/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:4;tab-width:4;coding:utf-8 -*-│ │ vi: set et ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi │ ╞══════════════════════════════════════════════════════════════════════════════╡ │ Copyright The Mbed TLS Contributors │ │ │ │ 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. │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "third_party/mbedtls/bignum.h" #include "libc/serialize.h" #include "libc/intrin/bsf.h" #include "libc/intrin/bswap.h" #include "libc/macros.internal.h" #include "libc/nexgen32e/nexgen32e.h" #include "libc/nexgen32e/x86feature.h" #include "libc/runtime/runtime.h" #include "libc/str/str.h" #include "third_party/mbedtls/bignum_internal.h" #include "third_party/mbedtls/chk.h" #include "third_party/mbedtls/common.h" #include "third_party/mbedtls/error.h" #include "third_party/mbedtls/fastdiv.h" #include "third_party/mbedtls/math.h" #include "third_party/mbedtls/platform.h" #include "third_party/mbedtls/profile.h" #include "third_party/mbedtls/select.h" asm(".ident\t\"\\n\\n\ Mbed TLS (Apache 2.0)\\n\ Copyright ARM Limited\\n\ Copyright Mbed TLS Contributors\""); asm(".include \"libc/disclaimer.inc\""); /** * @fileoverview Big Numbers. * * 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_BIGNUM_C) /* Implementation that should never be optimized out by the compiler */ static inline void mbedtls_mpi_zeroize( mbedtls_mpi_uint *v, size_t n ) { mbedtls_platform_zeroize( v, ciL * n ); } /** * \brief This function frees the components of an MPI context. * * \param X The MPI context to be cleared. This may be \c NULL, * in which case this function is a no-op. If it is * not \c NULL, it must point to an initialized MPI. */ void mbedtls_mpi_free( mbedtls_mpi *X ) { if( !X ) return; if( X->p ) { mbedtls_mpi_zeroize( X->p, X->n ); mbedtls_free( X->p ); } X->s = 1; X->n = 0; X->p = NULL; } /** * \brief Enlarge an MPI to the specified number of limbs. * * \note This function does nothing if the MPI is * already large enough. * * \param X The MPI to grow. It must be initialized. * \param nblimbs The target number of limbs. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs) { mbedtls_mpi_uint *p; MPI_VALIDATE_RET(X); if (nblimbs > MBEDTLS_MPI_MAX_LIMBS) return MBEDTLS_ERR_MPI_ALLOC_FAILED; if (nblimbs > X->n) { if (X->p && (p = realloc_in_place(X->p, nblimbs * ciL))) { mbedtls_mpi_zeroize(p + X->n, nblimbs - X->n); } else { if (!(p = malloc(nblimbs * ciL))) return MBEDTLS_ERR_MPI_ALLOC_FAILED; if (X->p) { memcpy(p, X->p, X->n * ciL); mbedtls_mpi_zeroize(p + X->n, nblimbs - X->n); mbedtls_mpi_zeroize(X->p, X->n); free(X->p); } else { mbedtls_mpi_zeroize(p, nblimbs); } } X->n = nblimbs; X->p = p; } return 0; } /** * \brief This function resizes an MPI to a number of limbs. * * \param X The MPI to resize. This must point to an initialized MPI. * \param n The minimum number of limbs to keep. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * which can only happen when resizing up * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_resize(mbedtls_mpi *X, size_t n) { mbedtls_mpi_uint *p; MPI_VALIDATE_RET(X); if (X->n == n) return 0; if (X->n <= n) return mbedtls_mpi_grow(X, n); if (n > MBEDTLS_MPI_MAX_LIMBS) return MBEDTLS_ERR_MPI_ALLOC_FAILED; mbedtls_mpi_zeroize(X->p + n, X->n - n); if (!realloc_in_place(X->p, n * ciL)) { if (!(p = malloc(n * ciL))) return MBEDTLS_ERR_MPI_ALLOC_FAILED; memcpy(p, X->p, n * ciL); mbedtls_mpi_zeroize(X->p, n); free(X->p); X->p = p; } X->n = n; return 0; } /** * \brief This function resizes an MPI downwards, keeping at * least the specified number of limbs. * * If \c X is smaller than \c nblimbs, it is resized up * instead. * * \param X The MPI to shrink. This must point to an initialized MPI. * \param nblimbs The minimum number of limbs to keep. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * which can only happen when resizing up * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs) { MPI_VALIDATE_RET(X); if (X->n <= nblimbs) return mbedtls_mpi_grow(X, nblimbs); return mbedtls_mpi_resize(X, MAX(MAX(1, nblimbs), mbedtls_mpi_limbs(X))); } /** * \brief Make a copy of an MPI. * * \param X The destination MPI. This must point to an initialized MPI. * \param Y The source MPI. This must point to an initialized MPI. * * \note The limb-buffer in the destination MPI is enlarged * if necessary to hold the value in the source MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y ) { int ret = 0; size_t i; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( Y ); if( X == Y ) return( 0 ); if( Y->n == 0 ) { mbedtls_mpi_free( X ); return( 0 ); } for( i = Y->n - 1; i > 0; i-- ) if( Y->p[i] != 0 ) break; i++; X->s = Y->s; if( X->n < i ) { MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) ); } else { mbedtls_platform_zeroize( X->p + i, ( X->n - i ) * ciL ); } memcpy( X->p, Y->p, i * ciL ); cleanup: return( ret ); } /** * \brief Swap the contents of two MPIs. * * \param X The first MPI. It must be initialized. * \param Y The second MPI. It must be initialized. */ void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y ) { mbedtls_mpi T; MPI_VALIDATE( X ); MPI_VALIDATE( Y ); memcpy( &T, X, sizeof( mbedtls_mpi ) ); memcpy( X, Y, sizeof( mbedtls_mpi ) ); memcpy( Y, &T, sizeof( mbedtls_mpi ) ); } /** * \brief Perform a safe conditional copy of MPI which doesn't * reveal whether the condition was true or not. * * \param X The MPI to conditionally assign to. This must point * to an initialized MPI. * \param Y The MPI to be assigned from. This must point to an * initialized MPI. * \param assign The condition deciding whether to perform the * assignment or not. Possible values: * * \c 1: Perform the assignment `X = Y`. * * \c 0: Keep the original value of \p X. * * \note This function is equivalent to * `if( assign ) mbedtls_mpi_copy( X, Y );` * except that it avoids leaking any information about whether * the assignment was done or not (the above code may leak * information through branch prediction and/or memory access * patterns analysis). * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign) { int ret = 0; size_t i; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(Y); /* make sure assign is 0 or 1 in a time-constant manner */ if (Y->n > X->n) MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) ); assign = (assign | (unsigned char)-assign) >> 7; X->s = Select(Y->s, X->s, -assign); for (i = 0; i < Y->n; i++) X->p[i] = Select(Y->p[i], X->p[i], -assign); for (i = Y->n; i < X->n; i++) X->p[i] &= __conceal("r", assign - 1); cleanup: return( ret ); } /** * \brief Perform a safe conditional swap which doesn't * reveal whether the condition was true or not. * * \param X The first MPI. This must be initialized. * \param Y The second MPI. This must be initialized. * \param assign The condition deciding whether to perform * the swap or not. Possible values: * * \c 1: Swap the values of \p X and \p Y. * * \c 0: Keep the original values of \p X and \p Y. * * \note This function is equivalent to * if( assign ) mbedtls_mpi_swap( X, Y ); * except that it avoids leaking any information about whether * the assignment was done or not (the above code may leak * information through branch prediction and/or memory access * patterns analysis). * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. * */ int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap ) { int ret, s; size_t i; mbedtls_mpi_uint tmp; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( Y ); 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 ); } /** * \brief Store integer value in MPI. * * \param X The MPI to set. This must be initialized. * \param z The value to use. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z ) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; MPI_VALIDATE_RET( X ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) ); mbedtls_platform_zeroize( X->p, X->n * ciL ); X->p[0] = ( z < 0 ) ? -z : z; X->s = ( z < 0 ) ? -1 : 1; cleanup: return( ret ); } /** * \brief Get a specific bit from an MPI. * * \param X The MPI to query. This must be initialized. * \param pos Zero-based index of the bit to query. * * \return \c 0 or \c 1 on success, depending on whether bit \c pos * of \c X is unset or set. * \return A negative error code on failure. */ int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos ) { MPI_VALIDATE_RET( X ); 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 ) /** * \brief Modify a specific bit in an MPI. * * \note This function will grow the target MPI if necessary to set a * bit to \c 1 in a not yet existing limb. It will not grow if * the bit should be set to \c 0. * * \param X The MPI to modify. This must be initialized. * \param pos Zero-based index of the bit to modify. * \param val The desired value of bit \c pos: \c 0 or \c 1. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ 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 ); if( val != 0 && val != 1 ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); if( X->n * biL <= pos ) { if( !val ) 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 ); } /** * \brief Return the number of bits of value \c 0 before the * least significant bit of value \c 1. * * \note This is the same as the zero-based index of * the least significant bit of value \c 1. * * \param X The MPI to query. * * \return The number of bits of value \c 0 before the least significant * bit of value \c 1 in \p X. */ size_t mbedtls_mpi_lsb( const mbedtls_mpi *X ) { size_t i, count = 0; MBEDTLS_INTERNAL_VALIDATE_RET(X, 0); for( i = 0; i < X->n; i++ ) { if ( X->p[i] ) return count + __builtin_ctzll(X->p[i]); else count += biL; } return 0; } /* * Count leading zero bits in a given integer */ static inline size_t mbedtls_clz( const mbedtls_mpi_uint x ) { return x ? __builtin_clzll(x) : biL; } /** * \brief Return the number of bits up to and including the most * significant bit of value \c 1. * * \note This is same as the one-based index of the most * significant bit of value \c 1. * * \param X The MPI to query. This must point to an initialized MPI. * * \return The number of bits up to and including the most * significant bit of value \c 1. */ size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X) { size_t n; n = mbedtls_mpi_limbs(X); if (!n) return 0; return biL - __builtin_clzll(X->p[n - 1]) + (n - 1) * biL; } /** * \brief Return the total size of an MPI value in bytes. * * \param X The MPI to use. This must point to an initialized MPI. * * \note The value returned by this function may be less than * the number of bytes used to store \p X internally. * This happens if and only if there are trailing bytes * of value zero. * * \return The least number of bytes capable of storing * the absolute value of \p X. */ 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 ); } /** * \brief Import an MPI from an ASCII string. * * \param X The destination MPI. This must point to an initialized MPI. * \param radix The numeric base of the input string. * \param s Null-terminated string buffer. * * \return \c 0 if successful. * \return A negative error code on failure. */ int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s ) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; size_t i, j, slen, n; mbedtls_mpi_uint d; mbedtls_mpi T; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( s ); if( radix < 2 || radix > 16 ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); mbedtls_mpi_init( &T ); slen = strlen( s ); if( radix == 16 ) { if( slen > MPI_SIZE_T_MAX >> 2 ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); n = BITS_TO_LIMBS( slen << 2 ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); for( i = slen, j = 0; i > 0; i--, j++ ) { if( i == 1 && s[i - 1] == '-' ) { X->s = -1; break; } MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) ); X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 ); } } else { MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); for( i = 0; i < slen; i++ ) { if( i == 0 && s[i] == '-' ) { X->s = -1; continue; } MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) ); if( X->s == 1 ) { MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) ); } else { MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, &T, d ) ); } } } cleanup: mbedtls_mpi_free( &T ); return( ret ); } /* * Helper to write the digits high-order first. */ static int mpi_write_hlp( mbedtls_mpi *X, int radix, char **p, const size_t buflen ) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; 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 ); } /** * \brief Export an MPI to an ASCII string. * * \param X The source MPI. This must point to an initialized MPI. * \param radix The numeric base of the output string. * \param buf The buffer to write the string to. This must be writable * buffer of length \p buflen Bytes. * \param buflen The available size in Bytes of \p buf. * \param olen The address at which to store the length of the string * written, including the final \c NULL byte. This must * not be \c NULL. * * \note You can call this function with `buflen == 0` to obtain the * minimum required buffer size in `*olen`. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf * is too small to hold the value of \p X in the desired base. * In this case, `*olen` is nonetheless updated to contain the * size of \p buf required for a successful call. * \return Another negative error code on different kinds of failure. */ 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 ); MPI_VALIDATE_RET( olen ); MPI_VALIDATE_RET( buflen == 0 || buf ); 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) /** * \brief Read an MPI from a line in an opened file. * * \param X The destination MPI. This must point to an initialized MPI. * \param radix The numeric base of the string representation used * in the source line. * \param fin The input file handle to use. This must not be \c NULL. * * \note On success, this function advances the file stream * to the end of the current line or to EOF. * * The function returns \c 0 on an empty line. * * Leading whitespaces are ignored, as is a * '0x' prefix for radix \c 16. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer * is too small. * \return Another negative error code on failure. */ 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 ); MPI_VALIDATE_RET( fin ); if( radix < 2 || radix > 16 ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); mbedtls_platform_zeroize( s, 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 ) ); } /** * \brief Export an MPI into an opened file. * * \param p A string prefix to emit prior to the MPI data. * For example, this might be a label, or "0x" when * printing in base \c 16. This may be \c NULL if no prefix * is needed. * \param X The source MPI. This must point to an initialized MPI. * \param radix The numeric base to be used in the emitted string. * \param fout The output file handle. This may be \c NULL, in which case * the output is written to \c stdout. * * \return \c 0 if successful. * \return A negative error code on failure. */ int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout ) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; 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 ); if( radix < 2 || radix > 16 ) return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); mbedtls_platform_zeroize( s, 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 ) { 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 */ #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ #define mpi_uint_bigendian_to_host(x) (x) #elif __SIZEOF_LONG__ == 8 #define mpi_uint_bigendian_to_host(x) __builtin_bswap64(x) #elif __SIZEOF_LONG__ == 4 #define mpi_uint_bigendian_to_host(x) __builtin_bswap32(x) #endif 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 ) 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; } } /** * \brief Import X from unsigned binary data, little endian * * \param X The destination MPI. This must point to an initialized MPI. * \param p The input buffer with \p n bytes. * \param n The length of the input buffer \p p in Bytes. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_read_binary_le(mbedtls_mpi *X, const unsigned char *p, size_t n) { int ret; size_t i; mbedtls_mpi_uint w; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(!n || p); if ((ret = mbedtls_mpi_resize(X, MAX(1, CHARS_TO_LIMBS(n))))) return ret; if (n) { for (i = 0; i + 8 <= n; i += 8) X->p[i / ciL] = READ64LE(p + i); if (i < n) { w = 0; do { w <<= 8; w |= p[i]; } while (++i < n); X->p[i / ciL] = w; } } else { X->p[0] = 0; } X->s = 1; return 0; } /** * \brief Import an MPI from unsigned big endian binary data. * * \param X The destination MPI. This must point to an initialized MPI. * \param p The input buffer. This must be a readable buffer of length * \p n Bytes. * \param n The length of the input buffer \p p in Bytes. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *p, size_t n) { int ret; size_t i, j, k; mbedtls_mpi_uint w; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(!n || p); if ((ret = mbedtls_mpi_resize(X, MAX(1, CHARS_TO_LIMBS(n))))) return ret; if (n) { for (j = 0, i = n; i >= 8; i -= 8) X->p[j++] = READ64BE(p + i - ciL); if (i) { k = 0; w = 0; do { --i; w <<= 8; w |= p[k++]; } while (i); X->p[j] = w; } } else { X->p[0] = 0; } X->s = 1; return 0; } /** * \brief Export X into unsigned binary data, little endian. * Always fills the whole buffer, which will end with zeros * if the number is smaller. * * \param X The source MPI. This must point to an initialized MPI. * \param buf The output buffer. This must be a writable buffer of length * \p buflen Bytes. * \param buflen The size of the output buffer \p buf in Bytes. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't * large enough to hold the value of \p X. * \return Another negative error code on different kinds of failure. */ 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 */ mbedtls_platform_zeroize( buf + stored_bytes, buflen - stored_bytes ); } return( 0 ); } /** * \brief Export X into unsigned binary data, big endian. * Always fills the whole buffer, which will start with zeros * if the number is smaller. * * \param X The source MPI. This must point to an initialized MPI. * \param buf The output buffer. This must be a writable buffer of length * \p buflen Bytes. * \param buflen The size of the output buffer \p buf in Bytes. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't * large enough to hold the value of \p X. * \return Another negative error code on different kinds of failure. */ 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 ); MPI_VALIDATE_RET( buflen == 0 || buf ); 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; mbedtls_platform_zeroize( buf, 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 ); } /** * \brief Compare the absolute values of two MPIs. * * \param X The left-hand MPI. This must point to an initialized MPI. * \param Y The right-hand MPI. This must point to an initialized MPI. * * \return \c 1 if `|X|` is greater than `|Y|`. * \return \c -1 if `|X|` is lesser than `|Y|`. * \return \c 0 if `|X|` is equal to `|Y|`. */ int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y ) { size_t i, j; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( Y ); i = mbedtls_mpi_limbs(X); j = mbedtls_mpi_limbs(Y); if( !i && !j ) 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 ); } /** * \brief Compare two MPIs. * * \param X The left-hand MPI. This must point to an initialized MPI. * \param Y The right-hand MPI. This must point to an initialized MPI. * * \return \c 1 if \p X is greater than \p Y. * \return \c -1 if \p X is lesser than \p Y. * \return \c 0 if \p X is equal to \p Y. */ int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y ) { size_t i, j; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( Y ); i = mbedtls_mpi_limbs(X); j = mbedtls_mpi_limbs(Y); if( !i && !j ) 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> ( biL - 1 ); return (unsigned) ret; } /** * \brief Check if an MPI is less than the other in constant time. * * \param X The left-hand MPI. This must point to an initialized MPI * with the same allocated length as Y. * \param Y The right-hand MPI. This must point to an initialized MPI * with the same allocated length as X. * \param ret The result of the comparison: * \c 1 if \p X is less than \p Y. * \c 0 if \p X is greater than or equal to \p Y. * * \return 0 on success. * \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of * the two input MPIs is not the same. */ 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 ); MPI_VALIDATE_RET( Y ); MPI_VALIDATE_RET( ret ); 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 ); } /** * \brief Compare an MPI with an integer. * * \param X The left-hand MPI. This must point to an initialized MPI. * \param z The integer value to compare \p X to. * * \return \c 1 if \p X is greater than \p z. * \return \c -1 if \p X is lesser than \p z. * \return \c 0 if \p X is equal to \p z. */ 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 ); *p = ( z < 0 ) ? -z : z; Y.s = ( z < 0 ) ? -1 : 1; Y.n = 1; Y.p = p; return( mbedtls_mpi_cmp_mpi( X, &Y ) ); } /** * \brief Perform an unsigned addition of MPIs: X = |A| + |B| * * \param X The destination MPI. This must point to an initialized MPI. * \param A The first summand. This must point to an initialized MPI. * \param B The second summand. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; size_t i, j; mbedtls_mpi_uint *o, *p, c, tmp; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( A ); MPI_VALIDATE_RET( B ); if( X == B ) { const mbedtls_mpi *T = A; A = X; B = T; } if( X != A ) MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) ); /* * X should always be positive as a result of unsigned additions. */ X->s = 1; for( j = B->n; j > 0; j-- ) if( B->p[j - 1] != 0 ) break; MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) ); o = B->p; p = X->p; c = 0; /* * tmp is used because it might happen that p == o */ for( i = 0; i < j; i++, o++, p++ ) { tmp= *o; *p += c; c = ( *p < c ); *p += tmp; c += ( *p < tmp ); } while( c != 0 ) { if( i >= X->n ) { MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + 1 ) ); p = X->p + i; } *p += c; c = ( *p < c ); i++; p++; } cleanup: return( ret ); } /** * Helper for mbedtls_mpi subtraction. * * Calculate d = a - b where d, a, and b have the same size. * This function operates modulo (2^ciL)^n and returns the carry * (1 if there was a wraparound, i.e. if `a < b`, and 0 otherwise). * * \param[out] d Result of subtraction. * \param[in] a Left operand. * \param[in] b Right operand. * \param n Number of limbs of \p a and \p b. * \return 1 if `d < s`. * 0 if `d >= s`. */ forceinline mbedtls_mpi_uint mpi_sub_hlp(mbedtls_mpi_uint *d, const mbedtls_mpi_uint *a, const mbedtls_mpi_uint *b, size_t n) { size_t i; unsigned char cf; mbedtls_mpi_uint c, x; (void)x; (void)cf; cf = c = i = 0; #if defined(__x86_64__) && !defined(__STRICT_ANSI__) if (!n) return 0; asm volatile("xor\t%1,%1\n\t" ".align\t16\n1:\t" "mov\t(%5,%3,8),%1\n\t" "sbb\t(%6,%3,8),%1\n\t" "mov\t%1,(%4,%3,8)\n\t" "lea\t1(%3),%3\n\t" "dec\t%2\n\t" "jnz\t1b" : "=@ccb"(cf), "=&r"(x), "+&c"(n), "=&r"(i) : "r"(d), "r"(a), "r"(b), "3"(0) : "cc", "memory"); return cf; #else for (; i < n; ++i) SBB(d[i], a[i], b[i], c, c); return c; #endif } /** * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B| * * \param X The destination MPI. This must point to an initialized MPI. * \param A The minuend. This must point to an initialized MPI. * \param B The subtrahend. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) { size_t n, m, r; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( A ); MPI_VALIDATE_RET( B ); if( X != A && !B->n ) return mbedtls_mpi_copy( X, A ); /* wut */ for( n = B->n; n > 0; n-- ) if( B->p[n - 1] != 0 ) break; if( n > A->n ) return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; /* B >= (2^ciL)^n > A */ if (X != A) { if (X->n < A->n) { if ((r = mbedtls_mpi_grow(X, A->n))) return r; } else if (X->n > A->n) { mbedtls_mpi_zeroize(X->p + A->n, X->n - A->n); } if ((m = A->n - n)) memcpy(X->p + n, A->p + n, m * ciL); } /* * X should always be positive as a result of unsigned subtractions. */ X->s = 1; if( mpi_sub_hlp( X->p, A->p, B->p, n ) ){ /* Propagate the carry to the first nonzero limb of X. */ for( ; n < A->n && A->p[n] == 0; n++ ) /* --X->p[n]; */ X->p[n] = A->p[n] - 1; /* If we ran out of space for the carry, it means that the result * is negative. */ if( n == X->n ) return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; --X->p[n]; } return( 0 ); } static int mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t *Xn, size_t *Yn) { size_t i, j; i = mbedtls_mpi_limbs(X); j = mbedtls_mpi_limbs(Y); *Xn = i; *Yn = j; if (!i && !j) 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; } static int mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B, size_t n ) { size_t m, r; if( X != A && !B->n ) return mbedtls_mpi_copy( X, A ); /* wut */ if( n > A->n ) return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; /* B >= (2^ciL)^n > A */ if (X != A) { if (X->n < A->n) { if ((r = mbedtls_mpi_grow(X, A->n))) return r; } else if (X->n > A->n) { mbedtls_mpi_zeroize(X->p + A->n, X->n - A->n); } if ((m = A->n - n)) memcpy(X->p + n, A->p + n, m * ciL); } /* * X should always be positive as a result of unsigned subtractions. */ X->s = 1; if( mpi_sub_hlp( X->p, A->p, B->p, n ) ){ /* Propagate the carry to the first nonzero limb of X. */ for( ; n < A->n && A->p[n] == 0; n++ ) /* --X->p[n]; */ X->p[n] = A->p[n] - 1; /* If we ran out of space for the carry, it means that the result * is negative. */ if( n == X->n ) return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; --X->p[n]; } return( 0 ); } /** * \brief Perform a signed addition of MPIs: X = A + B * * \param X The destination MPI. This must point to an initialized MPI. * \param A The first summand. This must point to an initialized MPI. * \param B The second summand. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) { int ret, s; size_t i, j; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( A ); MPI_VALIDATE_RET( B ); s = A->s; if( A->s * B->s < 0 ) { if( mpi_cmp_abs( A, B, &i, &j ) >= 0 ) { MBEDTLS_MPI_CHK( mpi_sub_abs( X, A, B, j ) ); X->s = s; } else { MBEDTLS_MPI_CHK( mpi_sub_abs( X, B, A, i ) ); X->s = -s; } } else { MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) ); X->s = s; } cleanup: return( ret ); } /** * \brief Perform a signed subtraction of MPIs: X = A - B * * \param X The destination MPI. This must point to an initialized MPI. * \param A The minuend. This must point to an initialized MPI. * \param B The subtrahend. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B ) { int ret, s; size_t i, j; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( A ); MPI_VALIDATE_RET( B ); s = A->s; if( A->s * B->s > 0 ) { if( mpi_cmp_abs( A, B, &i, &j ) >= 0 ) { MBEDTLS_MPI_CHK( mpi_sub_abs( X, A, B, j ) ); X->s = s; } else { MBEDTLS_MPI_CHK( mpi_sub_abs( X, B, A, i ) ); X->s = -s; } } else { MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) ); X->s = s; } cleanup: return( ret ); } /** * \brief Perform a signed addition of an MPI and an integer: X = A + b * * \param X The destination MPI. This must point to an initialized MPI. * \param A The first summand. This must point to an initialized MPI. * \param b The second summand. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ 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 ); MPI_VALIDATE_RET( A ); 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 ) ); } /** * \brief Perform a signed subtraction of an MPI and an integer: * X = A - b * * \param X The destination MPI. This must point to an initialized MPI. * \param A The minuend. This must point to an initialized MPI. * \param b The subtrahend. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ 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 ); MPI_VALIDATE_RET( A ); 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 ) ); } /* * 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(__x86_64__) && !defined(__STRICT_ANSI__) if (d && u1 < d) { mbedtls_mpi_uint quo, rem; asm("div\t%2" : "=a"(quo), "=d"(rem) : "r"(d), "0"(u0), "1"(u1) : "cc"); if (r) *r = rem; return quo; } else { if (r) *r = ~0; return ~0; } #else #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) *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 ) *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) *r = ( rAX * radix + u0_lsw - q0 * d ) >> s; quotient = q1 * radix + q0; return quotient; #endif #endif } static inline void Multiply2x1(uint64_t a[3], uint64_t b) { uint128_t x; uint64_t l, h; x = a[0]; x *= b; l = x; h = x >> 64; x = a[1]; x *= b; x += h + ((a[0] = l) < 0); l = x; h = x >> 64; a[2] = h + ((a[1] = l) < 0); } static inline bool GreaterThan3x3(uint64_t a[3], uint64_t b[3]) { if (a[2] > b[2]) return true; if (a[2] < b[2]) return false; if (a[1] > b[1]) return true; if (a[1] < b[1]) return false; return a[0] > b[0]; } /** * \brief Perform a division with remainder of two MPIs: * A = Q * B + R * * \param Q The destination MPI for the quotient. * This may be \c NULL if the value of the * quotient is not needed. * \param R The destination MPI for the remainder value. * This may be \c NULL if the value of the * remainder is not needed. * \param A The dividend. This must point to an initialized MPi. * \param B The divisor. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; size_t i, n, t, k; mbedtls_mpi X, Y, Z, T1, T2; mbedtls_mpi_uint TP2[3]; MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(B); if (mbedtls_mpi_is_zero(B)) 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) MBEDTLS_MPI_CHK(mbedtls_mpi_lset(Q, 0)); if (R) 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, 80)); /* we need left pad hard below */ 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_abs(&X, &Y) >= 0) { Z.p[n - t]++; MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&X, &X, &Y)); } 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]--; T1.p[0] = (t < 1) ? 0 : Y.p[t - 1]; T1.p[1] = Y.p[t]; Multiply2x1(T1.p, Z.p[i - t - 1]); } while (GreaterThan3x3(T1.p, T2.p)); 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 (X.s < 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) { MBEDTLS_MPI_CHK(mbedtls_mpi_copy(Q, &Z)); Q->s = A->s * B->s; } if (R) { mbedtls_mpi_shift_r(&X, k); X.s = A->s; MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, &X)); if (mbedtls_mpi_is_zero(R)) 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; } /** * \brief Perform a division with remainder of an MPI by an integer: * A = Q * b + R * * \param Q The destination MPI for the quotient. * This may be \c NULL if the value of the * quotient is not needed. * \param R The destination MPI for the remainder value. * This may be \c NULL if the value of the * remainder is not needed. * \param A The dividend. This must point to an initialized MPi. * \param b The divisor. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. * \return Another negative error code on different kinds of failure. */ 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 ); 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 ) ); } /** * \brief Perform a modular reduction. R = A mod B * * \param R The destination MPI for the residue value. * This must point to an initialized MPI. * \param A The MPI to compute the residue of. * This must point to an initialized MPI. * \param B The base of the modular reduction. * This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative. * \return Another negative error code on different kinds of failure. * */ int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B ) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; MPI_VALIDATE_RET( R ); MPI_VALIDATE_RET( A ); MPI_VALIDATE_RET( B ); 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 ); } /** * \brief Perform a modular reduction with respect to an integer. * r = A mod b * * \param r The address at which to store the residue. * This must not be \c NULL. * \param A The MPI to compute the residue of. * This must point to an initialized MPi. * \param b The integer base of the modular reduction. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative. * \return Another negative error code on different kinds of failure. */ 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 ); MPI_VALIDATE_RET( A ); 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; } /** * 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, *Ap, *Bp, *Np; mbedtls_platform_zeroize( T->p, T->n * ciL ); d = T->p; n = N->n; m = ( B->n < n ) ? B->n : n; Ap = A->p; Bp = B->p; Np = N->p; for( i = 0; i < n; i++ ) { /* * T = (T + u0*B + u1*N) / 2^biL */ u0 = Ap[i]; u1 = ( d[0] + u0 * Bp[0] ) * mm; mbedtls_mpi_mul_hlp( m, Bp, d, u0 ); mbedtls_mpi_mul_hlp( n, Np, 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( Ap, 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( d, d, Np, n ); /* 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. */ for (i = 0; i < n; ++i) { Ap[i] = Select(d[i], Ap[i], -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 ); } /** * \brief Perform a sliding-window exponentiation: X = A^E mod N * * \param X The destination MPI. This must point to an initialized MPI. * \param A The base of the exponentiation. * This must point to an initialized MPI. * \param E The exponent MPI. This must point to an initialized MPI. * \param N The base for the modular reduction. This must point to an * initialized MPI. * \param _RR A helper MPI depending solely on \p N which can be used to * speed-up multiple modular exponentiations for the same value * of \p N. This may be \c NULL. If it is not \c NULL, it must * point to an initialized MPI. If it hasn't been used after * the call to mbedtls_mpi_init(), this function will compute * the helper value and store it in \p _RR for reuse on * subsequent calls to this function. Otherwise, the function * will assume that \p _RR holds the helper value set by a * previous call to mbedtls_mpi_exp_mod(), and reuse it. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or * even, or if \c E is negative. * \return Another negative error code on different kinds of failures. * */ 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_THIS_CORRUPTION; size_t wbits, wsize, one = 1; size_t i, j, nblimbs; size_t bufsize, nbits; mbedtls_mpi_uint ei, mm, state; mbedtls_mpi RR, T, W[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], Apos; int neg; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( A ); MPI_VALIDATE_RET( E ); MPI_VALIDATE_RET( N ); 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_platform_zeroize( W, sizeof( W ) ); i = mbedtls_mpi_bitlen( E ); wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 : ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1; #if( MBEDTLS_MPI_WINDOW_SIZE < 6 ) if( wsize > MBEDTLS_MPI_WINDOW_SIZE ) wsize = MBEDTLS_MPI_WINDOW_SIZE; #endif j = N->n + 1; MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], j ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) ); /* * Compensate for negative A (and correct at the end) */ neg = ( A->s == -1 ); if( neg ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Apos, A ) ); Apos.s = 1; A = &Apos; } /* * If 1st call, pre-compute R^2 mod N */ if( _RR == NULL || _RR->p == NULL ) { MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &RR, 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &RR, N->n * 2 * biL ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &RR, &RR, N ) ); if( _RR ) memcpy( _RR, &RR, sizeof( mbedtls_mpi ) ); } else memcpy( &RR, _RR, sizeof( mbedtls_mpi ) ); /* * W[1] = A * R^2 * R^-1 mod N = A * R mod N */ if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 ) MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) ); else MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) ); mpi_montmul( &W[1], &RR, N, mm, &T ); /* * X = R^2 * R^-1 mod N = R mod N */ MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) ); mpi_montred( X, N, mm, &T ); if( wsize > 1 ) { /* * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1) */ j = one << ( wsize - 1 ); MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) ); for( i = 0; i < wsize - 1; i++ ) mpi_montmul( &W[j], &W[j], N, mm, &T ); /* * W[i] = W[i - 1] * W[1] */ for( i = j + 1; i < ( one << wsize ); i++ ) { MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) ); mpi_montmul( &W[i], &W[1], N, mm, &T ); } } nblimbs = E->n; bufsize = 0; nbits = 0; wbits = 0; state = 0; while( 1 ) { if( bufsize == 0 ) { if( nblimbs == 0 ) break; nblimbs--; bufsize = sizeof( mbedtls_mpi_uint ) << 3; } bufsize--; ei = (E->p[nblimbs] >> bufsize) & 1; /* * skip leading 0s */ if( ei == 0 && state == 0 ) continue; if( ei == 0 && state == 1 ) { /* * out of window, square X */ mpi_montmul( X, X, N, mm, &T ); continue; } /* * add ei to current window */ state = 2; nbits++; wbits |= ( ei << ( wsize - nbits ) ); if( nbits == wsize ) { /* * X = X^wsize R^-1 mod N */ for( i = 0; i < wsize; i++ ) mpi_montmul( X, X, N, mm, &T ); /* * X = X * W[wbits] R^-1 mod N */ mpi_montmul( X, &W[wbits], N, mm, &T ); state--; nbits = 0; wbits = 0; } } /* * process the remaining bits */ for( i = 0; i < nbits; i++ ) { mpi_montmul( X, X, N, mm, &T ); wbits <<= 1; if( ( wbits & ( one << wsize ) ) != 0 ) mpi_montmul( X, &W[1], N, mm, &T ); } /* * X = A^E * R * R^-1 mod N = A^E mod N */ mpi_montred( X, N, mm, &T ); if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 ) { X->s = -1; MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) ); } cleanup: for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ ) mbedtls_mpi_free( &W[i] ); mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos ); if( _RR == NULL || _RR->p == NULL ) mbedtls_mpi_free( &RR ); return( ret ); } /** * \brief Compute the greatest common divisor: G = gcd(A, B) * * \param G The destination MPI. This must point to an initialized MPI. * \param A The first operand. This must point to an initialized MPI. * \param B The second operand. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B ) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; mbedtls_mpi TA, TB; size_t lz, lzt, i, j; MPI_VALIDATE_RET( G ); MPI_VALIDATE_RET( A ); MPI_VALIDATE_RET( B ); 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_is_zero( &TA ) ) { 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( mpi_cmp_abs( &TA, &TB, &i, &j ) >= 0 ) { MBEDTLS_MPI_CHK( mpi_sub_abs( &TA, &TA, &TB, j ) ); ShiftRight( TA.p, TA.n, 1 ); } else { MBEDTLS_MPI_CHK( mpi_sub_abs( &TB, &TB, &TA, i ) ); ShiftRight( TB.p, TB.n, 1 ); } } 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 ); } /** * \brief Fill an MPI with a number of random bytes. * * 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). * * \param X The destination MPI. This must point to an initialized MPI. * \param size The number of random bytes to generate. * \param f_rng The RNG function to use. This must not be \c NULL. * \param p_rng The RNG parameter to be passed to \p f_rng. This may be * \c NULL if \p f_rng doesn't need a context argument. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on failure. * * \note The bytes obtained from the RNG are interpreted * as a big-endian representation of an MPI; this can * be relevant in applications like deterministic ECDSA. */ 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_THIS_CORRUPTION; size_t const limbs = CHARS_TO_LIMBS( size ); size_t const overhead = ( limbs * ciL ) - size; unsigned char *Xp; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( f_rng ); MBEDTLS_MPI_CHK(mbedtls_mpi_resize( X, limbs )); MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) ); Xp = (unsigned char*) X->p; MBEDTLS_MPI_CHK( f_rng( p_rng, Xp + overhead, size ) ); mpi_bigendian_to_host( X->p, limbs ); cleanup: return( ret ); } /** * \brief Compute the modular inverse: X = A^-1 mod N * * \param X The destination MPI. This must point to an initialized MPI. * \param A The MPI to calculate the modular inverse of. This must point * to an initialized MPI. * \param N The base of the modular inversion. This must point to an * initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than * or equal to one. * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse * with respect to \p N. */ int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N ) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( A ); MPI_VALIDATE_RET( N ); 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 ) { ShiftRight( TU.p, TU.n, 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 ) ); } ShiftRight( U1.p, U1.n, 1 ); ShiftRight( U2.p, U2.n, 1 ); } while( ( TV.p[0] & 1 ) == 0 ) { ShiftRight( TV.p, TV.n, 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 ) ); } ShiftRight( V1.p, V1.n, 1 ); ShiftRight( V2.p, V2.n, 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_is_zero(&TU) ); 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 short 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 ); MPI_VALIDATE_RET( f_rng ); 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 ); } /** * \brief Miller-Rabin primality test. * * \warning If \p X is potentially generated by an adversary, for example * when validating cryptographic parameters that you didn't * generate yourself and that are supposed to be prime, then * \p rounds should be at least the half of the security * strength of the cryptographic algorithm. On the other hand, * if \p X is chosen uniformly or non-adversially (as is the * case when mbedtls_mpi_gen_prime calls this function), then * \p rounds can be much lower. * * \param X The MPI to check for primality. * This must point to an initialized MPI. * \param rounds The number of bases to perform the Miller-Rabin primality * test for. The probability of returning 0 on a composite is * at most 2-2*\p rounds. * \param f_rng The RNG function to use. This must not be \c NULL. * \param p_rng The RNG parameter to be passed to \p f_rng. * This may be \c NULL if \p f_rng doesn't use * a context parameter. * * \return \c 0 if successful, i.e. \p X is probably prime. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime. * \return Another negative error code on other kinds of failure. */ 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_THIS_CORRUPTION; mbedtls_mpi XX; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( f_rng ); 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 ) ); } /** * \brief Generate a prime number. * * 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. * * \param X The destination MPI to store the generated prime in. * This must point to an initialized MPi. * \param nbits The required size of the destination MPI in bits. * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS. * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t. * \param f_rng The RNG function to use. This must not be \c NULL. * \param p_rng The RNG parameter to be passed to \p f_rng. * This may be \c NULL if \p f_rng doesn't use * a context parameter. * * \return \c 0 if successful, in which case \p X holds a * probably prime number. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between * \c 3 and #MBEDTLS_MPI_MAX_BITS. */ int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng ) { int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; size_t k, n; int rounds; mbedtls_mpi_uint r; mbedtls_mpi Y; MPI_VALIDATE_RET( X ); MPI_VALIDATE_RET( f_rng ); 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] < 0xb504f333f9de6485ULL /* ceil(2^63.5) */ ) 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 ) ); ShiftRight( Y.p, Y.n, 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 } }; /** * \brief Checkup routine * * \return 0 if successful, or 1 if the test failed */ 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 */