#endif + +#if defined(have_bswap) + /* The compiler is hopefully able to statically evaluate this! */ + switch( sizeof(mbedtls_mpi_uint) ) + { + case 4: + return( __builtin_bswap32(x) ); + case 8: + return( __builtin_bswap64(x) ); + } +#endif +#endif /* __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ */ +#endif /* __BYTE_ORDER__ */ + + /* Fall back to C-based reordering if we don't know the byte order + * or we couldn't use a compiler-specific builtin. */ + return( mpi_uint_bigendian_to_host_c( x ) ); +} + +static void mpi_bigendian_to_host( mbedtls_mpi_uint * const p, size_t limbs ) +{ + mbedtls_mpi_uint *cur_limb_left; + mbedtls_mpi_uint *cur_limb_right; + if( limbs == 0 ) + return; + + /* + * Traverse limbs and + * - adapt byte-order in each limb + * - swap the limbs themselves. + * For that, simultaneously traverse the limbs from left to right + * and from right to left, as long as the left index is not bigger + * than the right index (it's not a problem if limbs is odd and the + * indices coincide in the last iteration). + */ + for( cur_limb_left = p, cur_limb_right = p + ( limbs - 1 ); + cur_limb_left <= cur_limb_right; + cur_limb_left++, cur_limb_right-- ) + { + mbedtls_mpi_uint tmp; + /* Note that if cur_limb_left == cur_limb_right, + * this code effectively swaps the bytes only once. */ + tmp = mpi_uint_bigendian_to_host( *cur_limb_left ); + *cur_limb_left = mpi_uint_bigendian_to_host( *cur_limb_right ); + *cur_limb_right = tmp; + } +} + +/* + * Import X from unsigned binary data, little endian + */ +int mbedtls_mpi_read_binary_le( mbedtls_mpi *X, + const unsigned char *buf, size_t buflen ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i; + size_t const limbs = CHARS_TO_LIMBS( buflen ); + + /* Ensure that target MPI has exactly the necessary number of limbs */ + MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, limbs ) ); + + for( i = 0; i < buflen; i++ ) + X->p[i / ciL] |= ((mbedtls_mpi_uint) buf[i]) << ((i % ciL) << 3); + +cleanup: + + /* + * This function is also used to import keys. However, wiping the buffers + * upon failure is not necessary because failure only can happen before any + * input is copied. + */ + return( ret ); +} + +/* + * Import X from unsigned binary data, big endian + */ +int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t const limbs = CHARS_TO_LIMBS( buflen ); + size_t const overhead = ( limbs * ciL ) - buflen; + unsigned char *Xp; + + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( buflen == 0 || buf != NULL ); + + /* Ensure that target MPI has exactly the necessary number of limbs */ + MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, limbs ) ); + + /* Avoid calling `memcpy` with NULL source or destination argument, + * even if buflen is 0. */ + if( buflen != 0 ) + { + Xp = (unsigned char*) X->p; + memcpy( Xp + overhead, buf, buflen ); + + mpi_bigendian_to_host( X->p, limbs ); + } + +cleanup: + + /* + * This function is also used to import keys. However, wiping the buffers + * upon failure is not necessary because failure only can happen before any + * input is copied. + */ + return( ret ); +} + +/* + * Export X into unsigned binary data, little endian + */ +int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X, + unsigned char *buf, size_t buflen ) +{ + size_t stored_bytes = X->n * ciL; + size_t bytes_to_copy; + size_t i; + + if( stored_bytes < buflen ) + { + bytes_to_copy = stored_bytes; + } + else + { + bytes_to_copy = buflen; + + /* The output buffer is smaller than the allocated size of X. + * However X may fit if its leading bytes are zero. */ + for( i = bytes_to_copy; i < stored_bytes; i++ ) + { + if( GET_BYTE( X, i ) != 0 ) + return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); + } + } + + for( i = 0; i < bytes_to_copy; i++ ) + buf[i] = GET_BYTE( X, i ); + + if( stored_bytes < buflen ) + { + /* Write trailing 0 bytes */ + memset( buf + stored_bytes, 0, buflen - stored_bytes ); + } + + return( 0 ); +} + +/* + * Export X into unsigned binary data, big endian + */ +int mbedtls_mpi_write_binary( const mbedtls_mpi *X, + unsigned char *buf, size_t buflen ) +{ + size_t stored_bytes; + size_t bytes_to_copy; + unsigned char *p; + size_t i; + + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( buflen == 0 || buf != NULL ); + + stored_bytes = X->n * ciL; + + if( stored_bytes < buflen ) + { + /* There is enough space in the output buffer. Write initial + * null bytes and record the position at which to start + * writing the significant bytes. In this case, the execution + * trace of this function does not depend on the value of the + * number. */ + bytes_to_copy = stored_bytes; + p = buf + buflen - stored_bytes; + memset( buf, 0, buflen - stored_bytes ); + } + else + { + /* The output buffer is smaller than the allocated size of X. + * However X may fit if its leading bytes are zero. */ + bytes_to_copy = buflen; + p = buf; + for( i = bytes_to_copy; i < stored_bytes; i++ ) + { + if( GET_BYTE( X, i ) != 0 ) + return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); + } + } + + for( i = 0; i < bytes_to_copy; i++ ) + p[bytes_to_copy - i - 1] = GET_BYTE( X, i ); + + return( 0 ); +} + +/* + * Left-shift: X <<= count + */ +int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i, v0, t1; + mbedtls_mpi_uint r0 = 0, r1; + MPI_VALIDATE_RET( X != NULL ); + + v0 = count / (biL ); + t1 = count & (biL - 1); + + i = mbedtls_mpi_bitlen( X ) + count; + + if( X->n * biL < i ) + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, BITS_TO_LIMBS( i ) ) ); + + ret = 0; + + /* + * shift by count / limb_size + */ + if( v0 > 0 ) + { + for( i = X->n; i > v0; i-- ) + X->p[i - 1] = X->p[i - v0 - 1]; + + for( ; i > 0; i-- ) + X->p[i - 1] = 0; + } + + /* + * shift by count % limb_size + */ + if( t1 > 0 ) + { + for( i = v0; i < X->n; i++ ) + { + r1 = X->p[i] >> (biL - t1); + X->p[i] <<= t1; + X->p[i] |= r0; + r0 = r1; + } + } + +cleanup: + + return( ret ); +} + +/* + * Right-shift: X >>= count + */ +int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count ) +{ + size_t i, v0, v1; + mbedtls_mpi_uint r0 = 0, r1; + MPI_VALIDATE_RET( X != NULL ); + + v0 = count / biL; + v1 = count & (biL - 1); + + if( v0 > X->n || ( v0 == X->n && v1 > 0 ) ) + return mbedtls_mpi_lset( X, 0 ); + + /* + * shift by count / limb_size + */ + if( v0 > 0 ) + { + for( i = 0; i < X->n - v0; i++ ) + X->p[i] = X->p[i + v0]; + + for( ; i < X->n; i++ ) + X->p[i] = 0; + } + + /* + * shift by count % limb_size + */ + if( v1 > 0 ) + { + for( i = X->n; i > 0; i-- ) + { + r1 = X->p[i - 1] << (biL - v1); + X->p[i - 1] >>= v1; + X->p[i - 1] |= r0; + r0 = r1; + } + } + + return( 0 ); +} + +/* + * Compare unsigned values + */ +int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y ) +{ + size_t i, j; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( Y != NULL ); + + for( i = X->n; i > 0; i-- ) + if( X->p[i - 1] != 0 ) + break; + + for( j = Y->n; j > 0; j-- ) + if( Y->p[j - 1] != 0 ) + break; + + if( i == 0 && j == 0 ) + return( 0 ); + + if( i > j ) return( 1 ); + if( j > i ) return( -1 ); + + for( ; i > 0; i-- ) + { + if( X->p[i - 1] > Y->p[i - 1] ) return( 1 ); + if( X->p[i - 1] < Y->p[i - 1] ) return( -1 ); + } + + return( 0 ); +} + +/* + * Compare signed values + */ +int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y ) +{ + size_t i, j; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( Y != NULL ); + + for( i = X->n; i > 0; i-- ) + if( X->p[i - 1] != 0 ) + break; + + for( j = Y->n; j > 0; j-- ) + if( Y->p[j - 1] != 0 ) + break; + + if( i == 0 && j == 0 ) + return( 0 ); + + if( i > j ) return( X->s ); + if( j > i ) return( -Y->s ); + + if( X->s > 0 && Y->s < 0 ) return( 1 ); + if( Y->s > 0 && X->s < 0 ) return( -1 ); + + for( ; i > 0; i-- ) + { + if( X->p[i - 1] > Y->p[i - 1] ) return( X->s ); + if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s ); + } + + return( 0 ); +} + +/** Decide if an integer is less than the other, without branches. + * + * \param x First integer. + * \param y Second integer. + * + * \return 1 if \p x is less than \p y, 0 otherwise + */ +static unsigned ct_lt_mpi_uint( const mbedtls_mpi_uint x, + const mbedtls_mpi_uint y ) +{ + mbedtls_mpi_uint ret; + mbedtls_mpi_uint cond; + + /* + * Check if the most significant bits (MSB) of the operands are different. + */ + cond = ( x ^ y ); + /* + * If the MSB are the same then the difference x-y will be negative (and + * have its MSB set to 1 during conversion to unsigned) if and only if x<y. + */ + ret = ( x - y ) & ~cond; + /* + * If the MSB are different, then the operand with the MSB of 1 is the + * bigger. (That is if y has MSB of 1, then x<y is true and it is false if + * the MSB of y is 0.) + */ + ret |= y & cond; + + + ret = ret >> ( biL - 1 ); + + return (unsigned) ret; +} + +/* + * Compare signed values in constant time + */ +int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y, + unsigned *ret ) +{ + size_t i; + /* The value of any of these variables is either 0 or 1 at all times. */ + unsigned cond, done, X_is_negative, Y_is_negative; + + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( Y != NULL ); + MPI_VALIDATE_RET( ret != NULL ); + + if( X->n != Y->n ) + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + + /* + * Set sign_N to 1 if N >= 0, 0 if N < 0. + * We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0. + */ + X_is_negative = ( X->s & 2 ) >> 1; + Y_is_negative = ( Y->s & 2 ) >> 1; + + /* + * If the signs are different, then the positive operand is the bigger. + * That is if X is negative (X_is_negative == 1), then X < Y is true and it + * is false if X is positive (X_is_negative == 0). + */ + cond = ( X_is_negative ^ Y_is_negative ); + *ret = cond & X_is_negative; + + /* + * This is a constant-time function. We might have the result, but we still + * need to go through the loop. Record if we have the result already. + */ + done = cond; + + for( i = X->n; i > 0; i-- ) + { + /* + * If Y->p[i - 1] < X->p[i - 1] then X < Y is true if and only if both + * X and Y are negative. + * + * Again even if we can make a decision, we just mark the result and + * the fact that we are done and continue looping. + */ + cond = ct_lt_mpi_uint( Y->p[i - 1], X->p[i - 1] ); + *ret |= cond & ( 1 - done ) & X_is_negative; + done |= cond; + + /* + * If X->p[i - 1] < Y->p[i - 1] then X < Y is true if and only if both + * X and Y are positive. + * + * Again even if we can make a decision, we just mark the result and + * the fact that we are done and continue looping. + */ + cond = ct_lt_mpi_uint( X->p[i - 1], Y->p[i - 1] ); + *ret |= cond & ( 1 - done ) & ( 1 - X_is_negative ); + done |= cond; + } + + return( 0 ); +} + +/* + * Compare signed values + */ +int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z ) +{ + mbedtls_mpi Y; + mbedtls_mpi_uint p[1]; + MPI_VALIDATE_RET( X != NULL ); + + *p = ( z < 0 ) ? -z : z; + Y.s = ( z < 0 ) ? -1 : 1; + Y.n = 1; + Y.p = p; + + return( mbedtls_mpi_cmp_mpi( X, &Y ) ); +} + +/* + * Unsigned addition: X = |A| + |B| (HAC 14.7) + */ +int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i, j; + mbedtls_mpi_uint *o, *p, c, tmp; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( A != NULL ); + MPI_VALIDATE_RET( B != NULL ); + + if( X == B ) + { + const mbedtls_mpi *T = A; A = X; B = T; + } + + if( X != A ) + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) ); + + /* + * X should always be positive as a result of unsigned additions. + */ + X->s = 1; + + for( j = B->n; j > 0; j-- ) + if( B->p[j - 1] != 0 ) + break; + + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) ); + + o = B->p; p = X->p; c = 0; + + /* + * tmp is used because it might happen that p == o + */ + for( i = 0; i < j; i++, o++, p++ ) + { + tmp= *o; + *p += c; c = ( *p < c ); + *p += tmp; c += ( *p < tmp ); + } + + while( c != 0 ) + { + if( i >= X->n ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + 1 ) ); + p = X->p + i; + } + + *p += c; c = ( *p < c ); i++; p++; + } + +cleanup: + + return( ret ); +} + +/** + * Helper for mbedtls_mpi subtraction. + * + * Calculate l - r where l and r have the same size. + * This function operates modulo (2^ciL)^n and returns the carry + * (1 if there was a wraparound, i.e. if `l < r`, and 0 otherwise). + * + * d may be aliased to l or r. + * + * \param n Number of limbs of \p d, \p l and \p r. + * \param[out] d The result of the subtraction. + * \param[in] l The left operand. + * \param[in] r The right operand. + * + * \return 1 if `l < r`. + * 0 if `l >= r`. + */ +static mbedtls_mpi_uint mpi_sub_hlp( size_t n, + mbedtls_mpi_uint *d, + const mbedtls_mpi_uint *l, + const mbedtls_mpi_uint *r ) +{ + size_t i; + mbedtls_mpi_uint c = 0, t, z; + + for( i = 0; i < n; i++ ) + { + z = ( l[i] < c ); t = l[i] - c; + c = ( t < r[i] ) + z; d[i] = t - r[i]; + } + + 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 ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t n; + mbedtls_mpi_uint carry; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( A != NULL ); + MPI_VALIDATE_RET( B != NULL ); + + for( n = B->n; n > 0; n-- ) + if( B->p[n - 1] != 0 ) + break; + if( n > A->n ) + { + /* B >= (2^ciL)^n > A */ + ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE; + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, A->n ) ); + + /* Set the high limbs of X to match A. Don't touch the lower limbs + * because X might be aliased to B, and we must not overwrite the + * significant digits of B. */ + if( A->n > n ) + memcpy( X->p + n, A->p + n, ( A->n - n ) * ciL ); + if( X->n > A->n ) + memset( X->p + A->n, 0, ( X->n - A->n ) * ciL ); + + carry = mpi_sub_hlp( n, X->p, A->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]; + } + + /* X should always be positive as a result of unsigned subtractions. */ + X->s = 1; + +cleanup: + 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. + * + * Add \p b * \p s to \p d. + * + * \param i The number of limbs of \p s. + * \param[in] s A bignum to multiply, of size \p i. + * It may overlap with \p d, but only if + * \p d <= \p s. + * Its leading limb must not be \c 0. + * \param[in,out] d The bignum to add to. + * It must be sufficiently large to store the + * result of the multiplication. This means + * \p i + 1 limbs if \p d[\p i - 1] started as 0 and \p b + * is not known a priori. + * \param b A scalar to multiply. + */ +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, + const 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++; + + while( c != 0 ) + { + *d += c; c = ( *d < c ); d++; + } +} + +/* + * Baseline multiplication: X = A * B (HAC 14.12) + */ +int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i, j; + mbedtls_mpi TA, TB; + int result_is_zero = 0; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( A != NULL ); + MPI_VALIDATE_RET( B != NULL ); + + mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB ); + + if( X == A ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) ); A = &TA; } + if( X == B ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) ); B = &TB; } + + for( i = A->n; i > 0; i-- ) + if( A->p[i - 1] != 0 ) + break; + if( i == 0 ) + result_is_zero = 1; + + for( j = B->n; j > 0; j-- ) + if( B->p[j - 1] != 0 ) + break; + if( j == 0 ) + result_is_zero = 1; + + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); + + for( ; j > 0; j-- ) + mpi_mul_hlp( i, A->p, X->p + j - 1, B->p[j - 1] ); + + /* If the result is 0, we don't shortcut the operation, which reduces + * but does not eliminate side channels leaking the zero-ness. We do + * need to take care to set the sign bit properly since the library does + * not fully support an MPI object with a value of 0 and s == -1. */ + if( result_is_zero ) + X->s = 1; + else + X->s = A->s * B->s; + +cleanup: + + mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA ); + + return( ret ); +} + +/* + * Baseline multiplication: X = A * b + */ +int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b ) +{ + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( A != NULL ); + + /* mpi_mul_hlp can't deal with a leading 0. */ + size_t n = A->n; + while( n > 0 && A->p[n - 1] == 0 ) + --n; + + /* The general method below doesn't work if n==0 or b==0. By chance + * calculating the result is trivial in those cases. */ + if( b == 0 || n == 0 ) + { + return( mbedtls_mpi_lset( X, 0 ) ); + } + + /* Calculate A*b as A + A*(b-1) to take advantage of mpi_mul_hlp */ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + /* In general, A * b requires 1 limb more than b. If + * A->p[n - 1] * b / b == A->p[n - 1], then A * b fits in the same + * number of limbs as A and the call to grow() is not required since + * copy() will take care of the growth if needed. However, experimentally, + * making the call to grow() unconditional causes slightly fewer + * calls to calloc() in ECP code, presumably because it reuses the + * same mpi for a while and this way the mpi is more likely to directly + * grow to its final size. */ + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n + 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) ); + mpi_mul_hlp( n, A->p, X->p, b - 1 ); + +cleanup: + return( ret ); +} + +/* + * Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and + * mbedtls_mpi_uint divisor, d + */ +static mbedtls_mpi_uint mbedtls_int_div_int( mbedtls_mpi_uint u1, + mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r ) +{ +#if defined(MBEDTLS_HAVE_UDBL) + mbedtls_t_udbl dividend, quotient; +#else + const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH; + const mbedtls_mpi_uint uint_halfword_mask = ( (mbedtls_mpi_uint) 1 << biH ) - 1; + mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient; + mbedtls_mpi_uint u0_msw, u0_lsw; + size_t s; +#endif + + /* + * Check for overflow + */ + if( 0 == d || u1 >= d ) + { + if (r != NULL) *r = ~0; + + return ( ~0 ); + } + +#if defined(MBEDTLS_HAVE_UDBL) + dividend = (mbedtls_t_udbl) u1 << biL; + dividend |= (mbedtls_t_udbl) u0; + quotient = dividend / d; + if( quotient > ( (mbedtls_t_udbl) 1 << biL ) - 1 ) + quotient = ( (mbedtls_t_udbl) 1 << biL ) - 1; + + if( r != NULL ) + *r = (mbedtls_mpi_uint)( dividend - (quotient * d ) ); + + return (mbedtls_mpi_uint) quotient; +#else + + /* + * Algorithm D, Section 4.3.1 - The Art of Computer Programming + * Vol. 2 - Seminumerical Algorithms, Knuth + */ + + /* + * Normalize the divisor, d, and dividend, u0, u1 + */ + s = mbedtls_clz( d ); + d = d << s; + + u1 = u1 << s; + u1 |= ( u0 >> ( biL - s ) ) & ( -(mbedtls_mpi_sint)s >> ( biL - 1 ) ); + u0 = u0 << s; + + d1 = d >> biH; + d0 = d & uint_halfword_mask; + + u0_msw = u0 >> biH; + u0_lsw = u0 & uint_halfword_mask; + + /* + * Find the first quotient and remainder + */ + q1 = u1 / d1; + r0 = u1 - d1 * q1; + + while( q1 >= radix || ( q1 * d0 > radix * r0 + u0_msw ) ) + { + q1 -= 1; + r0 += d1; + + if ( r0 >= radix ) break; + } + + rAX = ( u1 * radix ) + ( u0_msw - q1 * d ); + q0 = rAX / d1; + r0 = rAX - q0 * d1; + + while( q0 >= radix || ( q0 * d0 > radix * r0 + u0_lsw ) ) + { + q0 -= 1; + r0 += d1; + + if ( r0 >= radix ) break; + } + + if (r != NULL) + *r = ( rAX * radix + u0_lsw - q0 * d ) >> s; + + quotient = q1 * radix + q0; + + return quotient; +#endif +} + +/* + * Division by mbedtls_mpi: A = Q * B + R (HAC 14.20) + */ +int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, + const mbedtls_mpi *B ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i, n, t, k; + mbedtls_mpi X, Y, Z, T1, T2; + mbedtls_mpi_uint TP2[3]; + MPI_VALIDATE_RET( A != NULL ); + MPI_VALIDATE_RET( B != NULL ); + + if( mbedtls_mpi_cmp_int( B, 0 ) == 0 ) + return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO ); + + mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); + mbedtls_mpi_init( &T1 ); + /* + * Avoid dynamic memory allocations for constant-size T2. + * + * T2 is used for comparison only and the 3 limbs are assigned explicitly, + * so nobody increase the size of the MPI and we're safe to use an on-stack + * buffer. + */ + T2.s = 1; + T2.n = sizeof( TP2 ) / sizeof( *TP2 ); + T2.p = TP2; + + if( mbedtls_mpi_cmp_abs( A, B ) < 0 ) + { + if( Q != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_lset( Q, 0 ) ); + if( R != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, A ) ); + return( 0 ); + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &X, A ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, B ) ); + X.s = Y.s = 1; + + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &Z, A->n + 2 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Z, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T1, A->n + 2 ) ); + + k = mbedtls_mpi_bitlen( &Y ) % biL; + if( k < biL - 1 ) + { + k = biL - 1 - k; + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &X, k ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, k ) ); + } + else k = 0; + + n = X.n - 1; + t = Y.n - 1; + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, biL * ( n - t ) ) ); + + while( mbedtls_mpi_cmp_mpi( &X, &Y ) >= 0 ) + { + Z.p[n - t]++; + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &Y ) ); + } + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, biL * ( n - t ) ) ); + + for( i = n; i > t ; i-- ) + { + if( X.p[i] >= Y.p[t] ) + Z.p[i - t - 1] = ~0; + else + { + Z.p[i - t - 1] = mbedtls_int_div_int( X.p[i], X.p[i - 1], + Y.p[t], NULL); + } + + T2.p[0] = ( i < 2 ) ? 0 : X.p[i - 2]; + T2.p[1] = ( i < 1 ) ? 0 : X.p[i - 1]; + T2.p[2] = X.p[i]; + + Z.p[i - t - 1]++; + do + { + Z.p[i - t - 1]--; + + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T1, 0 ) ); + T1.p[0] = ( t < 1 ) ? 0 : Y.p[t - 1]; + T1.p[1] = Y.p[t]; + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) ); + } + while( mbedtls_mpi_cmp_mpi( &T1, &T2 ) > 0 ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) ); + + if( mbedtls_mpi_cmp_int( &X, 0 ) < 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &Y ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &X, &X, &T1 ) ); + Z.p[i - t - 1]--; + } + } + + if( Q != NULL ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( Q, &Z ) ); + Q->s = A->s * B->s; + } + + if( R != NULL ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &X, k ) ); + X.s = A->s; + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, &X ) ); + + if( mbedtls_mpi_cmp_int( R, 0 ) == 0 ) + R->s = 1; + } + +cleanup: + + mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); + mbedtls_mpi_free( &T1 ); + mbedtls_platform_zeroize( TP2, sizeof( TP2 ) ); + + return( ret ); +} + +/* + * Division by int: A = Q * b + R + */ +int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, + const mbedtls_mpi *A, + mbedtls_mpi_sint b ) +{ + mbedtls_mpi _B; + mbedtls_mpi_uint p[1]; + MPI_VALIDATE_RET( A != NULL ); + + p[0] = ( b < 0 ) ? -b : b; + _B.s = ( b < 0 ) ? -1 : 1; + _B.n = 1; + _B.p = p; + + return( mbedtls_mpi_div_mpi( Q, R, A, &_B ) ); +} + +/* + * Modulo: R = A mod B + */ +int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + MPI_VALIDATE_RET( R != NULL ); + MPI_VALIDATE_RET( A != NULL ); + MPI_VALIDATE_RET( B != NULL ); + + if( mbedtls_mpi_cmp_int( B, 0 ) < 0 ) + return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( NULL, R, A, B ) ); + + while( mbedtls_mpi_cmp_int( R, 0 ) < 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( R, R, B ) ); + + while( mbedtls_mpi_cmp_mpi( R, B ) >= 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( R, R, B ) ); + +cleanup: + + return( ret ); +} + +/* + * Modulo: r = A mod b + */ +int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b ) +{ + size_t i; + mbedtls_mpi_uint x, y, z; + MPI_VALIDATE_RET( r != NULL ); + MPI_VALIDATE_RET( A != NULL ); + + if( b == 0 ) + return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO ); + + if( b < 0 ) + return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE ); + + /* + * handle trivial cases + */ + if( b == 1 ) + { + *r = 0; + return( 0 ); + } + + if( b == 2 ) + { + *r = A->p[0] & 1; + return( 0 ); + } + + /* + * general case + */ + for( i = A->n, y = 0; i > 0; i-- ) + { + x = A->p[i - 1]; + y = ( y << biH ) | ( x >> biH ); + z = y / b; + y -= z * b; + + x <<= biH; + y = ( y << biH ) | ( x >> biH ); + z = y / b; + y -= z * b; + } + + /* + * If A is negative, then the current y represents a negative value. + * Flipping it to the positive side. + */ + if( A->s < 0 && y != 0 ) + y = b - y; + + *r = y; + + return( 0 ); +} + +/* + * Fast Montgomery initialization (thanks to Tom St Denis) + */ +static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N ) +{ + mbedtls_mpi_uint x, m0 = N->p[0]; + unsigned int i; + + x = m0; + x += ( ( m0 + 2 ) & 4 ) << 1; + + for( i = biL; i >= 8; i /= 2 ) + x *= ( 2 - ( m0 * x ) ); + + *mm = ~x + 1; +} + +/** Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36) + * + * \param[in,out] A One of the numbers to multiply. + * It must have at least as many limbs as N + * (A->n >= N->n), and any limbs beyond n are ignored. + * On successful completion, A contains the result of + * the multiplication A * B * R^-1 mod N where + * R = (2^ciL)^n. + * \param[in] B One of the numbers to multiply. + * It must be nonzero and must not have more limbs than N + * (B->n <= N->n). + * \param[in] N The modulo. N must be odd. + * \param mm The value calculated by `mpi_montg_init(&mm, N)`. + * This is -N^-1 mod 2^ciL. + * \param[in,out] T A bignum for temporary storage. + * It must be at least twice the limb size of N plus 2 + * (T->n >= 2 * (N->n + 1)). + * Its initial content is unused and + * its final content is indeterminate. + * Note that unlike the usual convention in the library + * for `const mbedtls_mpi*`, the content of T can change. + */ +static void mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm, + const mbedtls_mpi *T ) +{ + size_t i, n, m; + mbedtls_mpi_uint u0, u1, *d; + + memset( T->p, 0, T->n * ciL ); + + d = T->p; + n = N->n; + m = ( B->n < n ) ? B->n : n; + + for( i = 0; i < n; i++ ) + { + /* + * T = (T + u0*B + u1*N) / 2^biL + */ + u0 = A->p[i]; + u1 = ( d[0] + u0 * B->p[0] ) * mm; + + mpi_mul_hlp( m, B->p, d, u0 ); + mpi_mul_hlp( n, N->p, d, u1 ); + + *d++ = u0; d[n + 1] = 0; + } + + /* At this point, d is either the desired result or the desired result + * plus N. We now potentially subtract N, avoiding leaking whether the + * subtraction is performed through side channels. */ + + /* Copy the n least significant limbs of d to A, so that + * A = d if d < N (recall that N has n limbs). */ + memcpy( A->p, d, n * ciL ); + /* If d >= N then we want to set A to d - N. To prevent timing attacks, + * do the calculation without using conditional tests. */ + /* Set d to d0 + (2^biL)^n - N where d0 is the current value of d. */ + d[n] += 1; + d[n] -= mpi_sub_hlp( n, d, 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 ); +} + +/* + * Constant-flow boolean "equal" comparison: + * return x == y + * + * This function can be used to write constant-time code by replacing branches + * with bit operations - it can be used in conjunction with + * mbedtls_ssl_cf_mask_from_bit(). + * + * This function is implemented without using comparison operators, as those + * might be translated to branches by some compilers on some platforms. + */ +static size_t mbedtls_mpi_cf_bool_eq( size_t x, size_t y ) +{ + /* diff = 0 if x == y, non-zero otherwise */ + const size_t diff = x ^ y; + + /* MSVC has a warning about unary minus on unsigned integer types, + * but this is well-defined and precisely what we want to do here. */ +#if defined(_MSC_VER) +#pragma warning( push ) +#pragma warning( disable : 4146 ) +#endif + + /* diff_msb's most significant bit is equal to x != y */ + const size_t diff_msb = ( diff | (size_t) -diff ); + +#if defined(_MSC_VER) +#pragma warning( pop ) +#endif + + /* diff1 = (x != y) ? 1 : 0 */ + const size_t diff1 = diff_msb >> ( sizeof( diff_msb ) * 8 - 1 ); + + return( 1 ^ diff1 ); +} + +/** + * Select an MPI from a table without leaking the index. + * + * This is functionally equivalent to mbedtls_mpi_copy(R, T[idx]) except it + * reads the entire table in order to avoid leaking the value of idx to an + * attacker able to observe memory access patterns. + * + * \param[out] R Where to write the selected MPI. + * \param[in] T The table to read from. + * \param[in] T_size The number of elements in the table. + * \param[in] idx The index of the element to select; + * this must satisfy 0 <= idx < T_size. + * + * \return \c 0 on success, or a negative error code. + */ +static int mpi_select( mbedtls_mpi *R, const mbedtls_mpi *T, size_t T_size, size_t idx ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + + for( size_t i = 0; i < T_size; i++ ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( R, &T[i], + (unsigned char) mbedtls_mpi_cf_bool_eq( i, idx ) ) ); + } + +cleanup: + return( ret ); +} + +/* + * Sliding-window exponentiation: X = A^E mod N (HAC 14.85) + */ +int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, + const mbedtls_mpi *E, const mbedtls_mpi *N, + mbedtls_mpi *_RR ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t wbits, wsize, one = 1; + size_t i, j, nblimbs; + size_t bufsize, nbits; + mbedtls_mpi_uint ei, mm, state; + mbedtls_mpi RR, T, W[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], WW, Apos; + int neg; + + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( A != NULL ); + MPI_VALIDATE_RET( E != NULL ); + MPI_VALIDATE_RET( N != NULL ); + + if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 || ( N->p[0] & 1 ) == 0 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + if( mbedtls_mpi_cmp_int( E, 0 ) < 0 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + if( mbedtls_mpi_bitlen( E ) > MBEDTLS_MPI_MAX_BITS || + mbedtls_mpi_bitlen( N ) > MBEDTLS_MPI_MAX_BITS ) + return ( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + /* + * Init temps and window size + */ + mpi_montg_init( &mm, N ); + mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &T ); + mbedtls_mpi_init( &Apos ); + mbedtls_mpi_init( &WW ); + memset( W, 0, sizeof( W ) ); + + i = mbedtls_mpi_bitlen( E ); + + 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; + /* All W[i] and X must have at least N->n limbs for the mpi_montmul() + * and mpi_montred() calls later. Here we ensure that W[1] and X are + * large enough, and later we'll grow other W[i] to the same length. + * They must not be shrunk midway through this function! + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( 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 ) ); + /* This should be a no-op because W[1] is already that large before + * mbedtls_mpi_mod_mpi(), but it's necessary to avoid an overflow + * in mpi_montmul() below, so let's make sure. */ + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], N->n + 1 ) ); + } + else + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) ); + + /* Note that this is safe because W[1] always has at least N->n limbs + * (it grew above and was preserved by mbedtls_mpi_copy()). */ + mpi_montmul( &W[1], &RR, N, mm, &T ); + + /* + * 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 + */ + MBEDTLS_MPI_CHK( mpi_select( &WW, W, (size_t) 1 << wsize, wbits ) ); + mpi_montmul( X, &WW, 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 ); + mbedtls_mpi_free( &WW ); + + if( _RR == NULL || _RR->p == NULL ) + mbedtls_mpi_free( &RR ); + + return( ret ); +} + +/* + * Greatest common divisor: G = gcd(A, B) (HAC 14.54) + */ +int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t lz, lzt; + mbedtls_mpi TA, TB; + + MPI_VALIDATE_RET( G != NULL ); + MPI_VALIDATE_RET( A != NULL ); + MPI_VALIDATE_RET( B != NULL ); + + mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) ); + + lz = mbedtls_mpi_lsb( &TA ); + lzt = mbedtls_mpi_lsb( &TB ); + + /* The loop below gives the correct result when A==0 but not when B==0. + * So have a special case for B==0. Leverage the fact that we just + * calculated the lsb and lsb(B)==0 iff B is odd or 0 to make the test + * slightly more efficient than cmp_int(). */ + if( lzt == 0 && mbedtls_mpi_get_bit( &TB, 0 ) == 0 ) + { + ret = mbedtls_mpi_copy( G, A ); + goto cleanup; + } + + if( lzt < lz ) + lz = lzt; + + TA.s = TB.s = 1; + + /* We mostly follow the procedure described in HAC 14.54, but with some + * minor differences: + * - Sequences of multiplications or divisions by 2 are grouped into a + * single shift operation. + * - The procedure in HAC assumes that 0 < TB <= TA. + * - The condition TB <= TA is not actually necessary for correctness. + * TA and TB have symmetric roles except for the loop termination + * condition, and the shifts at the beginning of the loop body + * remove any significance from the ordering of TA vs TB before + * the shifts. + * - If TA = 0, the loop goes through 0 iterations and the result is + * correctly TB. + * - The case TB = 0 was short-circuited above. + * + * For the correctness proof below, decompose the original values of + * A and B as + * A = sa * 2^a * A' with A'=0 or A' odd, and sa = +-1 + * B = sb * 2^b * B' with B'=0 or B' odd, and sb = +-1 + * Then gcd(A, B) = 2^{min(a,b)} * gcd(A',B'), + * and gcd(A',B') is odd or 0. + * + * At the beginning, we have TA = |A| and TB = |B| so gcd(A,B) = gcd(TA,TB). + * The code maintains the following invariant: + * gcd(A,B) = 2^k * gcd(TA,TB) for some k (I) + */ + + /* Proof that the loop terminates: + * At each iteration, either the right-shift by 1 is made on a nonzero + * value and the nonnegative integer bitlen(TA) + bitlen(TB) decreases + * by at least 1, or the right-shift by 1 is made on zero and then + * TA becomes 0 which ends the loop (TB cannot be 0 if it is right-shifted + * since in that case TB is calculated from TB-TA with the condition TB>TA). + */ + while( mbedtls_mpi_cmp_int( &TA, 0 ) != 0 ) + { + /* Divisions by 2 preserve the invariant (I). */ + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) ); + + /* Set either TA or TB to |TA-TB|/2. Since TA and TB are both odd, + * TA-TB is even so the division by 2 has an integer result. + * Invariant (I) is preserved since any odd divisor of both TA and TB + * also divides |TA-TB|/2, and any odd divisor of both TA and |TA-TB|/2 + * also divides TB, and any odd divisior of both TB and |TA-TB|/2 also + * divides TA. + */ + if( mbedtls_mpi_cmp_mpi( &TA, &TB ) >= 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TA, &TA, &TB ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, 1 ) ); + } + else + { + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TB, &TB, &TA ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, 1 ) ); + } + /* Note that one of TA or TB is still odd. */ + } + + /* By invariant (I), gcd(A,B) = 2^k * gcd(TA,TB) for some k. + * At the loop exit, TA = 0, so gcd(TA,TB) = TB. + * - If there was at least one loop iteration, then one of TA or TB is odd, + * and TA = 0, so TB is odd and gcd(TA,TB) = gcd(A',B'). In this case, + * lz = min(a,b) so gcd(A,B) = 2^lz * TB. + * - If there was no loop iteration, then A was 0, and gcd(A,B) = B. + * In this case, lz = 0 and B = TB so gcd(A,B) = B = 2^lz * TB as well. + */ + + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) ); + +cleanup: + + mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB ); + + return( ret ); +} + +/* Fill X with n_bytes random bytes. + * X must already have room for those bytes. + * The ordering of the bytes returned from the RNG is suitable for + * deterministic ECDSA (see RFC 6979 §3.3 and mbedtls_mpi_random()). + * The size and sign of X are unchanged. + * n_bytes must not be 0. + */ +static int mpi_fill_random_internal( + mbedtls_mpi *X, size_t n_bytes, + int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + const size_t limbs = CHARS_TO_LIMBS( n_bytes ); + const size_t overhead = ( limbs * ciL ) - n_bytes; + + if( X->n < limbs ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + memset( X->p, 0, overhead ); + memset( (unsigned char *) X->p + limbs * ciL, 0, ( X->n - limbs ) * ciL ); + MBEDTLS_MPI_CHK( f_rng( p_rng, (unsigned char *) X->p + overhead, n_bytes ) ); + mpi_bigendian_to_host( X->p, limbs ); + +cleanup: + return( ret ); +} + +/* + * Fill X with size bytes of random. + * + * Use a temporary bytes representation to make sure the result is the same + * regardless of the platform endianness (useful when f_rng is actually + * deterministic, eg for tests). + */ +int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t const limbs = CHARS_TO_LIMBS( size ); + + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( f_rng != NULL ); + + /* Ensure that target MPI has exactly the necessary number of limbs */ + MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, limbs ) ); + if( size == 0 ) + return( 0 ); + + ret = mpi_fill_random_internal( X, size, f_rng, p_rng ); + +cleanup: + return( ret ); +} + +int mbedtls_mpi_random( mbedtls_mpi *X, + mbedtls_mpi_sint min, + const mbedtls_mpi *N, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + int ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + int count; + unsigned lt_lower = 1, lt_upper = 0; + size_t n_bits = mbedtls_mpi_bitlen( N ); + size_t n_bytes = ( n_bits + 7 ) / 8; + mbedtls_mpi lower_bound; + + if( min < 0 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + if( mbedtls_mpi_cmp_int( N, min ) <= 0 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + /* + * When min == 0, each try has at worst a probability 1/2 of failing + * (the msb has a probability 1/2 of being 0, and then the result will + * be < N), so after 30 tries failure probability is a most 2**(-30). + * + * When N is just below a power of 2, as is the case when generating + * a random scalar on most elliptic curves, 1 try is enough with + * overwhelming probability. When N is just above a power of 2, + * as when generating a random scalar on secp224k1, each try has + * a probability of failing that is almost 1/2. + * + * The probabilities are almost the same if min is nonzero but negligible + * compared to N. This is always the case when N is crypto-sized, but + * it's convenient to support small N for testing purposes. When N + * is small, use a higher repeat count, otherwise the probability of + * failure is macroscopic. + */ + count = ( n_bytes > 4 ? 30 : 250 ); + + mbedtls_mpi_init( &lower_bound ); + + /* Ensure that target MPI has exactly the same number of limbs + * as the upper bound, even if the upper bound has leading zeros. + * This is necessary for the mbedtls_mpi_lt_mpi_ct() check. */ + MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, N->n ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &lower_bound, N->n ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &lower_bound, min ) ); + + /* + * Match the procedure given in RFC 6979 §3.3 (deterministic ECDSA) + * when f_rng is a suitably parametrized instance of HMAC_DRBG: + * - use the same byte ordering; + * - keep the leftmost n_bits bits of the generated octet string; + * - try until result is in the desired range. + * This also avoids any bias, which is especially important for ECDSA. + */ + do + { + MBEDTLS_MPI_CHK( mpi_fill_random_internal( X, n_bytes, f_rng, p_rng ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, 8 * n_bytes - n_bits ) ); + + if( --count == 0 ) + { + ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_lt_mpi_ct( X, &lower_bound, <_lower ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lt_mpi_ct( X, N, <_upper ) ); + } + while( lt_lower != 0 || lt_upper == 0 ); + +cleanup: + mbedtls_mpi_free( &lower_bound ); + return( ret ); +} + +/* + * Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64) + */ +int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( A != NULL ); + MPI_VALIDATE_RET( N != NULL ); + + if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TU ); mbedtls_mpi_init( &U1 ); mbedtls_mpi_init( &U2 ); + mbedtls_mpi_init( &G ); mbedtls_mpi_init( &TB ); mbedtls_mpi_init( &TV ); + mbedtls_mpi_init( &V1 ); mbedtls_mpi_init( &V2 ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, A, N ) ); + + if( mbedtls_mpi_cmp_int( &G, 1 ) != 0 ) + { + ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + goto cleanup; + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &TA, A, N ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TU, &TA ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, N ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TV, N ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U1, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U2, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V1, 0 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V2, 1 ) ); + + do + { + while( ( TU.p[0] & 1 ) == 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TU, 1 ) ); + + if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &U1, &U1, &TB ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &TA ) ); + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U1, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U2, 1 ) ); + } + + while( ( TV.p[0] & 1 ) == 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TV, 1 ) ); + + if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, &TB ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &TA ) ); + } + + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V1, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V2, 1 ) ); + } + + if( mbedtls_mpi_cmp_mpi( &TU, &TV ) >= 0 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TU, &TU, &TV ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U1, &U1, &V1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &V2 ) ); + } + else + { + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TV, &TV, &TU ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, &U1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &U2 ) ); + } + } + while( mbedtls_mpi_cmp_int( &TU, 0 ) != 0 ); + + while( mbedtls_mpi_cmp_int( &V1, 0 ) < 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, N ) ); + + while( mbedtls_mpi_cmp_mpi( &V1, N ) >= 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, N ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &V1 ) ); + +cleanup: + + mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TU ); mbedtls_mpi_free( &U1 ); mbedtls_mpi_free( &U2 ); + mbedtls_mpi_free( &G ); mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TV ); + mbedtls_mpi_free( &V1 ); mbedtls_mpi_free( &V2 ); + + return( ret ); +} + +#if defined(MBEDTLS_GENPRIME) + +static const int small_prime[] = +{ + 3, 5, 7, 11, 13, 17, 19, 23, + 29, 31, 37, 41, 43, 47, 53, 59, + 61, 67, 71, 73, 79, 83, 89, 97, + 101, 103, 107, 109, 113, 127, 131, 137, + 139, 149, 151, 157, 163, 167, 173, 179, + 181, 191, 193, 197, 199, 211, 223, 227, + 229, 233, 239, 241, 251, 257, 263, 269, + 271, 277, 281, 283, 293, 307, 311, 313, + 317, 331, 337, 347, 349, 353, 359, 367, + 373, 379, 383, 389, 397, 401, 409, 419, + 421, 431, 433, 439, 443, 449, 457, 461, + 463, 467, 479, 487, 491, 499, 503, 509, + 521, 523, 541, 547, 557, 563, 569, 571, + 577, 587, 593, 599, 601, 607, 613, 617, + 619, 631, 641, 643, 647, 653, 659, 661, + 673, 677, 683, 691, 701, 709, 719, 727, + 733, 739, 743, 751, 757, 761, 769, 773, + 787, 797, 809, 811, 821, 823, 827, 829, + 839, 853, 857, 859, 863, 877, 881, 883, + 887, 907, 911, 919, 929, 937, 941, 947, + 953, 967, 971, 977, 983, 991, 997, -103 +}; + +/* + * Small divisors test (X must be positive) + * + * Return values: + * 0: no small factor (possible prime, more tests needed) + * 1: certain prime + * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime + * other negative: error + */ +static int mpi_check_small_factors( const mbedtls_mpi *X ) +{ + int ret = 0; + size_t i; + mbedtls_mpi_uint r; + + if( ( X->p[0] & 1 ) == 0 ) + return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ); + + for( i = 0; small_prime[i] > 0; i++ ) + { + if( mbedtls_mpi_cmp_int( X, small_prime[i] ) <= 0 ) + return( 1 ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, small_prime[i] ) ); + + if( r == 0 ) + return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ); + } + +cleanup: + return( ret ); +} + +/* + * Miller-Rabin pseudo-primality test (HAC 4.24) + */ +static int mpi_miller_rabin( const mbedtls_mpi *X, size_t rounds, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + int ret, count; + size_t i, j, k, s; + mbedtls_mpi W, R, T, A, RR; + + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( f_rng != NULL ); + + mbedtls_mpi_init( &W ); mbedtls_mpi_init( &R ); + mbedtls_mpi_init( &T ); mbedtls_mpi_init( &A ); + mbedtls_mpi_init( &RR ); + + /* + * W = |X| - 1 + * R = W >> lsb( W ) + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &W, X, 1 ) ); + s = mbedtls_mpi_lsb( &W ); + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R, &W ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &R, s ) ); + + for( i = 0; i < rounds; i++ ) + { + /* + * pick a random A, 1 < A < |X| - 1 + */ + count = 0; + do { + MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) ); + + j = mbedtls_mpi_bitlen( &A ); + k = mbedtls_mpi_bitlen( &W ); + if (j > k) { + A.p[A.n - 1] &= ( (mbedtls_mpi_uint) 1 << ( k - ( A.n - 1 ) * biL - 1 ) ) - 1; + } + + if (count++ > 30) { + ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + goto cleanup; + } + + } while ( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 || + mbedtls_mpi_cmp_int( &A, 1 ) <= 0 ); + + /* + * A = A^R mod |X| + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &A, &A, &R, X, &RR ) ); + + if( mbedtls_mpi_cmp_mpi( &A, &W ) == 0 || + mbedtls_mpi_cmp_int( &A, 1 ) == 0 ) + continue; + + j = 1; + while( j < s && mbedtls_mpi_cmp_mpi( &A, &W ) != 0 ) + { + /* + * A = A * A mod |X| + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &A, &A ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &A, &T, X ) ); + + if( mbedtls_mpi_cmp_int( &A, 1 ) == 0 ) + break; + + j++; + } + + /* + * not prime if A != |X| - 1 or A == 1 + */ + if( mbedtls_mpi_cmp_mpi( &A, &W ) != 0 || + mbedtls_mpi_cmp_int( &A, 1 ) == 0 ) + { + ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + break; + } + } + +cleanup: + mbedtls_mpi_free( &W ); mbedtls_mpi_free( &R ); + mbedtls_mpi_free( &T ); mbedtls_mpi_free( &A ); + mbedtls_mpi_free( &RR ); + + return( ret ); +} + +/* + * Pseudo-primality test: small factors, then Miller-Rabin + */ +int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi XX; + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( f_rng != NULL ); + + XX.s = 1; + XX.n = X->n; + XX.p = X->p; + + if( mbedtls_mpi_cmp_int( &XX, 0 ) == 0 || + mbedtls_mpi_cmp_int( &XX, 1 ) == 0 ) + return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ); + + if( mbedtls_mpi_cmp_int( &XX, 2 ) == 0 ) + return( 0 ); + + if( ( ret = mpi_check_small_factors( &XX ) ) != 0 ) + { + if( ret == 1 ) + return( 0 ); + + return( ret ); + } + + return( mpi_miller_rabin( &XX, rounds, f_rng, p_rng ) ); +} + +#if !defined(MBEDTLS_DEPRECATED_REMOVED) +/* + * Pseudo-primality test, error probability 2^-80 + */ +int mbedtls_mpi_is_prime( const mbedtls_mpi *X, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( f_rng != NULL ); + + /* + * In the past our key generation aimed for an error rate of at most + * 2^-80. Since this function is deprecated, aim for the same certainty + * here as well. + */ + return( mbedtls_mpi_is_prime_ext( X, 40, f_rng, p_rng ) ); +} +#endif + +/* + * Prime number generation + * + * To generate an RSA key in a way recommended by FIPS 186-4, both primes must + * be either 1024 bits or 1536 bits long, and flags must contain + * MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR. + */ +int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng ) +{ +#ifdef MBEDTLS_HAVE_INT64 +// ceil(2^63.5) +#define CEIL_MAXUINT_DIV_SQRT2 0xb504f333f9de6485ULL +#else +// ceil(2^31.5) +#define CEIL_MAXUINT_DIV_SQRT2 0xb504f334U +#endif + int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + size_t k, n; + int rounds; + mbedtls_mpi_uint r; + mbedtls_mpi Y; + + MPI_VALIDATE_RET( X != NULL ); + MPI_VALIDATE_RET( f_rng != NULL ); + + if( nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS ) + return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); + + mbedtls_mpi_init( &Y ); + + n = BITS_TO_LIMBS( nbits ); + + if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR ) == 0 ) + { + /* + * 2^-80 error probability, number of rounds chosen per HAC, table 4.4 + */ + rounds = ( ( nbits >= 1300 ) ? 2 : ( nbits >= 850 ) ? 3 : + ( nbits >= 650 ) ? 4 : ( nbits >= 350 ) ? 8 : + ( nbits >= 250 ) ? 12 : ( nbits >= 150 ) ? 18 : 27 ); + } + else + { + /* + * 2^-100 error probability, number of rounds computed based on HAC, + * fact 4.48 + */ + rounds = ( ( nbits >= 1450 ) ? 4 : ( nbits >= 1150 ) ? 5 : + ( nbits >= 1000 ) ? 6 : ( nbits >= 850 ) ? 7 : + ( nbits >= 750 ) ? 8 : ( nbits >= 500 ) ? 13 : + ( nbits >= 250 ) ? 28 : ( nbits >= 150 ) ? 40 : 51 ); + } + + while( 1 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) ); + /* make sure generated number is at least (nbits-1)+0.5 bits (FIPS 186-4 §B.3.3 steps 4.4, 5.5) */ + if( X->p[n-1] < CEIL_MAXUINT_DIV_SQRT2 ) continue; + + k = n * biL; + if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits ) ); + X->p[0] |= 1; + + if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH ) == 0 ) + { + ret = mbedtls_mpi_is_prime_ext( X, rounds, f_rng, p_rng ); + + if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ) + goto cleanup; + } + else + { + /* + * An necessary condition for Y and X = 2Y + 1 to be prime + * is X = 2 mod 3 (which is equivalent to Y = 2 mod 3). + * Make sure it is satisfied, while keeping X = 3 mod 4 + */ + + X->p[0] |= 2; + + MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, 3 ) ); + if( r == 0 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 8 ) ); + else if( r == 1 ) + MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 4 ) ); + + /* Set Y = (X-1) / 2, which is X / 2 because X is odd */ + MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, X ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, 1 ) ); + + while( 1 ) + { + /* + * First, check small factors for X and Y + * before doing Miller-Rabin on any of them + */ + if( ( ret = mpi_check_small_factors( X ) ) == 0 && + ( ret = mpi_check_small_factors( &Y ) ) == 0 && + ( ret = mpi_miller_rabin( X, rounds, f_rng, p_rng ) ) + == 0 && + ( ret = mpi_miller_rabin( &Y, rounds, f_rng, p_rng ) ) + == 0 ) + goto cleanup; + + if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ) + goto cleanup; + + /* + * Next candidates. We want to preserve Y = (X-1) / 2 and + * Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3) + * so up Y by 6 and X by 12. + */ + MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 12 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &Y, &Y, 6 ) ); + } + } + } + +cleanup: + + mbedtls_mpi_free( &Y ); + + return( ret ); +} + +#endif /* MBEDTLS_GENPRIME */ + +#if defined(MBEDTLS_SELF_TEST) + +#define GCD_PAIR_COUNT 3 + +static const int gcd_pairs[GCD_PAIR_COUNT][3] = +{ + { 693, 609, 21 }, + { 1764, 868, 28 }, + { 768454923, 542167814, 1 } +}; + +/* + * Checkup routine + */ +int mbedtls_mpi_self_test( int verbose ) +{ + int ret, i; + mbedtls_mpi A, E, N, X, Y, U, V; + + mbedtls_mpi_init( &A ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &N ); mbedtls_mpi_init( &X ); + mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &U ); mbedtls_mpi_init( &V ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &A, 16, + "EFE021C2645FD1DC586E69184AF4A31E" \ + "D5F53E93B5F123FA41680867BA110131" \ + "944FE7952E2517337780CB0DB80E61AA" \ + "E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &E, 16, + "B2E7EFD37075B9F03FF989C7C5051C20" \ + "34D2A323810251127E7BF8625A4F49A5" \ + "F3E27F4DA8BD59C47D6DAABA4C8127BD" \ + "5B5C25763222FEFCCFC38B832366C29E" ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &N, 16, + "0066A198186C18C10B2F5ED9B522752A" \ + "9830B69916E535C8F047518A889A43A5" \ + "94B6BED27A168D31D4A52F88925AA8F5" ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &A, &N ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16, + "602AB7ECA597A3D6B56FF9829A5E8B85" \ + "9E857EA95A03512E2BAE7391688D264A" \ + "A5663B0341DB9CCFD2C4C5F421FEC814" \ + "8001B72E848A38CAE1C65F78E56ABDEF" \ + "E12D3C039B8A02D6BE593F0BBBDA56F1" \ + "ECF677152EF804370C1A305CAF3B5BF1" \ + "30879B56C61DE584A0F53A2447A51E" ) ); + + if( verbose != 0 ) + mbedtls_printf( " MPI test #1 (mul_mpi): " ); + + if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 ) + { + if( verbose != 0 ) + mbedtls_printf( "failed\n" ); + + ret = 1; + goto cleanup; + } + + if( verbose != 0 ) + mbedtls_printf( "passed\n" ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &X, &Y, &A, &N ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16, + "256567336059E52CAE22925474705F39A94" ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &V, 16, + "6613F26162223DF488E9CD48CC132C7A" \ + "0AC93C701B001B092E4E5B9F73BCD27B" \ + "9EE50D0657C77F374E903CDFA4C642" ) ); + + if( verbose != 0 ) + mbedtls_printf( " MPI test #2 (div_mpi): " ); + + if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 || + mbedtls_mpi_cmp_mpi( &Y, &V ) != 0 ) + { + if( verbose != 0 ) + mbedtls_printf( "failed\n" ); + + ret = 1; + goto cleanup; + } + + if( verbose != 0 ) + mbedtls_printf( "passed\n" ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &X, &A, &E, &N, NULL ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16, + "36E139AEA55215609D2816998ED020BB" \ + "BD96C37890F65171D948E9BC7CBAA4D9" \ + "325D24D6A3C12710F10A09FA08AB87" ) ); + + if( verbose != 0 ) + mbedtls_printf( " MPI test #3 (exp_mod): " ); + + if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 ) + { + if( verbose != 0 ) + mbedtls_printf( "failed\n" ); + + ret = 1; + goto cleanup; + } + + if( verbose != 0 ) + mbedtls_printf( "passed\n" ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &X, &A, &N ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16, + "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \ + "C3DBA76456363A10869622EAC2DD84EC" \ + "C5B8A74DAC4D09E03B5E0BE779F2DF61" ) ); + + if( verbose != 0 ) + mbedtls_printf( " MPI test #4 (inv_mod): " ); + + if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 ) + { + if( verbose != 0 ) + mbedtls_printf( "failed\n" ); + + ret = 1; + goto cleanup; + } + + if( verbose != 0 ) + mbedtls_printf( "passed\n" ); + + if( verbose != 0 ) + mbedtls_printf( " MPI test #5 (simple gcd): " ); + + for( i = 0; i < GCD_PAIR_COUNT; i++ ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &X, gcd_pairs[i][0] ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Y, gcd_pairs[i][1] ) ); + + MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &A, &X, &Y ) ); + + if( mbedtls_mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 ) + { + if( verbose != 0 ) + mbedtls_printf( "failed at %d\n", i ); + + ret = 1; + goto cleanup; + } + } + + if( verbose != 0 ) + mbedtls_printf( "passed\n" ); + +cleanup: + + if( ret != 0 && verbose != 0 ) + mbedtls_printf( "Unexpected error, return code = %08X\n", (unsigned int) ret ); + + mbedtls_mpi_free( &A ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &N ); mbedtls_mpi_free( &X ); + mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &U ); mbedtls_mpi_free( &V ); + + if( verbose != 0 ) + mbedtls_printf( "\n" ); + + return( ret ); +} + +#endif /* MBEDTLS_SELF_TEST */ + +#endif /* MBEDTLS_BIGNUM_C */ |