/* * 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 "c_types.h" #include "mbedtls/bignum.h" #include "mbedtls/bn_mul.h" #include #if defined(MBEDTLS_PLATFORM_C) #include "mbedtls/platform.h" #else #include #include #define mbedtls_printf printf #define mbedtls_calloc calloc #define mbedtls_free free #endif /* Implementation that should never be optimized out by the compiler */ static void mbedtls_zeroize( void *v, size_t n ) { volatile unsigned char *p = v; while( n-- ) *p++ = 0; } #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 ) ) /* * Initialize one MPI */ void mbedtls_mpi_init( mbedtls_mpi *X ) { if( X == NULL ) return; 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_zeroize( X->p, X->n * ciL ); 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; if( nblimbs > MBEDTLS_MPI_MAX_LIMBS ) return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); if( X->n < nblimbs ) { if( ( p = mbedtls_calloc( nblimbs, ciL ) ) == NULL ) return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); if( X->p != NULL ) { memcpy( p, X->p, X->n * ciL ); mbedtls_zeroize( X->p, X->n * ciL ); 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; /* 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_calloc( i, ciL ) ) == NULL ) return( MBEDTLS_ERR_MPI_ALLOC_FAILED ); if( X->p != NULL ) { memcpy( p, X->p, i * ciL ); mbedtls_zeroize( X->p, X->n * ciL ); 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; size_t i; 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; MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) ); memset( X->p, 0, X->n * 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; 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; /* 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; if( X == Y ) return( 0 ); /* make sure swap is 0 or 1 in a time-constant manner */ swap = (swap | (unsigned char)-swap) >> 7; MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) ); s = X->s; X->s = X->s * ( 1 - swap ) + Y->s * swap; Y->s = Y->s * ( 1 - swap ) + s * swap; for( i = 0; i < X->n; i++ ) { tmp = X->p[i]; X->p[i] = X->p[i] * ( 1 - swap ) + Y->p[i] * swap; Y->p[i] = Y->p[i] * ( 1 - swap ) + tmp * swap; } cleanup: return( ret ); } /* * Set value from integer */ int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z ) { int ret; MBEDTLS_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 ) { if( X->n * biL <= pos ) return( 0 ); return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 ); } /* * Set a bit to a specific value of 0 or 1 */ int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val ) { int ret = 0; size_t off = pos / biL; size_t idx = pos % biL; 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; 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; 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 ) { int ret; mbedtls_mpi_uint r; if( radix < 2 || radix > 16 ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, radix ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_div_int( X, NULL, X, radix ) ); if( mbedtls_mpi_cmp_int( X, 0 ) != 0 ) MBEDTLS_MPI_CHK( mpi_write_hlp( X, radix, p ) ); if( r < 10 ) *(*p)++ = (char)( r + 0x30 ); else *(*p)++ = (char)( r + 0x37 ); 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; if( radix < 2 || radix > 16 ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); n = mbedtls_mpi_bitlen( X ); if( radix >= 4 ) n >>= 1; if( radix >= 16 ) n >>= 1; n += 3; if( buflen < n ) { *olen = n; return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); } p = buf; mbedtls_mpi_init( &T ); if( X->s == -1 ) *p++ = '-'; 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 ) ); } *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 ]; 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( s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; } if( 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 ]; memset( s, 0, sizeof( s ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_write_string( X, radix, s, sizeof( s ) - 2, &n ) ); if( p == NULL ) p = ""; plen = strlen( p ); slen = strlen( s ); s[slen++] = '\r'; s[slen++] = '\n'; if( fout != NULL ) { if( fwrite( p, 1, plen, fout ) != plen || fwrite( s, 1, slen, fout ) != slen ) return( MBEDTLS_ERR_MPI_FILE_IO_ERROR ); } else mbedtls_printf( "%s%s", p, s ); cleanup: return( ret ); } #endif /* MBEDTLS_FS_IO */ /* * Import X from unsigned binary data, big endian */ int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen ) { int ret; size_t i, j, n; for( n = 0; n < buflen; n++ ) if( buf[n] != 0 ) break; MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, CHARS_TO_LIMBS( buflen - n ) ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); for( i = buflen, j = 0; i > n; i--, j++ ) X->p[j / ciL] |= ((mbedtls_mpi_uint) buf[i - 1]) << ((j % ciL) << 3); cleanup: return( ret ); } /* * Export X into unsigned binary data, big endian */ int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf, size_t buflen ) { size_t i, j, n; n = mbedtls_mpi_size( X ); if( buflen < n ) return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL ); memset( buf, 0, buflen ); for( i = buflen - 1, j = 0; n > 0; i--, j++, n-- ) buf[i] = (unsigned char)( X->p[j / ciL] >> ((j % ciL) << 3) ); 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; 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; 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; 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; 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]; *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; 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; for( i = 0; i < j; i++, o++, p++ ) { *p += c; c = ( *p < c ); *p += *o; c += ( *p < *o ); } 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; i++; 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; 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 = 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 = 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]; 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]; 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; 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( i++; j > 0; j-- ) mpi_mul_hlp( i - 1, 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]; _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; 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]; 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; 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; 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 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; } 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 ); } /* * Montgomery reduction: A = A * R^-1 mod N */ static void mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T ) { mbedtls_mpi_uint z = 1; mbedtls_mpi U; U.n = U.s = (int) z; U.p = &z; mpi_montmul( A, &U, N, mm, T ); } /* * Sliding-window exponentiation: X = A^E mod N (HAC 14.85) */ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR ) { int ret; size_t wbits, wsize, one = 1; size_t i, j, nblimbs; size_t bufsize, nbits; mbedtls_mpi_uint ei, mm, state; mbedtls_mpi RR, T, W[ 2 << MBEDTLS_MPI_WINDOW_SIZE ], Apos; int neg; 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( wsize > MBEDTLS_MPI_WINDOW_SIZE ) wsize = MBEDTLS_MPI_WINDOW_SIZE; j = N->n + 1; MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], j ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) ); /* * Compensate for negative A (and correct at the end) */ neg = ( A->s == -1 ); if( neg ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Apos, A ) ); Apos.s = 1; A = &Apos; } /* * If 1st call, pre-compute R^2 mod N */ if( _RR == NULL || _RR->p == NULL ) { MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &RR, 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &RR, N->n * 2 * biL ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &RR, &RR, N ) ); if( _RR != NULL ) memcpy( _RR, &RR, sizeof( mbedtls_mpi ) ); } else memcpy( &RR, _RR, sizeof( mbedtls_mpi ) ); /* * W[1] = A * R^2 * R^-1 mod N = A * R mod N */ if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 ) MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) ); else MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) ); mpi_montmul( &W[1], &RR, N, mm, &T ); /* * X = R^2 * R^-1 mod N = R mod N */ MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) ); mpi_montred( X, N, mm, &T ); if( wsize > 1 ) { /* * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1) */ j = one << ( wsize - 1 ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) ); for( i = 0; i < wsize - 1; i++ ) mpi_montmul( &W[j], &W[j], N, mm, &T ); /* * W[i] = W[i - 1] * W[1] */ for( i = j + 1; i < ( one << wsize ); i++ ) { MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) ); mpi_montmul( &W[i], &W[1], N, mm, &T ); } } nblimbs = E->n; bufsize = 0; nbits = 0; wbits = 0; state = 0; while( 1 ) { if( bufsize == 0 ) { if( nblimbs == 0 ) break; nblimbs--; bufsize = sizeof( mbedtls_mpi_uint ) << 3; } bufsize--; ei = (E->p[nblimbs] >> bufsize) & 1; /* * skip leading 0s */ if( ei == 0 && state == 0 ) continue; if( ei == 0 && state == 1 ) { /* * out of window, square X */ mpi_montmul( X, X, N, mm, &T ); continue; } /* * add ei to current window */ state = 2; nbits++; wbits |= ( ei << ( wsize - nbits ) ); if( nbits == wsize ) { /* * X = X^wsize R^-1 mod N */ for( i = 0; i < wsize; i++ ) mpi_montmul( X, X, N, mm, &T ); /* * X = X * W[wbits] R^-1 mod N */ mpi_montmul( X, &W[wbits], N, mm, &T ); state--; nbits = 0; wbits = 0; } } /* * process the remaining bits */ for( i = 0; i < nbits; i++ ) { mpi_montmul( X, X, N, mm, &T ); wbits <<= 1; if( ( wbits & ( one << wsize ) ) != 0 ) mpi_montmul( X, &W[1], N, mm, &T ); } /* * X = A^E * R * R^-1 mod N = A^E mod N */ mpi_montred( X, N, mm, &T ); if( neg ) { 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; 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; unsigned char buf[MBEDTLS_MPI_MAX_SIZE]; if( size > MBEDTLS_MPI_MAX_SIZE ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); MBEDTLS_MPI_CHK( f_rng( p_rng, buf, size ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( X, buf, size ) ); 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; if( mbedtls_mpi_cmp_int( N, 0 ) <= 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[] ICACHE_RODATA_ATTR STORE_ATTR = { 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, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret, count; size_t i, j, k, n, s; mbedtls_mpi W, R, T, A, RR; 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 ); /* * HAC, table 4.4 */ n = ( ( i >= 1300 ) ? 2 : ( i >= 850 ) ? 3 : ( i >= 650 ) ? 4 : ( i >= 350 ) ? 8 : ( i >= 250 ) ? 12 : ( i >= 150 ) ? 18 : 27 ); for( i = 0; i < n; i++ ) { /* * pick a random A, 1 < A < |X| - 1 */ MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) ); if( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 ) { j = mbedtls_mpi_bitlen( &A ) - mbedtls_mpi_bitlen( &W ); MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &A, j + 1 ) ); } A.p[0] |= 3; 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) { MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &A, j - k ) ); } 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( const mbedtls_mpi *X, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret; mbedtls_mpi XX; 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, f_rng, p_rng ) ); } /* * Prime number generation */ int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int dh_flag, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret; size_t k, n; mbedtls_mpi_uint r; mbedtls_mpi Y; if( nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); mbedtls_mpi_init( &Y ); n = BITS_TO_LIMBS( nbits ); MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) ); k = mbedtls_mpi_bitlen( X ); if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits + 1 ) ); mbedtls_mpi_set_bit( X, nbits-1, 1 ); X->p[0] |= 1; if( dh_flag == 0 ) { while( ( ret = mbedtls_mpi_is_prime( X, f_rng, p_rng ) ) != 0 ) { if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE ) goto cleanup; MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 2 ) ); } } 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, f_rng, p_rng ) ) == 0 && ( ret = mpi_miller_rabin( &Y, f_rng, p_rng ) ) == 0 ) { break; } 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 */