[398] | 1 | /*
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| 2 | * Multi-precision integer library
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| 3 | *
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| 4 | * Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
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| 5 | * SPDX-License-Identifier: Apache-2.0
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| 6 | *
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| 7 | * Licensed under the Apache License, Version 2.0 (the "License"); you may
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| 8 | * not use this file except in compliance with the License.
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| 9 | * You may obtain a copy of the License at
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| 10 | *
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| 11 | * http://www.apache.org/licenses/LICENSE-2.0
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| 12 | *
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| 13 | * Unless required by applicable law or agreed to in writing, software
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| 14 | * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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| 15 | * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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| 16 | * See the License for the specific language governing permissions and
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| 17 | * limitations under the License.
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| 18 | *
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| 19 | * This file is part of mbed TLS (https://tls.mbed.org)
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| 20 | */
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| 21 |
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| 22 | /*
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| 23 | * The following sources were referenced in the design of this Multi-precision
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| 24 | * Integer library:
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| 25 | *
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| 26 | * [1] Handbook of Applied Cryptography - 1997
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| 27 | * Menezes, van Oorschot and Vanstone
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| 28 | *
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| 29 | * [2] Multi-Precision Math
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| 30 | * Tom St Denis
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| 31 | * https://github.com/libtom/libtommath/blob/develop/tommath.pdf
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| 32 | *
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| 33 | * [3] GNU Multi-Precision Arithmetic Library
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| 34 | * https://gmplib.org/manual/index.html
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| 35 | *
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| 36 | */
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| 37 |
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| 38 | #if !defined(MBEDTLS_CONFIG_FILE)
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| 39 | #include "mbedtls/config.h"
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| 40 | #else
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| 41 | #include MBEDTLS_CONFIG_FILE
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| 42 | #endif
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| 43 |
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| 44 | #if defined(MBEDTLS_BIGNUM_C)
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| 45 |
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| 46 | #include "mbedtls/bignum.h"
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| 47 | #include "mbedtls/bn_mul.h"
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| 48 | #include "mbedtls/platform_util.h"
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| 49 |
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| 50 | #include <string.h>
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| 51 |
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| 52 | #if defined(MBEDTLS_PLATFORM_C)
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| 53 | #include "mbedtls/platform.h"
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| 54 | #else
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| 55 | #include <stdio.h>
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| 56 | #include <stdlib.h>
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| 57 | #define mbedtls_printf printf
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| 58 | #define mbedtls_calloc calloc
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| 59 | #define mbedtls_free free
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| 60 | #endif
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| 61 |
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| 62 | #define MPI_VALIDATE_RET( cond ) \
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| 63 | MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_MPI_BAD_INPUT_DATA )
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| 64 | #define MPI_VALIDATE( cond ) \
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| 65 | MBEDTLS_INTERNAL_VALIDATE( cond )
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| 66 |
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| 67 | #define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */
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| 68 | #define biL (ciL << 3) /* bits in limb */
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| 69 | #define biH (ciL << 2) /* half limb size */
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| 70 |
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| 71 | #define MPI_SIZE_T_MAX ( (size_t) -1 ) /* SIZE_T_MAX is not standard */
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| 72 |
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| 73 | /*
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| 74 | * Convert between bits/chars and number of limbs
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| 75 | * Divide first in order to avoid potential overflows
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| 76 | */
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| 77 | #define BITS_TO_LIMBS(i) ( (i) / biL + ( (i) % biL != 0 ) )
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| 78 | #define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) )
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| 79 |
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| 80 | /* Implementation that should never be optimized out by the compiler */
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| 81 | static void mbedtls_mpi_zeroize( mbedtls_mpi_uint *v, size_t n )
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| 82 | {
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| 83 | mbedtls_platform_zeroize( v, ciL * n );
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| 84 | }
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| 85 |
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| 86 | /*
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| 87 | * Initialize one MPI
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| 88 | */
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| 89 | void mbedtls_mpi_init( mbedtls_mpi *X )
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| 90 | {
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| 91 | MPI_VALIDATE( X != NULL );
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| 92 |
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| 93 | X->s = 1;
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| 94 | X->n = 0;
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| 95 | X->p = NULL;
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| 96 | }
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| 97 |
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| 98 | /*
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| 99 | * Unallocate one MPI
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| 100 | */
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| 101 | void mbedtls_mpi_free( mbedtls_mpi *X )
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| 102 | {
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| 103 | if( X == NULL )
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| 104 | return;
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| 105 |
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| 106 | if( X->p != NULL )
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| 107 | {
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| 108 | mbedtls_mpi_zeroize( X->p, X->n );
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| 109 | mbedtls_free( X->p );
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| 110 | }
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| 111 |
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| 112 | X->s = 1;
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| 113 | X->n = 0;
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| 114 | X->p = NULL;
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| 115 | }
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| 116 |
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| 117 | /*
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| 118 | * Enlarge to the specified number of limbs
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| 119 | */
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| 120 | int mbedtls_mpi_grow( mbedtls_mpi *X, size_t nblimbs )
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| 121 | {
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| 122 | mbedtls_mpi_uint *p;
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| 123 | MPI_VALIDATE_RET( X != NULL );
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| 124 |
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| 125 | if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
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| 126 | return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
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| 127 |
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| 128 | if( X->n < nblimbs )
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| 129 | {
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| 130 | if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( nblimbs, ciL ) ) == NULL )
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| 131 | return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
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| 132 |
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| 133 | if( X->p != NULL )
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| 134 | {
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| 135 | memcpy( p, X->p, X->n * ciL );
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| 136 | mbedtls_mpi_zeroize( X->p, X->n );
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| 137 | mbedtls_free( X->p );
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| 138 | }
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| 139 |
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| 140 | X->n = nblimbs;
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| 141 | X->p = p;
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| 142 | }
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| 143 |
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| 144 | return( 0 );
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| 145 | }
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| 146 |
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| 147 | /*
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| 148 | * Resize down as much as possible,
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| 149 | * while keeping at least the specified number of limbs
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| 150 | */
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| 151 | int mbedtls_mpi_shrink( mbedtls_mpi *X, size_t nblimbs )
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| 152 | {
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| 153 | mbedtls_mpi_uint *p;
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| 154 | size_t i;
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| 155 | MPI_VALIDATE_RET( X != NULL );
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| 156 |
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| 157 | if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
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| 158 | return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
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| 159 |
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| 160 | /* Actually resize up in this case */
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| 161 | if( X->n <= nblimbs )
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| 162 | return( mbedtls_mpi_grow( X, nblimbs ) );
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| 163 |
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| 164 | for( i = X->n - 1; i > 0; i-- )
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| 165 | if( X->p[i] != 0 )
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| 166 | break;
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| 167 | i++;
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| 168 |
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| 169 | if( i < nblimbs )
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| 170 | i = nblimbs;
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| 171 |
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| 172 | if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( i, ciL ) ) == NULL )
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| 173 | return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
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| 174 |
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| 175 | if( X->p != NULL )
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| 176 | {
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| 177 | memcpy( p, X->p, i * ciL );
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| 178 | mbedtls_mpi_zeroize( X->p, X->n );
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| 179 | mbedtls_free( X->p );
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| 180 | }
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| 181 |
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| 182 | X->n = i;
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| 183 | X->p = p;
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| 184 |
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| 185 | return( 0 );
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| 186 | }
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| 187 |
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| 188 | /*
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| 189 | * Copy the contents of Y into X
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| 190 | */
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| 191 | int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
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| 192 | {
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| 193 | int ret = 0;
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| 194 | size_t i;
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| 195 | MPI_VALIDATE_RET( X != NULL );
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| 196 | MPI_VALIDATE_RET( Y != NULL );
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| 197 |
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| 198 | if( X == Y )
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| 199 | return( 0 );
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| 200 |
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| 201 | if( Y->p == NULL )
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| 202 | {
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| 203 | mbedtls_mpi_free( X );
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| 204 | return( 0 );
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| 205 | }
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| 206 |
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| 207 | for( i = Y->n - 1; i > 0; i-- )
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| 208 | if( Y->p[i] != 0 )
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| 209 | break;
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| 210 | i++;
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| 211 |
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| 212 | X->s = Y->s;
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| 213 |
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| 214 | if( X->n < i )
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| 215 | {
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| 216 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) );
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| 217 | }
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| 218 | else
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| 219 | {
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| 220 | memset( X->p + i, 0, ( X->n - i ) * ciL );
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| 221 | }
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| 222 |
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| 223 | memcpy( X->p, Y->p, i * ciL );
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| 224 |
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| 225 | cleanup:
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| 226 |
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| 227 | return( ret );
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| 228 | }
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| 229 |
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| 230 | /*
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| 231 | * Swap the contents of X and Y
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| 232 | */
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| 233 | void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y )
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| 234 | {
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| 235 | mbedtls_mpi T;
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| 236 | MPI_VALIDATE( X != NULL );
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| 237 | MPI_VALIDATE( Y != NULL );
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| 238 |
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| 239 | memcpy( &T, X, sizeof( mbedtls_mpi ) );
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| 240 | memcpy( X, Y, sizeof( mbedtls_mpi ) );
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| 241 | memcpy( Y, &T, sizeof( mbedtls_mpi ) );
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| 242 | }
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| 243 |
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| 244 | /*
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| 245 | * Conditionally assign X = Y, without leaking information
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| 246 | * about whether the assignment was made or not.
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| 247 | * (Leaking information about the respective sizes of X and Y is ok however.)
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| 248 | */
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| 249 | int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign )
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| 250 | {
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| 251 | int ret = 0;
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| 252 | size_t i;
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| 253 | MPI_VALIDATE_RET( X != NULL );
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| 254 | MPI_VALIDATE_RET( Y != NULL );
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| 255 |
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| 256 | /* make sure assign is 0 or 1 in a time-constant manner */
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| 257 | assign = (assign | (unsigned char)-assign) >> 7;
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| 258 |
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| 259 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
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| 260 |
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| 261 | X->s = X->s * ( 1 - assign ) + Y->s * assign;
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| 262 |
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| 263 | for( i = 0; i < Y->n; i++ )
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| 264 | X->p[i] = X->p[i] * ( 1 - assign ) + Y->p[i] * assign;
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| 265 |
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| 266 | for( ; i < X->n; i++ )
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| 267 | X->p[i] *= ( 1 - assign );
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| 268 |
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| 269 | cleanup:
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| 270 | return( ret );
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| 271 | }
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| 272 |
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| 273 | /*
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| 274 | * Conditionally swap X and Y, without leaking information
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| 275 | * about whether the swap was made or not.
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| 276 | * Here it is not ok to simply swap the pointers, which whould lead to
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| 277 | * different memory access patterns when X and Y are used afterwards.
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| 278 | */
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| 279 | int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap )
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| 280 | {
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| 281 | int ret, s;
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| 282 | size_t i;
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| 283 | mbedtls_mpi_uint tmp;
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| 284 | MPI_VALIDATE_RET( X != NULL );
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| 285 | MPI_VALIDATE_RET( Y != NULL );
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| 286 |
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| 287 | if( X == Y )
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| 288 | return( 0 );
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| 289 |
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| 290 | /* make sure swap is 0 or 1 in a time-constant manner */
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| 291 | swap = (swap | (unsigned char)-swap) >> 7;
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| 292 |
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| 293 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
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| 294 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
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| 295 |
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| 296 | s = X->s;
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| 297 | X->s = X->s * ( 1 - swap ) + Y->s * swap;
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| 298 | Y->s = Y->s * ( 1 - swap ) + s * swap;
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| 299 |
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| 300 |
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| 301 | for( i = 0; i < X->n; i++ )
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| 302 | {
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| 303 | tmp = X->p[i];
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| 304 | X->p[i] = X->p[i] * ( 1 - swap ) + Y->p[i] * swap;
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| 305 | Y->p[i] = Y->p[i] * ( 1 - swap ) + tmp * swap;
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| 306 | }
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| 307 |
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| 308 | cleanup:
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| 309 | return( ret );
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| 310 | }
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| 311 |
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| 312 | /*
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| 313 | * Set value from integer
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| 314 | */
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| 315 | int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z )
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| 316 | {
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| 317 | int ret;
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| 318 | MPI_VALIDATE_RET( X != NULL );
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| 319 |
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| 320 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) );
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| 321 | memset( X->p, 0, X->n * ciL );
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| 322 |
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| 323 | X->p[0] = ( z < 0 ) ? -z : z;
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| 324 | X->s = ( z < 0 ) ? -1 : 1;
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| 325 |
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| 326 | cleanup:
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| 327 |
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| 328 | return( ret );
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| 329 | }
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| 330 |
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| 331 | /*
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| 332 | * Get a specific bit
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| 333 | */
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| 334 | int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos )
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| 335 | {
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| 336 | MPI_VALIDATE_RET( X != NULL );
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| 337 |
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| 338 | if( X->n * biL <= pos )
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| 339 | return( 0 );
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| 340 |
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| 341 | return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 );
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| 342 | }
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| 343 |
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| 344 | /* Get a specific byte, without range checks. */
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| 345 | #define GET_BYTE( X, i ) \
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| 346 | ( ( ( X )->p[( i ) / ciL] >> ( ( ( i ) % ciL ) * 8 ) ) & 0xff )
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| 347 |
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| 348 | /*
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| 349 | * Set a bit to a specific value of 0 or 1
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| 350 | */
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| 351 | int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val )
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| 352 | {
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| 353 | int ret = 0;
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| 354 | size_t off = pos / biL;
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| 355 | size_t idx = pos % biL;
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| 356 | MPI_VALIDATE_RET( X != NULL );
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| 357 |
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| 358 | if( val != 0 && val != 1 )
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| 359 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
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| 360 |
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| 361 | if( X->n * biL <= pos )
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| 362 | {
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| 363 | if( val == 0 )
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| 364 | return( 0 );
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| 365 |
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| 366 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, off + 1 ) );
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| 367 | }
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| 368 |
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| 369 | X->p[off] &= ~( (mbedtls_mpi_uint) 0x01 << idx );
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| 370 | X->p[off] |= (mbedtls_mpi_uint) val << idx;
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| 371 |
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| 372 | cleanup:
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| 373 |
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| 374 | return( ret );
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| 375 | }
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| 376 |
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| 377 | /*
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| 378 | * Return the number of less significant zero-bits
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| 379 | */
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| 380 | size_t mbedtls_mpi_lsb( const mbedtls_mpi *X )
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| 381 | {
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| 382 | size_t i, j, count = 0;
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| 383 | MBEDTLS_INTERNAL_VALIDATE_RET( X != NULL, 0 );
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| 384 |
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| 385 | for( i = 0; i < X->n; i++ )
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| 386 | for( j = 0; j < biL; j++, count++ )
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| 387 | if( ( ( X->p[i] >> j ) & 1 ) != 0 )
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| 388 | return( count );
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| 389 |
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| 390 | return( 0 );
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| 391 | }
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| 392 |
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| 393 | /*
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| 394 | * Count leading zero bits in a given integer
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| 395 | */
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| 396 | static size_t mbedtls_clz( const mbedtls_mpi_uint x )
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| 397 | {
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| 398 | size_t j;
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| 399 | mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);
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| 400 |
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| 401 | for( j = 0; j < biL; j++ )
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| 402 | {
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| 403 | if( x & mask ) break;
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| 404 |
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| 405 | mask >>= 1;
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| 406 | }
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| 407 |
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| 408 | return j;
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| 409 | }
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| 410 |
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| 411 | /*
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| 412 | * Return the number of bits
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| 413 | */
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| 414 | size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X )
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| 415 | {
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| 416 | size_t i, j;
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| 417 |
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| 418 | if( X->n == 0 )
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| 419 | return( 0 );
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| 420 |
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| 421 | for( i = X->n - 1; i > 0; i-- )
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| 422 | if( X->p[i] != 0 )
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| 423 | break;
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| 424 |
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| 425 | j = biL - mbedtls_clz( X->p[i] );
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| 426 |
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| 427 | return( ( i * biL ) + j );
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| 428 | }
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| 429 |
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| 430 | /*
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| 431 | * Return the total size in bytes
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| 432 | */
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| 433 | size_t mbedtls_mpi_size( const mbedtls_mpi *X )
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| 434 | {
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| 435 | return( ( mbedtls_mpi_bitlen( X ) + 7 ) >> 3 );
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| 436 | }
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| 437 |
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| 438 | /*
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| 439 | * Convert an ASCII character to digit value
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| 440 | */
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| 441 | static int mpi_get_digit( mbedtls_mpi_uint *d, int radix, char c )
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| 442 | {
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| 443 | *d = 255;
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| 444 |
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| 445 | if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30;
|
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| 446 | if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37;
|
---|
| 447 | if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57;
|
---|
| 448 |
|
---|
| 449 | if( *d >= (mbedtls_mpi_uint) radix )
|
---|
| 450 | return( MBEDTLS_ERR_MPI_INVALID_CHARACTER );
|
---|
| 451 |
|
---|
| 452 | return( 0 );
|
---|
| 453 | }
|
---|
| 454 |
|
---|
| 455 | /*
|
---|
| 456 | * Import from an ASCII string
|
---|
| 457 | */
|
---|
| 458 | int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s )
|
---|
| 459 | {
|
---|
| 460 | int ret;
|
---|
| 461 | size_t i, j, slen, n;
|
---|
| 462 | mbedtls_mpi_uint d;
|
---|
| 463 | mbedtls_mpi T;
|
---|
| 464 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 465 | MPI_VALIDATE_RET( s != NULL );
|
---|
| 466 |
|
---|
| 467 | if( radix < 2 || radix > 16 )
|
---|
| 468 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 469 |
|
---|
| 470 | mbedtls_mpi_init( &T );
|
---|
| 471 |
|
---|
| 472 | slen = strlen( s );
|
---|
| 473 |
|
---|
| 474 | if( radix == 16 )
|
---|
| 475 | {
|
---|
| 476 | if( slen > MPI_SIZE_T_MAX >> 2 )
|
---|
| 477 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 478 |
|
---|
| 479 | n = BITS_TO_LIMBS( slen << 2 );
|
---|
| 480 |
|
---|
| 481 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n ) );
|
---|
| 482 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
|
---|
| 483 |
|
---|
| 484 | for( i = slen, j = 0; i > 0; i--, j++ )
|
---|
| 485 | {
|
---|
| 486 | if( i == 1 && s[i - 1] == '-' )
|
---|
| 487 | {
|
---|
| 488 | X->s = -1;
|
---|
| 489 | break;
|
---|
| 490 | }
|
---|
| 491 |
|
---|
| 492 | MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
|
---|
| 493 | X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 );
|
---|
| 494 | }
|
---|
| 495 | }
|
---|
| 496 | else
|
---|
| 497 | {
|
---|
| 498 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
|
---|
| 499 |
|
---|
| 500 | for( i = 0; i < slen; i++ )
|
---|
| 501 | {
|
---|
| 502 | if( i == 0 && s[i] == '-' )
|
---|
| 503 | {
|
---|
| 504 | X->s = -1;
|
---|
| 505 | continue;
|
---|
| 506 | }
|
---|
| 507 |
|
---|
| 508 | MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
|
---|
| 509 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) );
|
---|
| 510 |
|
---|
| 511 | if( X->s == 1 )
|
---|
| 512 | {
|
---|
| 513 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) );
|
---|
| 514 | }
|
---|
| 515 | else
|
---|
| 516 | {
|
---|
| 517 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, &T, d ) );
|
---|
| 518 | }
|
---|
| 519 | }
|
---|
| 520 | }
|
---|
| 521 |
|
---|
| 522 | cleanup:
|
---|
| 523 |
|
---|
| 524 | mbedtls_mpi_free( &T );
|
---|
| 525 |
|
---|
| 526 | return( ret );
|
---|
| 527 | }
|
---|
| 528 |
|
---|
| 529 | /*
|
---|
| 530 | * Helper to write the digits high-order first.
|
---|
| 531 | */
|
---|
| 532 | static int mpi_write_hlp( mbedtls_mpi *X, int radix,
|
---|
| 533 | char **p, const size_t buflen )
|
---|
| 534 | {
|
---|
| 535 | int ret;
|
---|
| 536 | mbedtls_mpi_uint r;
|
---|
| 537 | size_t length = 0;
|
---|
| 538 | char *p_end = *p + buflen;
|
---|
| 539 |
|
---|
| 540 | do
|
---|
| 541 | {
|
---|
| 542 | if( length >= buflen )
|
---|
| 543 | {
|
---|
| 544 | return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
|
---|
| 545 | }
|
---|
| 546 |
|
---|
| 547 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, radix ) );
|
---|
| 548 | MBEDTLS_MPI_CHK( mbedtls_mpi_div_int( X, NULL, X, radix ) );
|
---|
| 549 | /*
|
---|
| 550 | * Write the residue in the current position, as an ASCII character.
|
---|
| 551 | */
|
---|
| 552 | if( r < 0xA )
|
---|
| 553 | *(--p_end) = (char)( '0' + r );
|
---|
| 554 | else
|
---|
| 555 | *(--p_end) = (char)( 'A' + ( r - 0xA ) );
|
---|
| 556 |
|
---|
| 557 | length++;
|
---|
| 558 | } while( mbedtls_mpi_cmp_int( X, 0 ) != 0 );
|
---|
| 559 |
|
---|
| 560 | memmove( *p, p_end, length );
|
---|
| 561 | *p += length;
|
---|
| 562 |
|
---|
| 563 | cleanup:
|
---|
| 564 |
|
---|
| 565 | return( ret );
|
---|
| 566 | }
|
---|
| 567 |
|
---|
| 568 | /*
|
---|
| 569 | * Export into an ASCII string
|
---|
| 570 | */
|
---|
| 571 | int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
|
---|
| 572 | char *buf, size_t buflen, size_t *olen )
|
---|
| 573 | {
|
---|
| 574 | int ret = 0;
|
---|
| 575 | size_t n;
|
---|
| 576 | char *p;
|
---|
| 577 | mbedtls_mpi T;
|
---|
| 578 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 579 | MPI_VALIDATE_RET( olen != NULL );
|
---|
| 580 | MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
|
---|
| 581 |
|
---|
| 582 | if( radix < 2 || radix > 16 )
|
---|
| 583 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 584 |
|
---|
| 585 | n = mbedtls_mpi_bitlen( X );
|
---|
| 586 | if( radix >= 4 ) n >>= 1;
|
---|
| 587 | if( radix >= 16 ) n >>= 1;
|
---|
| 588 | /*
|
---|
| 589 | * Round up the buffer length to an even value to ensure that there is
|
---|
| 590 | * enough room for hexadecimal values that can be represented in an odd
|
---|
| 591 | * number of digits.
|
---|
| 592 | */
|
---|
| 593 | n += 3 + ( ( n + 1 ) & 1 );
|
---|
| 594 |
|
---|
| 595 | if( buflen < n )
|
---|
| 596 | {
|
---|
| 597 | *olen = n;
|
---|
| 598 | return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
|
---|
| 599 | }
|
---|
| 600 |
|
---|
| 601 | p = buf;
|
---|
| 602 | mbedtls_mpi_init( &T );
|
---|
| 603 |
|
---|
| 604 | if( X->s == -1 )
|
---|
| 605 | *p++ = '-';
|
---|
| 606 |
|
---|
| 607 | if( radix == 16 )
|
---|
| 608 | {
|
---|
| 609 | int c;
|
---|
| 610 | size_t i, j, k;
|
---|
| 611 |
|
---|
| 612 | for( i = X->n, k = 0; i > 0; i-- )
|
---|
| 613 | {
|
---|
| 614 | for( j = ciL; j > 0; j-- )
|
---|
| 615 | {
|
---|
| 616 | c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF;
|
---|
| 617 |
|
---|
| 618 | if( c == 0 && k == 0 && ( i + j ) != 2 )
|
---|
| 619 | continue;
|
---|
| 620 |
|
---|
| 621 | *(p++) = "0123456789ABCDEF" [c / 16];
|
---|
| 622 | *(p++) = "0123456789ABCDEF" [c % 16];
|
---|
| 623 | k = 1;
|
---|
| 624 | }
|
---|
| 625 | }
|
---|
| 626 | }
|
---|
| 627 | else
|
---|
| 628 | {
|
---|
| 629 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T, X ) );
|
---|
| 630 |
|
---|
| 631 | if( T.s == -1 )
|
---|
| 632 | T.s = 1;
|
---|
| 633 |
|
---|
| 634 | MBEDTLS_MPI_CHK( mpi_write_hlp( &T, radix, &p, buflen ) );
|
---|
| 635 | }
|
---|
| 636 |
|
---|
| 637 | *p++ = '\0';
|
---|
| 638 | *olen = p - buf;
|
---|
| 639 |
|
---|
| 640 | cleanup:
|
---|
| 641 |
|
---|
| 642 | mbedtls_mpi_free( &T );
|
---|
| 643 |
|
---|
| 644 | return( ret );
|
---|
| 645 | }
|
---|
| 646 |
|
---|
| 647 | #if defined(MBEDTLS_FS_IO)
|
---|
| 648 | /*
|
---|
| 649 | * Read X from an opened file
|
---|
| 650 | */
|
---|
| 651 | int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin )
|
---|
| 652 | {
|
---|
| 653 | mbedtls_mpi_uint d;
|
---|
| 654 | size_t slen;
|
---|
| 655 | char *p;
|
---|
| 656 | /*
|
---|
| 657 | * Buffer should have space for (short) label and decimal formatted MPI,
|
---|
| 658 | * newline characters and '\0'
|
---|
| 659 | */
|
---|
| 660 | char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
|
---|
| 661 |
|
---|
| 662 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 663 | MPI_VALIDATE_RET( fin != NULL );
|
---|
| 664 |
|
---|
| 665 | if( radix < 2 || radix > 16 )
|
---|
| 666 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 667 |
|
---|
| 668 | memset( s, 0, sizeof( s ) );
|
---|
| 669 | if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
|
---|
| 670 | return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
|
---|
| 671 |
|
---|
| 672 | slen = strlen( s );
|
---|
| 673 | if( slen == sizeof( s ) - 2 )
|
---|
| 674 | return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
|
---|
| 675 |
|
---|
| 676 | if( slen > 0 && s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; }
|
---|
| 677 | if( slen > 0 && s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; }
|
---|
| 678 |
|
---|
| 679 | p = s + slen;
|
---|
| 680 | while( p-- > s )
|
---|
| 681 | if( mpi_get_digit( &d, radix, *p ) != 0 )
|
---|
| 682 | break;
|
---|
| 683 |
|
---|
| 684 | return( mbedtls_mpi_read_string( X, radix, p + 1 ) );
|
---|
| 685 | }
|
---|
| 686 |
|
---|
| 687 | /*
|
---|
| 688 | * Write X into an opened file (or stdout if fout == NULL)
|
---|
| 689 | */
|
---|
| 690 | int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout )
|
---|
| 691 | {
|
---|
| 692 | int ret;
|
---|
| 693 | size_t n, slen, plen;
|
---|
| 694 | /*
|
---|
| 695 | * Buffer should have space for (short) label and decimal formatted MPI,
|
---|
| 696 | * newline characters and '\0'
|
---|
| 697 | */
|
---|
| 698 | char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
|
---|
| 699 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 700 |
|
---|
| 701 | if( radix < 2 || radix > 16 )
|
---|
| 702 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 703 |
|
---|
| 704 | memset( s, 0, sizeof( s ) );
|
---|
| 705 |
|
---|
| 706 | MBEDTLS_MPI_CHK( mbedtls_mpi_write_string( X, radix, s, sizeof( s ) - 2, &n ) );
|
---|
| 707 |
|
---|
| 708 | if( p == NULL ) p = "";
|
---|
| 709 |
|
---|
| 710 | plen = strlen( p );
|
---|
| 711 | slen = strlen( s );
|
---|
| 712 | s[slen++] = '\r';
|
---|
| 713 | s[slen++] = '\n';
|
---|
| 714 |
|
---|
| 715 | if( fout != NULL )
|
---|
| 716 | {
|
---|
| 717 | if( fwrite( p, 1, plen, fout ) != plen ||
|
---|
| 718 | fwrite( s, 1, slen, fout ) != slen )
|
---|
| 719 | return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
|
---|
| 720 | }
|
---|
| 721 | else
|
---|
| 722 | mbedtls_printf( "%s%s", p, s );
|
---|
| 723 |
|
---|
| 724 | cleanup:
|
---|
| 725 |
|
---|
| 726 | return( ret );
|
---|
| 727 | }
|
---|
| 728 | #endif /* MBEDTLS_FS_IO */
|
---|
| 729 |
|
---|
| 730 |
|
---|
| 731 | /* Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
|
---|
| 732 | * into the storage form used by mbedtls_mpi. */
|
---|
| 733 |
|
---|
| 734 | static mbedtls_mpi_uint mpi_uint_bigendian_to_host_c( mbedtls_mpi_uint x )
|
---|
| 735 | {
|
---|
| 736 | uint8_t i;
|
---|
| 737 | mbedtls_mpi_uint tmp = 0;
|
---|
| 738 | /* This works regardless of the endianness. */
|
---|
| 739 | for( i = 0; i < ciL; i++, x >>= 8 )
|
---|
| 740 | tmp |= ( x & 0xFF ) << ( ( ciL - 1 - i ) << 3 );
|
---|
| 741 | return( tmp );
|
---|
| 742 | }
|
---|
| 743 |
|
---|
| 744 | static mbedtls_mpi_uint mpi_uint_bigendian_to_host( mbedtls_mpi_uint x )
|
---|
| 745 | {
|
---|
| 746 | #if defined(__BYTE_ORDER__)
|
---|
| 747 |
|
---|
| 748 | /* Nothing to do on bigendian systems. */
|
---|
| 749 | #if ( __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ )
|
---|
| 750 | return( x );
|
---|
| 751 | #endif /* __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ */
|
---|
| 752 |
|
---|
| 753 | #if ( __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ )
|
---|
| 754 |
|
---|
| 755 | /* For GCC and Clang, have builtins for byte swapping. */
|
---|
| 756 | #if defined(__GNUC__) && defined(__GNUC_PREREQ)
|
---|
| 757 | #if __GNUC_PREREQ(4,3)
|
---|
| 758 | #define have_bswap
|
---|
| 759 | #endif
|
---|
| 760 | #endif
|
---|
| 761 |
|
---|
| 762 | #if defined(__clang__) && defined(__has_builtin)
|
---|
| 763 | #if __has_builtin(__builtin_bswap32) && \
|
---|
| 764 | __has_builtin(__builtin_bswap64)
|
---|
| 765 | #define have_bswap
|
---|
| 766 | #endif
|
---|
| 767 | #endif
|
---|
| 768 |
|
---|
| 769 | #if defined(have_bswap)
|
---|
| 770 | /* The compiler is hopefully able to statically evaluate this! */
|
---|
| 771 | switch( sizeof(mbedtls_mpi_uint) )
|
---|
| 772 | {
|
---|
| 773 | case 4:
|
---|
| 774 | return( __builtin_bswap32(x) );
|
---|
| 775 | case 8:
|
---|
| 776 | return( __builtin_bswap64(x) );
|
---|
| 777 | }
|
---|
| 778 | #endif
|
---|
| 779 | #endif /* __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ */
|
---|
| 780 | #endif /* __BYTE_ORDER__ */
|
---|
| 781 |
|
---|
| 782 | /* Fall back to C-based reordering if we don't know the byte order
|
---|
| 783 | * or we couldn't use a compiler-specific builtin. */
|
---|
| 784 | return( mpi_uint_bigendian_to_host_c( x ) );
|
---|
| 785 | }
|
---|
| 786 |
|
---|
| 787 | static void mpi_bigendian_to_host( mbedtls_mpi_uint * const p, size_t limbs )
|
---|
| 788 | {
|
---|
| 789 | mbedtls_mpi_uint *cur_limb_left;
|
---|
| 790 | mbedtls_mpi_uint *cur_limb_right;
|
---|
| 791 | if( limbs == 0 )
|
---|
| 792 | return;
|
---|
| 793 |
|
---|
| 794 | /*
|
---|
| 795 | * Traverse limbs and
|
---|
| 796 | * - adapt byte-order in each limb
|
---|
| 797 | * - swap the limbs themselves.
|
---|
| 798 | * For that, simultaneously traverse the limbs from left to right
|
---|
| 799 | * and from right to left, as long as the left index is not bigger
|
---|
| 800 | * than the right index (it's not a problem if limbs is odd and the
|
---|
| 801 | * indices coincide in the last iteration).
|
---|
| 802 | */
|
---|
| 803 | for( cur_limb_left = p, cur_limb_right = p + ( limbs - 1 );
|
---|
| 804 | cur_limb_left <= cur_limb_right;
|
---|
| 805 | cur_limb_left++, cur_limb_right-- )
|
---|
| 806 | {
|
---|
| 807 | mbedtls_mpi_uint tmp;
|
---|
| 808 | /* Note that if cur_limb_left == cur_limb_right,
|
---|
| 809 | * this code effectively swaps the bytes only once. */
|
---|
| 810 | tmp = mpi_uint_bigendian_to_host( *cur_limb_left );
|
---|
| 811 | *cur_limb_left = mpi_uint_bigendian_to_host( *cur_limb_right );
|
---|
| 812 | *cur_limb_right = tmp;
|
---|
| 813 | }
|
---|
| 814 | }
|
---|
| 815 |
|
---|
| 816 | /*
|
---|
| 817 | * Import X from unsigned binary data, big endian
|
---|
| 818 | */
|
---|
| 819 | int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen )
|
---|
| 820 | {
|
---|
| 821 | int ret;
|
---|
| 822 | size_t const limbs = CHARS_TO_LIMBS( buflen );
|
---|
| 823 | size_t const overhead = ( limbs * ciL ) - buflen;
|
---|
| 824 | unsigned char *Xp;
|
---|
| 825 |
|
---|
| 826 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 827 | MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
|
---|
| 828 |
|
---|
| 829 | /* Ensure that target MPI has exactly the necessary number of limbs */
|
---|
| 830 | if( X->n != limbs )
|
---|
| 831 | {
|
---|
| 832 | mbedtls_mpi_free( X );
|
---|
| 833 | mbedtls_mpi_init( X );
|
---|
| 834 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
|
---|
| 835 | }
|
---|
| 836 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
|
---|
| 837 |
|
---|
| 838 | /* Avoid calling `memcpy` with NULL source argument,
|
---|
| 839 | * even if buflen is 0. */
|
---|
| 840 | if( buf != NULL )
|
---|
| 841 | {
|
---|
| 842 | Xp = (unsigned char*) X->p;
|
---|
| 843 | memcpy( Xp + overhead, buf, buflen );
|
---|
| 844 |
|
---|
| 845 | mpi_bigendian_to_host( X->p, limbs );
|
---|
| 846 | }
|
---|
| 847 |
|
---|
| 848 | cleanup:
|
---|
| 849 |
|
---|
| 850 | return( ret );
|
---|
| 851 | }
|
---|
| 852 |
|
---|
| 853 | /*
|
---|
| 854 | * Export X into unsigned binary data, big endian
|
---|
| 855 | */
|
---|
| 856 | int mbedtls_mpi_write_binary( const mbedtls_mpi *X,
|
---|
| 857 | unsigned char *buf, size_t buflen )
|
---|
| 858 | {
|
---|
| 859 | size_t stored_bytes;
|
---|
| 860 | size_t bytes_to_copy;
|
---|
| 861 | unsigned char *p;
|
---|
| 862 | size_t i;
|
---|
| 863 |
|
---|
| 864 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 865 | MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
|
---|
| 866 |
|
---|
| 867 | stored_bytes = X->n * ciL;
|
---|
| 868 |
|
---|
| 869 | if( stored_bytes < buflen )
|
---|
| 870 | {
|
---|
| 871 | /* There is enough space in the output buffer. Write initial
|
---|
| 872 | * null bytes and record the position at which to start
|
---|
| 873 | * writing the significant bytes. In this case, the execution
|
---|
| 874 | * trace of this function does not depend on the value of the
|
---|
| 875 | * number. */
|
---|
| 876 | bytes_to_copy = stored_bytes;
|
---|
| 877 | p = buf + buflen - stored_bytes;
|
---|
| 878 | memset( buf, 0, buflen - stored_bytes );
|
---|
| 879 | }
|
---|
| 880 | else
|
---|
| 881 | {
|
---|
| 882 | /* The output buffer is smaller than the allocated size of X.
|
---|
| 883 | * However X may fit if its leading bytes are zero. */
|
---|
| 884 | bytes_to_copy = buflen;
|
---|
| 885 | p = buf;
|
---|
| 886 | for( i = bytes_to_copy; i < stored_bytes; i++ )
|
---|
| 887 | {
|
---|
| 888 | if( GET_BYTE( X, i ) != 0 )
|
---|
| 889 | return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
|
---|
| 890 | }
|
---|
| 891 | }
|
---|
| 892 |
|
---|
| 893 | for( i = 0; i < bytes_to_copy; i++ )
|
---|
| 894 | p[bytes_to_copy - i - 1] = GET_BYTE( X, i );
|
---|
| 895 |
|
---|
| 896 | return( 0 );
|
---|
| 897 | }
|
---|
| 898 |
|
---|
| 899 | /*
|
---|
| 900 | * Left-shift: X <<= count
|
---|
| 901 | */
|
---|
| 902 | int mbedtls_mpi_shift_l( mbedtls_mpi *X, size_t count )
|
---|
| 903 | {
|
---|
| 904 | int ret;
|
---|
| 905 | size_t i, v0, t1;
|
---|
| 906 | mbedtls_mpi_uint r0 = 0, r1;
|
---|
| 907 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 908 |
|
---|
| 909 | v0 = count / (biL );
|
---|
| 910 | t1 = count & (biL - 1);
|
---|
| 911 |
|
---|
| 912 | i = mbedtls_mpi_bitlen( X ) + count;
|
---|
| 913 |
|
---|
| 914 | if( X->n * biL < i )
|
---|
| 915 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, BITS_TO_LIMBS( i ) ) );
|
---|
| 916 |
|
---|
| 917 | ret = 0;
|
---|
| 918 |
|
---|
| 919 | /*
|
---|
| 920 | * shift by count / limb_size
|
---|
| 921 | */
|
---|
| 922 | if( v0 > 0 )
|
---|
| 923 | {
|
---|
| 924 | for( i = X->n; i > v0; i-- )
|
---|
| 925 | X->p[i - 1] = X->p[i - v0 - 1];
|
---|
| 926 |
|
---|
| 927 | for( ; i > 0; i-- )
|
---|
| 928 | X->p[i - 1] = 0;
|
---|
| 929 | }
|
---|
| 930 |
|
---|
| 931 | /*
|
---|
| 932 | * shift by count % limb_size
|
---|
| 933 | */
|
---|
| 934 | if( t1 > 0 )
|
---|
| 935 | {
|
---|
| 936 | for( i = v0; i < X->n; i++ )
|
---|
| 937 | {
|
---|
| 938 | r1 = X->p[i] >> (biL - t1);
|
---|
| 939 | X->p[i] <<= t1;
|
---|
| 940 | X->p[i] |= r0;
|
---|
| 941 | r0 = r1;
|
---|
| 942 | }
|
---|
| 943 | }
|
---|
| 944 |
|
---|
| 945 | cleanup:
|
---|
| 946 |
|
---|
| 947 | return( ret );
|
---|
| 948 | }
|
---|
| 949 |
|
---|
| 950 | /*
|
---|
| 951 | * Right-shift: X >>= count
|
---|
| 952 | */
|
---|
| 953 | int mbedtls_mpi_shift_r( mbedtls_mpi *X, size_t count )
|
---|
| 954 | {
|
---|
| 955 | size_t i, v0, v1;
|
---|
| 956 | mbedtls_mpi_uint r0 = 0, r1;
|
---|
| 957 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 958 |
|
---|
| 959 | v0 = count / biL;
|
---|
| 960 | v1 = count & (biL - 1);
|
---|
| 961 |
|
---|
| 962 | if( v0 > X->n || ( v0 == X->n && v1 > 0 ) )
|
---|
| 963 | return mbedtls_mpi_lset( X, 0 );
|
---|
| 964 |
|
---|
| 965 | /*
|
---|
| 966 | * shift by count / limb_size
|
---|
| 967 | */
|
---|
| 968 | if( v0 > 0 )
|
---|
| 969 | {
|
---|
| 970 | for( i = 0; i < X->n - v0; i++ )
|
---|
| 971 | X->p[i] = X->p[i + v0];
|
---|
| 972 |
|
---|
| 973 | for( ; i < X->n; i++ )
|
---|
| 974 | X->p[i] = 0;
|
---|
| 975 | }
|
---|
| 976 |
|
---|
| 977 | /*
|
---|
| 978 | * shift by count % limb_size
|
---|
| 979 | */
|
---|
| 980 | if( v1 > 0 )
|
---|
| 981 | {
|
---|
| 982 | for( i = X->n; i > 0; i-- )
|
---|
| 983 | {
|
---|
| 984 | r1 = X->p[i - 1] << (biL - v1);
|
---|
| 985 | X->p[i - 1] >>= v1;
|
---|
| 986 | X->p[i - 1] |= r0;
|
---|
| 987 | r0 = r1;
|
---|
| 988 | }
|
---|
| 989 | }
|
---|
| 990 |
|
---|
| 991 | return( 0 );
|
---|
| 992 | }
|
---|
| 993 |
|
---|
| 994 | /*
|
---|
| 995 | * Compare unsigned values
|
---|
| 996 | */
|
---|
| 997 | int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y )
|
---|
| 998 | {
|
---|
| 999 | size_t i, j;
|
---|
| 1000 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1001 | MPI_VALIDATE_RET( Y != NULL );
|
---|
| 1002 |
|
---|
| 1003 | for( i = X->n; i > 0; i-- )
|
---|
| 1004 | if( X->p[i - 1] != 0 )
|
---|
| 1005 | break;
|
---|
| 1006 |
|
---|
| 1007 | for( j = Y->n; j > 0; j-- )
|
---|
| 1008 | if( Y->p[j - 1] != 0 )
|
---|
| 1009 | break;
|
---|
| 1010 |
|
---|
| 1011 | if( i == 0 && j == 0 )
|
---|
| 1012 | return( 0 );
|
---|
| 1013 |
|
---|
| 1014 | if( i > j ) return( 1 );
|
---|
| 1015 | if( j > i ) return( -1 );
|
---|
| 1016 |
|
---|
| 1017 | for( ; i > 0; i-- )
|
---|
| 1018 | {
|
---|
| 1019 | if( X->p[i - 1] > Y->p[i - 1] ) return( 1 );
|
---|
| 1020 | if( X->p[i - 1] < Y->p[i - 1] ) return( -1 );
|
---|
| 1021 | }
|
---|
| 1022 |
|
---|
| 1023 | return( 0 );
|
---|
| 1024 | }
|
---|
| 1025 |
|
---|
| 1026 | /*
|
---|
| 1027 | * Compare signed values
|
---|
| 1028 | */
|
---|
| 1029 | int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y )
|
---|
| 1030 | {
|
---|
| 1031 | size_t i, j;
|
---|
| 1032 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1033 | MPI_VALIDATE_RET( Y != NULL );
|
---|
| 1034 |
|
---|
| 1035 | for( i = X->n; i > 0; i-- )
|
---|
| 1036 | if( X->p[i - 1] != 0 )
|
---|
| 1037 | break;
|
---|
| 1038 |
|
---|
| 1039 | for( j = Y->n; j > 0; j-- )
|
---|
| 1040 | if( Y->p[j - 1] != 0 )
|
---|
| 1041 | break;
|
---|
| 1042 |
|
---|
| 1043 | if( i == 0 && j == 0 )
|
---|
| 1044 | return( 0 );
|
---|
| 1045 |
|
---|
| 1046 | if( i > j ) return( X->s );
|
---|
| 1047 | if( j > i ) return( -Y->s );
|
---|
| 1048 |
|
---|
| 1049 | if( X->s > 0 && Y->s < 0 ) return( 1 );
|
---|
| 1050 | if( Y->s > 0 && X->s < 0 ) return( -1 );
|
---|
| 1051 |
|
---|
| 1052 | for( ; i > 0; i-- )
|
---|
| 1053 | {
|
---|
| 1054 | if( X->p[i - 1] > Y->p[i - 1] ) return( X->s );
|
---|
| 1055 | if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s );
|
---|
| 1056 | }
|
---|
| 1057 |
|
---|
| 1058 | return( 0 );
|
---|
| 1059 | }
|
---|
| 1060 |
|
---|
| 1061 | /*
|
---|
| 1062 | * Compare signed values
|
---|
| 1063 | */
|
---|
| 1064 | int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z )
|
---|
| 1065 | {
|
---|
| 1066 | mbedtls_mpi Y;
|
---|
| 1067 | mbedtls_mpi_uint p[1];
|
---|
| 1068 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1069 |
|
---|
| 1070 | *p = ( z < 0 ) ? -z : z;
|
---|
| 1071 | Y.s = ( z < 0 ) ? -1 : 1;
|
---|
| 1072 | Y.n = 1;
|
---|
| 1073 | Y.p = p;
|
---|
| 1074 |
|
---|
| 1075 | return( mbedtls_mpi_cmp_mpi( X, &Y ) );
|
---|
| 1076 | }
|
---|
| 1077 |
|
---|
| 1078 | /*
|
---|
| 1079 | * Unsigned addition: X = |A| + |B| (HAC 14.7)
|
---|
| 1080 | */
|
---|
| 1081 | int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
|
---|
| 1082 | {
|
---|
| 1083 | int ret;
|
---|
| 1084 | size_t i, j;
|
---|
| 1085 | mbedtls_mpi_uint *o, *p, c, tmp;
|
---|
| 1086 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1087 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1088 | MPI_VALIDATE_RET( B != NULL );
|
---|
| 1089 |
|
---|
| 1090 | if( X == B )
|
---|
| 1091 | {
|
---|
| 1092 | const mbedtls_mpi *T = A; A = X; B = T;
|
---|
| 1093 | }
|
---|
| 1094 |
|
---|
| 1095 | if( X != A )
|
---|
| 1096 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
|
---|
| 1097 |
|
---|
| 1098 | /*
|
---|
| 1099 | * X should always be positive as a result of unsigned additions.
|
---|
| 1100 | */
|
---|
| 1101 | X->s = 1;
|
---|
| 1102 |
|
---|
| 1103 | for( j = B->n; j > 0; j-- )
|
---|
| 1104 | if( B->p[j - 1] != 0 )
|
---|
| 1105 | break;
|
---|
| 1106 |
|
---|
| 1107 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
|
---|
| 1108 |
|
---|
| 1109 | o = B->p; p = X->p; c = 0;
|
---|
| 1110 |
|
---|
| 1111 | /*
|
---|
| 1112 | * tmp is used because it might happen that p == o
|
---|
| 1113 | */
|
---|
| 1114 | for( i = 0; i < j; i++, o++, p++ )
|
---|
| 1115 | {
|
---|
| 1116 | tmp= *o;
|
---|
| 1117 | *p += c; c = ( *p < c );
|
---|
| 1118 | *p += tmp; c += ( *p < tmp );
|
---|
| 1119 | }
|
---|
| 1120 |
|
---|
| 1121 | while( c != 0 )
|
---|
| 1122 | {
|
---|
| 1123 | if( i >= X->n )
|
---|
| 1124 | {
|
---|
| 1125 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + 1 ) );
|
---|
| 1126 | p = X->p + i;
|
---|
| 1127 | }
|
---|
| 1128 |
|
---|
| 1129 | *p += c; c = ( *p < c ); i++; p++;
|
---|
| 1130 | }
|
---|
| 1131 |
|
---|
| 1132 | cleanup:
|
---|
| 1133 |
|
---|
| 1134 | return( ret );
|
---|
| 1135 | }
|
---|
| 1136 |
|
---|
| 1137 | /*
|
---|
| 1138 | * Helper for mbedtls_mpi subtraction
|
---|
| 1139 | */
|
---|
| 1140 | static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
|
---|
| 1141 | {
|
---|
| 1142 | size_t i;
|
---|
| 1143 | mbedtls_mpi_uint c, z;
|
---|
| 1144 |
|
---|
| 1145 | for( i = c = 0; i < n; i++, s++, d++ )
|
---|
| 1146 | {
|
---|
| 1147 | z = ( *d < c ); *d -= c;
|
---|
| 1148 | c = ( *d < *s ) + z; *d -= *s;
|
---|
| 1149 | }
|
---|
| 1150 |
|
---|
| 1151 | while( c != 0 )
|
---|
| 1152 | {
|
---|
| 1153 | z = ( *d < c ); *d -= c;
|
---|
| 1154 | c = z; d++;
|
---|
| 1155 | }
|
---|
| 1156 | }
|
---|
| 1157 |
|
---|
| 1158 | /*
|
---|
| 1159 | * Unsigned subtraction: X = |A| - |B| (HAC 14.9)
|
---|
| 1160 | */
|
---|
| 1161 | int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
|
---|
| 1162 | {
|
---|
| 1163 | mbedtls_mpi TB;
|
---|
| 1164 | int ret;
|
---|
| 1165 | size_t n;
|
---|
| 1166 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1167 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1168 | MPI_VALIDATE_RET( B != NULL );
|
---|
| 1169 |
|
---|
| 1170 | if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
|
---|
| 1171 | return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
|
---|
| 1172 |
|
---|
| 1173 | mbedtls_mpi_init( &TB );
|
---|
| 1174 |
|
---|
| 1175 | if( X == B )
|
---|
| 1176 | {
|
---|
| 1177 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
|
---|
| 1178 | B = &TB;
|
---|
| 1179 | }
|
---|
| 1180 |
|
---|
| 1181 | if( X != A )
|
---|
| 1182 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
|
---|
| 1183 |
|
---|
| 1184 | /*
|
---|
| 1185 | * X should always be positive as a result of unsigned subtractions.
|
---|
| 1186 | */
|
---|
| 1187 | X->s = 1;
|
---|
| 1188 |
|
---|
| 1189 | ret = 0;
|
---|
| 1190 |
|
---|
| 1191 | for( n = B->n; n > 0; n-- )
|
---|
| 1192 | if( B->p[n - 1] != 0 )
|
---|
| 1193 | break;
|
---|
| 1194 |
|
---|
| 1195 | mpi_sub_hlp( n, B->p, X->p );
|
---|
| 1196 |
|
---|
| 1197 | cleanup:
|
---|
| 1198 |
|
---|
| 1199 | mbedtls_mpi_free( &TB );
|
---|
| 1200 |
|
---|
| 1201 | return( ret );
|
---|
| 1202 | }
|
---|
| 1203 |
|
---|
| 1204 | /*
|
---|
| 1205 | * Signed addition: X = A + B
|
---|
| 1206 | */
|
---|
| 1207 | int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
|
---|
| 1208 | {
|
---|
| 1209 | int ret, s;
|
---|
| 1210 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1211 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1212 | MPI_VALIDATE_RET( B != NULL );
|
---|
| 1213 |
|
---|
| 1214 | s = A->s;
|
---|
| 1215 | if( A->s * B->s < 0 )
|
---|
| 1216 | {
|
---|
| 1217 | if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
|
---|
| 1218 | {
|
---|
| 1219 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
|
---|
| 1220 | X->s = s;
|
---|
| 1221 | }
|
---|
| 1222 | else
|
---|
| 1223 | {
|
---|
| 1224 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
|
---|
| 1225 | X->s = -s;
|
---|
| 1226 | }
|
---|
| 1227 | }
|
---|
| 1228 | else
|
---|
| 1229 | {
|
---|
| 1230 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
|
---|
| 1231 | X->s = s;
|
---|
| 1232 | }
|
---|
| 1233 |
|
---|
| 1234 | cleanup:
|
---|
| 1235 |
|
---|
| 1236 | return( ret );
|
---|
| 1237 | }
|
---|
| 1238 |
|
---|
| 1239 | /*
|
---|
| 1240 | * Signed subtraction: X = A - B
|
---|
| 1241 | */
|
---|
| 1242 | int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
|
---|
| 1243 | {
|
---|
| 1244 | int ret, s;
|
---|
| 1245 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1246 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1247 | MPI_VALIDATE_RET( B != NULL );
|
---|
| 1248 |
|
---|
| 1249 | s = A->s;
|
---|
| 1250 | if( A->s * B->s > 0 )
|
---|
| 1251 | {
|
---|
| 1252 | if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
|
---|
| 1253 | {
|
---|
| 1254 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
|
---|
| 1255 | X->s = s;
|
---|
| 1256 | }
|
---|
| 1257 | else
|
---|
| 1258 | {
|
---|
| 1259 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
|
---|
| 1260 | X->s = -s;
|
---|
| 1261 | }
|
---|
| 1262 | }
|
---|
| 1263 | else
|
---|
| 1264 | {
|
---|
| 1265 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
|
---|
| 1266 | X->s = s;
|
---|
| 1267 | }
|
---|
| 1268 |
|
---|
| 1269 | cleanup:
|
---|
| 1270 |
|
---|
| 1271 | return( ret );
|
---|
| 1272 | }
|
---|
| 1273 |
|
---|
| 1274 | /*
|
---|
| 1275 | * Signed addition: X = A + b
|
---|
| 1276 | */
|
---|
| 1277 | int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
|
---|
| 1278 | {
|
---|
| 1279 | mbedtls_mpi _B;
|
---|
| 1280 | mbedtls_mpi_uint p[1];
|
---|
| 1281 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1282 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1283 |
|
---|
| 1284 | p[0] = ( b < 0 ) ? -b : b;
|
---|
| 1285 | _B.s = ( b < 0 ) ? -1 : 1;
|
---|
| 1286 | _B.n = 1;
|
---|
| 1287 | _B.p = p;
|
---|
| 1288 |
|
---|
| 1289 | return( mbedtls_mpi_add_mpi( X, A, &_B ) );
|
---|
| 1290 | }
|
---|
| 1291 |
|
---|
| 1292 | /*
|
---|
| 1293 | * Signed subtraction: X = A - b
|
---|
| 1294 | */
|
---|
| 1295 | int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
|
---|
| 1296 | {
|
---|
| 1297 | mbedtls_mpi _B;
|
---|
| 1298 | mbedtls_mpi_uint p[1];
|
---|
| 1299 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1300 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1301 |
|
---|
| 1302 | p[0] = ( b < 0 ) ? -b : b;
|
---|
| 1303 | _B.s = ( b < 0 ) ? -1 : 1;
|
---|
| 1304 | _B.n = 1;
|
---|
| 1305 | _B.p = p;
|
---|
| 1306 |
|
---|
| 1307 | return( mbedtls_mpi_sub_mpi( X, A, &_B ) );
|
---|
| 1308 | }
|
---|
| 1309 |
|
---|
| 1310 | /*
|
---|
| 1311 | * Helper for mbedtls_mpi multiplication
|
---|
| 1312 | */
|
---|
| 1313 | static
|
---|
| 1314 | #if defined(__APPLE__) && defined(__arm__)
|
---|
| 1315 | /*
|
---|
| 1316 | * Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
|
---|
| 1317 | * appears to need this to prevent bad ARM code generation at -O3.
|
---|
| 1318 | */
|
---|
| 1319 | __attribute__ ((noinline))
|
---|
| 1320 | #endif
|
---|
| 1321 | void mpi_mul_hlp( size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b )
|
---|
| 1322 | {
|
---|
| 1323 | mbedtls_mpi_uint c = 0, t = 0;
|
---|
| 1324 |
|
---|
| 1325 | #if defined(MULADDC_HUIT)
|
---|
| 1326 | for( ; i >= 8; i -= 8 )
|
---|
| 1327 | {
|
---|
| 1328 | MULADDC_INIT
|
---|
| 1329 | MULADDC_HUIT
|
---|
| 1330 | MULADDC_STOP
|
---|
| 1331 | }
|
---|
| 1332 |
|
---|
| 1333 | for( ; i > 0; i-- )
|
---|
| 1334 | {
|
---|
| 1335 | MULADDC_INIT
|
---|
| 1336 | MULADDC_CORE
|
---|
| 1337 | MULADDC_STOP
|
---|
| 1338 | }
|
---|
| 1339 | #else /* MULADDC_HUIT */
|
---|
| 1340 | for( ; i >= 16; i -= 16 )
|
---|
| 1341 | {
|
---|
| 1342 | MULADDC_INIT
|
---|
| 1343 | MULADDC_CORE MULADDC_CORE
|
---|
| 1344 | MULADDC_CORE MULADDC_CORE
|
---|
| 1345 | MULADDC_CORE MULADDC_CORE
|
---|
| 1346 | MULADDC_CORE MULADDC_CORE
|
---|
| 1347 |
|
---|
| 1348 | MULADDC_CORE MULADDC_CORE
|
---|
| 1349 | MULADDC_CORE MULADDC_CORE
|
---|
| 1350 | MULADDC_CORE MULADDC_CORE
|
---|
| 1351 | MULADDC_CORE MULADDC_CORE
|
---|
| 1352 | MULADDC_STOP
|
---|
| 1353 | }
|
---|
| 1354 |
|
---|
| 1355 | for( ; i >= 8; i -= 8 )
|
---|
| 1356 | {
|
---|
| 1357 | MULADDC_INIT
|
---|
| 1358 | MULADDC_CORE MULADDC_CORE
|
---|
| 1359 | MULADDC_CORE MULADDC_CORE
|
---|
| 1360 |
|
---|
| 1361 | MULADDC_CORE MULADDC_CORE
|
---|
| 1362 | MULADDC_CORE MULADDC_CORE
|
---|
| 1363 | MULADDC_STOP
|
---|
| 1364 | }
|
---|
| 1365 |
|
---|
| 1366 | for( ; i > 0; i-- )
|
---|
| 1367 | {
|
---|
| 1368 | MULADDC_INIT
|
---|
| 1369 | MULADDC_CORE
|
---|
| 1370 | MULADDC_STOP
|
---|
| 1371 | }
|
---|
| 1372 | #endif /* MULADDC_HUIT */
|
---|
| 1373 |
|
---|
| 1374 | t++;
|
---|
| 1375 |
|
---|
| 1376 | do {
|
---|
| 1377 | *d += c; c = ( *d < c ); d++;
|
---|
| 1378 | }
|
---|
| 1379 | while( c != 0 );
|
---|
| 1380 | }
|
---|
| 1381 |
|
---|
| 1382 | /*
|
---|
| 1383 | * Baseline multiplication: X = A * B (HAC 14.12)
|
---|
| 1384 | */
|
---|
| 1385 | int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
|
---|
| 1386 | {
|
---|
| 1387 | int ret;
|
---|
| 1388 | size_t i, j;
|
---|
| 1389 | mbedtls_mpi TA, TB;
|
---|
| 1390 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1391 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1392 | MPI_VALIDATE_RET( B != NULL );
|
---|
| 1393 |
|
---|
| 1394 | mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
|
---|
| 1395 |
|
---|
| 1396 | if( X == A ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) ); A = &TA; }
|
---|
| 1397 | if( X == B ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) ); B = &TB; }
|
---|
| 1398 |
|
---|
| 1399 | for( i = A->n; i > 0; i-- )
|
---|
| 1400 | if( A->p[i - 1] != 0 )
|
---|
| 1401 | break;
|
---|
| 1402 |
|
---|
| 1403 | for( j = B->n; j > 0; j-- )
|
---|
| 1404 | if( B->p[j - 1] != 0 )
|
---|
| 1405 | break;
|
---|
| 1406 |
|
---|
| 1407 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) );
|
---|
| 1408 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
|
---|
| 1409 |
|
---|
| 1410 | for( ; j > 0; j-- )
|
---|
| 1411 | mpi_mul_hlp( i, A->p, X->p + j - 1, B->p[j - 1] );
|
---|
| 1412 |
|
---|
| 1413 | X->s = A->s * B->s;
|
---|
| 1414 |
|
---|
| 1415 | cleanup:
|
---|
| 1416 |
|
---|
| 1417 | mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA );
|
---|
| 1418 |
|
---|
| 1419 | return( ret );
|
---|
| 1420 | }
|
---|
| 1421 |
|
---|
| 1422 | /*
|
---|
| 1423 | * Baseline multiplication: X = A * b
|
---|
| 1424 | */
|
---|
| 1425 | int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b )
|
---|
| 1426 | {
|
---|
| 1427 | mbedtls_mpi _B;
|
---|
| 1428 | mbedtls_mpi_uint p[1];
|
---|
| 1429 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1430 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1431 |
|
---|
| 1432 | _B.s = 1;
|
---|
| 1433 | _B.n = 1;
|
---|
| 1434 | _B.p = p;
|
---|
| 1435 | p[0] = b;
|
---|
| 1436 |
|
---|
| 1437 | return( mbedtls_mpi_mul_mpi( X, A, &_B ) );
|
---|
| 1438 | }
|
---|
| 1439 |
|
---|
| 1440 | /*
|
---|
| 1441 | * Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and
|
---|
| 1442 | * mbedtls_mpi_uint divisor, d
|
---|
| 1443 | */
|
---|
| 1444 | static mbedtls_mpi_uint mbedtls_int_div_int( mbedtls_mpi_uint u1,
|
---|
| 1445 | mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r )
|
---|
| 1446 | {
|
---|
| 1447 | #if defined(MBEDTLS_HAVE_UDBL)
|
---|
| 1448 | mbedtls_t_udbl dividend, quotient;
|
---|
| 1449 | #else
|
---|
| 1450 | const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH;
|
---|
| 1451 | const mbedtls_mpi_uint uint_halfword_mask = ( (mbedtls_mpi_uint) 1 << biH ) - 1;
|
---|
| 1452 | mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient;
|
---|
| 1453 | mbedtls_mpi_uint u0_msw, u0_lsw;
|
---|
| 1454 | size_t s;
|
---|
| 1455 | #endif
|
---|
| 1456 |
|
---|
| 1457 | /*
|
---|
| 1458 | * Check for overflow
|
---|
| 1459 | */
|
---|
| 1460 | if( 0 == d || u1 >= d )
|
---|
| 1461 | {
|
---|
| 1462 | if (r != NULL) *r = ~0;
|
---|
| 1463 |
|
---|
| 1464 | return ( ~0 );
|
---|
| 1465 | }
|
---|
| 1466 |
|
---|
| 1467 | #if defined(MBEDTLS_HAVE_UDBL)
|
---|
| 1468 | dividend = (mbedtls_t_udbl) u1 << biL;
|
---|
| 1469 | dividend |= (mbedtls_t_udbl) u0;
|
---|
| 1470 | quotient = dividend / d;
|
---|
| 1471 | if( quotient > ( (mbedtls_t_udbl) 1 << biL ) - 1 )
|
---|
| 1472 | quotient = ( (mbedtls_t_udbl) 1 << biL ) - 1;
|
---|
| 1473 |
|
---|
| 1474 | if( r != NULL )
|
---|
| 1475 | *r = (mbedtls_mpi_uint)( dividend - (quotient * d ) );
|
---|
| 1476 |
|
---|
| 1477 | return (mbedtls_mpi_uint) quotient;
|
---|
| 1478 | #else
|
---|
| 1479 |
|
---|
| 1480 | /*
|
---|
| 1481 | * Algorithm D, Section 4.3.1 - The Art of Computer Programming
|
---|
| 1482 | * Vol. 2 - Seminumerical Algorithms, Knuth
|
---|
| 1483 | */
|
---|
| 1484 |
|
---|
| 1485 | /*
|
---|
| 1486 | * Normalize the divisor, d, and dividend, u0, u1
|
---|
| 1487 | */
|
---|
| 1488 | s = mbedtls_clz( d );
|
---|
| 1489 | d = d << s;
|
---|
| 1490 |
|
---|
| 1491 | u1 = u1 << s;
|
---|
| 1492 | u1 |= ( u0 >> ( biL - s ) ) & ( -(mbedtls_mpi_sint)s >> ( biL - 1 ) );
|
---|
| 1493 | u0 = u0 << s;
|
---|
| 1494 |
|
---|
| 1495 | d1 = d >> biH;
|
---|
| 1496 | d0 = d & uint_halfword_mask;
|
---|
| 1497 |
|
---|
| 1498 | u0_msw = u0 >> biH;
|
---|
| 1499 | u0_lsw = u0 & uint_halfword_mask;
|
---|
| 1500 |
|
---|
| 1501 | /*
|
---|
| 1502 | * Find the first quotient and remainder
|
---|
| 1503 | */
|
---|
| 1504 | q1 = u1 / d1;
|
---|
| 1505 | r0 = u1 - d1 * q1;
|
---|
| 1506 |
|
---|
| 1507 | while( q1 >= radix || ( q1 * d0 > radix * r0 + u0_msw ) )
|
---|
| 1508 | {
|
---|
| 1509 | q1 -= 1;
|
---|
| 1510 | r0 += d1;
|
---|
| 1511 |
|
---|
| 1512 | if ( r0 >= radix ) break;
|
---|
| 1513 | }
|
---|
| 1514 |
|
---|
| 1515 | rAX = ( u1 * radix ) + ( u0_msw - q1 * d );
|
---|
| 1516 | q0 = rAX / d1;
|
---|
| 1517 | r0 = rAX - q0 * d1;
|
---|
| 1518 |
|
---|
| 1519 | while( q0 >= radix || ( q0 * d0 > radix * r0 + u0_lsw ) )
|
---|
| 1520 | {
|
---|
| 1521 | q0 -= 1;
|
---|
| 1522 | r0 += d1;
|
---|
| 1523 |
|
---|
| 1524 | if ( r0 >= radix ) break;
|
---|
| 1525 | }
|
---|
| 1526 |
|
---|
| 1527 | if (r != NULL)
|
---|
| 1528 | *r = ( rAX * radix + u0_lsw - q0 * d ) >> s;
|
---|
| 1529 |
|
---|
| 1530 | quotient = q1 * radix + q0;
|
---|
| 1531 |
|
---|
| 1532 | return quotient;
|
---|
| 1533 | #endif
|
---|
| 1534 | }
|
---|
| 1535 |
|
---|
| 1536 | /*
|
---|
| 1537 | * Division by mbedtls_mpi: A = Q * B + R (HAC 14.20)
|
---|
| 1538 | */
|
---|
| 1539 | int mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
|
---|
| 1540 | const mbedtls_mpi *B )
|
---|
| 1541 | {
|
---|
| 1542 | int ret;
|
---|
| 1543 | size_t i, n, t, k;
|
---|
| 1544 | mbedtls_mpi X, Y, Z, T1, T2;
|
---|
| 1545 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1546 | MPI_VALIDATE_RET( B != NULL );
|
---|
| 1547 |
|
---|
| 1548 | if( mbedtls_mpi_cmp_int( B, 0 ) == 0 )
|
---|
| 1549 | return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
|
---|
| 1550 |
|
---|
| 1551 | mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
|
---|
| 1552 | mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 );
|
---|
| 1553 |
|
---|
| 1554 | if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
|
---|
| 1555 | {
|
---|
| 1556 | if( Q != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_lset( Q, 0 ) );
|
---|
| 1557 | if( R != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, A ) );
|
---|
| 1558 | return( 0 );
|
---|
| 1559 | }
|
---|
| 1560 |
|
---|
| 1561 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &X, A ) );
|
---|
| 1562 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, B ) );
|
---|
| 1563 | X.s = Y.s = 1;
|
---|
| 1564 |
|
---|
| 1565 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &Z, A->n + 2 ) );
|
---|
| 1566 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Z, 0 ) );
|
---|
| 1567 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T1, 2 ) );
|
---|
| 1568 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T2, 3 ) );
|
---|
| 1569 |
|
---|
| 1570 | k = mbedtls_mpi_bitlen( &Y ) % biL;
|
---|
| 1571 | if( k < biL - 1 )
|
---|
| 1572 | {
|
---|
| 1573 | k = biL - 1 - k;
|
---|
| 1574 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &X, k ) );
|
---|
| 1575 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, k ) );
|
---|
| 1576 | }
|
---|
| 1577 | else k = 0;
|
---|
| 1578 |
|
---|
| 1579 | n = X.n - 1;
|
---|
| 1580 | t = Y.n - 1;
|
---|
| 1581 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &Y, biL * ( n - t ) ) );
|
---|
| 1582 |
|
---|
| 1583 | while( mbedtls_mpi_cmp_mpi( &X, &Y ) >= 0 )
|
---|
| 1584 | {
|
---|
| 1585 | Z.p[n - t]++;
|
---|
| 1586 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &Y ) );
|
---|
| 1587 | }
|
---|
| 1588 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, biL * ( n - t ) ) );
|
---|
| 1589 |
|
---|
| 1590 | for( i = n; i > t ; i-- )
|
---|
| 1591 | {
|
---|
| 1592 | if( X.p[i] >= Y.p[t] )
|
---|
| 1593 | Z.p[i - t - 1] = ~0;
|
---|
| 1594 | else
|
---|
| 1595 | {
|
---|
| 1596 | Z.p[i - t - 1] = mbedtls_int_div_int( X.p[i], X.p[i - 1],
|
---|
| 1597 | Y.p[t], NULL);
|
---|
| 1598 | }
|
---|
| 1599 |
|
---|
| 1600 | Z.p[i - t - 1]++;
|
---|
| 1601 | do
|
---|
| 1602 | {
|
---|
| 1603 | Z.p[i - t - 1]--;
|
---|
| 1604 |
|
---|
| 1605 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T1, 0 ) );
|
---|
| 1606 | T1.p[0] = ( t < 1 ) ? 0 : Y.p[t - 1];
|
---|
| 1607 | T1.p[1] = Y.p[t];
|
---|
| 1608 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
|
---|
| 1609 |
|
---|
| 1610 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T2, 0 ) );
|
---|
| 1611 | T2.p[0] = ( i < 2 ) ? 0 : X.p[i - 2];
|
---|
| 1612 | T2.p[1] = ( i < 1 ) ? 0 : X.p[i - 1];
|
---|
| 1613 | T2.p[2] = X.p[i];
|
---|
| 1614 | }
|
---|
| 1615 | while( mbedtls_mpi_cmp_mpi( &T1, &T2 ) > 0 );
|
---|
| 1616 |
|
---|
| 1617 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &Y, Z.p[i - t - 1] ) );
|
---|
| 1618 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
|
---|
| 1619 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &T1 ) );
|
---|
| 1620 |
|
---|
| 1621 | if( mbedtls_mpi_cmp_int( &X, 0 ) < 0 )
|
---|
| 1622 | {
|
---|
| 1623 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &Y ) );
|
---|
| 1624 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &T1, biL * ( i - t - 1 ) ) );
|
---|
| 1625 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &X, &X, &T1 ) );
|
---|
| 1626 | Z.p[i - t - 1]--;
|
---|
| 1627 | }
|
---|
| 1628 | }
|
---|
| 1629 |
|
---|
| 1630 | if( Q != NULL )
|
---|
| 1631 | {
|
---|
| 1632 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( Q, &Z ) );
|
---|
| 1633 | Q->s = A->s * B->s;
|
---|
| 1634 | }
|
---|
| 1635 |
|
---|
| 1636 | if( R != NULL )
|
---|
| 1637 | {
|
---|
| 1638 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &X, k ) );
|
---|
| 1639 | X.s = A->s;
|
---|
| 1640 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, &X ) );
|
---|
| 1641 |
|
---|
| 1642 | if( mbedtls_mpi_cmp_int( R, 0 ) == 0 )
|
---|
| 1643 | R->s = 1;
|
---|
| 1644 | }
|
---|
| 1645 |
|
---|
| 1646 | cleanup:
|
---|
| 1647 |
|
---|
| 1648 | mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
|
---|
| 1649 | mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 );
|
---|
| 1650 |
|
---|
| 1651 | return( ret );
|
---|
| 1652 | }
|
---|
| 1653 |
|
---|
| 1654 | /*
|
---|
| 1655 | * Division by int: A = Q * b + R
|
---|
| 1656 | */
|
---|
| 1657 | int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R,
|
---|
| 1658 | const mbedtls_mpi *A,
|
---|
| 1659 | mbedtls_mpi_sint b )
|
---|
| 1660 | {
|
---|
| 1661 | mbedtls_mpi _B;
|
---|
| 1662 | mbedtls_mpi_uint p[1];
|
---|
| 1663 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1664 |
|
---|
| 1665 | p[0] = ( b < 0 ) ? -b : b;
|
---|
| 1666 | _B.s = ( b < 0 ) ? -1 : 1;
|
---|
| 1667 | _B.n = 1;
|
---|
| 1668 | _B.p = p;
|
---|
| 1669 |
|
---|
| 1670 | return( mbedtls_mpi_div_mpi( Q, R, A, &_B ) );
|
---|
| 1671 | }
|
---|
| 1672 |
|
---|
| 1673 | /*
|
---|
| 1674 | * Modulo: R = A mod B
|
---|
| 1675 | */
|
---|
| 1676 | int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B )
|
---|
| 1677 | {
|
---|
| 1678 | int ret;
|
---|
| 1679 | MPI_VALIDATE_RET( R != NULL );
|
---|
| 1680 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1681 | MPI_VALIDATE_RET( B != NULL );
|
---|
| 1682 |
|
---|
| 1683 | if( mbedtls_mpi_cmp_int( B, 0 ) < 0 )
|
---|
| 1684 | return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
|
---|
| 1685 |
|
---|
| 1686 | MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( NULL, R, A, B ) );
|
---|
| 1687 |
|
---|
| 1688 | while( mbedtls_mpi_cmp_int( R, 0 ) < 0 )
|
---|
| 1689 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( R, R, B ) );
|
---|
| 1690 |
|
---|
| 1691 | while( mbedtls_mpi_cmp_mpi( R, B ) >= 0 )
|
---|
| 1692 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( R, R, B ) );
|
---|
| 1693 |
|
---|
| 1694 | cleanup:
|
---|
| 1695 |
|
---|
| 1696 | return( ret );
|
---|
| 1697 | }
|
---|
| 1698 |
|
---|
| 1699 | /*
|
---|
| 1700 | * Modulo: r = A mod b
|
---|
| 1701 | */
|
---|
| 1702 | int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b )
|
---|
| 1703 | {
|
---|
| 1704 | size_t i;
|
---|
| 1705 | mbedtls_mpi_uint x, y, z;
|
---|
| 1706 | MPI_VALIDATE_RET( r != NULL );
|
---|
| 1707 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1708 |
|
---|
| 1709 | if( b == 0 )
|
---|
| 1710 | return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
|
---|
| 1711 |
|
---|
| 1712 | if( b < 0 )
|
---|
| 1713 | return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
|
---|
| 1714 |
|
---|
| 1715 | /*
|
---|
| 1716 | * handle trivial cases
|
---|
| 1717 | */
|
---|
| 1718 | if( b == 1 )
|
---|
| 1719 | {
|
---|
| 1720 | *r = 0;
|
---|
| 1721 | return( 0 );
|
---|
| 1722 | }
|
---|
| 1723 |
|
---|
| 1724 | if( b == 2 )
|
---|
| 1725 | {
|
---|
| 1726 | *r = A->p[0] & 1;
|
---|
| 1727 | return( 0 );
|
---|
| 1728 | }
|
---|
| 1729 |
|
---|
| 1730 | /*
|
---|
| 1731 | * general case
|
---|
| 1732 | */
|
---|
| 1733 | for( i = A->n, y = 0; i > 0; i-- )
|
---|
| 1734 | {
|
---|
| 1735 | x = A->p[i - 1];
|
---|
| 1736 | y = ( y << biH ) | ( x >> biH );
|
---|
| 1737 | z = y / b;
|
---|
| 1738 | y -= z * b;
|
---|
| 1739 |
|
---|
| 1740 | x <<= biH;
|
---|
| 1741 | y = ( y << biH ) | ( x >> biH );
|
---|
| 1742 | z = y / b;
|
---|
| 1743 | y -= z * b;
|
---|
| 1744 | }
|
---|
| 1745 |
|
---|
| 1746 | /*
|
---|
| 1747 | * If A is negative, then the current y represents a negative value.
|
---|
| 1748 | * Flipping it to the positive side.
|
---|
| 1749 | */
|
---|
| 1750 | if( A->s < 0 && y != 0 )
|
---|
| 1751 | y = b - y;
|
---|
| 1752 |
|
---|
| 1753 | *r = y;
|
---|
| 1754 |
|
---|
| 1755 | return( 0 );
|
---|
| 1756 | }
|
---|
| 1757 |
|
---|
| 1758 | /*
|
---|
| 1759 | * Fast Montgomery initialization (thanks to Tom St Denis)
|
---|
| 1760 | */
|
---|
| 1761 | static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N )
|
---|
| 1762 | {
|
---|
| 1763 | mbedtls_mpi_uint x, m0 = N->p[0];
|
---|
| 1764 | unsigned int i;
|
---|
| 1765 |
|
---|
| 1766 | x = m0;
|
---|
| 1767 | x += ( ( m0 + 2 ) & 4 ) << 1;
|
---|
| 1768 |
|
---|
| 1769 | for( i = biL; i >= 8; i /= 2 )
|
---|
| 1770 | x *= ( 2 - ( m0 * x ) );
|
---|
| 1771 |
|
---|
| 1772 | *mm = ~x + 1;
|
---|
| 1773 | }
|
---|
| 1774 |
|
---|
| 1775 | /*
|
---|
| 1776 | * Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
|
---|
| 1777 | */
|
---|
| 1778 | static int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
|
---|
| 1779 | const mbedtls_mpi *T )
|
---|
| 1780 | {
|
---|
| 1781 | size_t i, n, m;
|
---|
| 1782 | mbedtls_mpi_uint u0, u1, *d;
|
---|
| 1783 |
|
---|
| 1784 | if( T->n < N->n + 1 || T->p == NULL )
|
---|
| 1785 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 1786 |
|
---|
| 1787 | memset( T->p, 0, T->n * ciL );
|
---|
| 1788 |
|
---|
| 1789 | d = T->p;
|
---|
| 1790 | n = N->n;
|
---|
| 1791 | m = ( B->n < n ) ? B->n : n;
|
---|
| 1792 |
|
---|
| 1793 | for( i = 0; i < n; i++ )
|
---|
| 1794 | {
|
---|
| 1795 | /*
|
---|
| 1796 | * T = (T + u0*B + u1*N) / 2^biL
|
---|
| 1797 | */
|
---|
| 1798 | u0 = A->p[i];
|
---|
| 1799 | u1 = ( d[0] + u0 * B->p[0] ) * mm;
|
---|
| 1800 |
|
---|
| 1801 | mpi_mul_hlp( m, B->p, d, u0 );
|
---|
| 1802 | mpi_mul_hlp( n, N->p, d, u1 );
|
---|
| 1803 |
|
---|
| 1804 | *d++ = u0; d[n + 1] = 0;
|
---|
| 1805 | }
|
---|
| 1806 |
|
---|
| 1807 | memcpy( A->p, d, ( n + 1 ) * ciL );
|
---|
| 1808 |
|
---|
| 1809 | if( mbedtls_mpi_cmp_abs( A, N ) >= 0 )
|
---|
| 1810 | mpi_sub_hlp( n, N->p, A->p );
|
---|
| 1811 | else
|
---|
| 1812 | /* prevent timing attacks */
|
---|
| 1813 | mpi_sub_hlp( n, A->p, T->p );
|
---|
| 1814 |
|
---|
| 1815 | return( 0 );
|
---|
| 1816 | }
|
---|
| 1817 |
|
---|
| 1818 | /*
|
---|
| 1819 | * Montgomery reduction: A = A * R^-1 mod N
|
---|
| 1820 | */
|
---|
| 1821 | static int mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
|
---|
| 1822 | mbedtls_mpi_uint mm, const mbedtls_mpi *T )
|
---|
| 1823 | {
|
---|
| 1824 | mbedtls_mpi_uint z = 1;
|
---|
| 1825 | mbedtls_mpi U;
|
---|
| 1826 |
|
---|
| 1827 | U.n = U.s = (int) z;
|
---|
| 1828 | U.p = &z;
|
---|
| 1829 |
|
---|
| 1830 | return( mpi_montmul( A, &U, N, mm, T ) );
|
---|
| 1831 | }
|
---|
| 1832 |
|
---|
| 1833 | /*
|
---|
| 1834 | * Sliding-window exponentiation: X = A^E mod N (HAC 14.85)
|
---|
| 1835 | */
|
---|
| 1836 | int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
|
---|
| 1837 | const mbedtls_mpi *E, const mbedtls_mpi *N,
|
---|
| 1838 | mbedtls_mpi *_RR )
|
---|
| 1839 | {
|
---|
| 1840 | int ret;
|
---|
| 1841 | size_t wbits, wsize, one = 1;
|
---|
| 1842 | size_t i, j, nblimbs;
|
---|
| 1843 | size_t bufsize, nbits;
|
---|
| 1844 | mbedtls_mpi_uint ei, mm, state;
|
---|
| 1845 | mbedtls_mpi RR, T, W[ 2 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
|
---|
| 1846 | int neg;
|
---|
| 1847 |
|
---|
| 1848 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 1849 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 1850 | MPI_VALIDATE_RET( E != NULL );
|
---|
| 1851 | MPI_VALIDATE_RET( N != NULL );
|
---|
| 1852 |
|
---|
| 1853 | if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 || ( N->p[0] & 1 ) == 0 )
|
---|
| 1854 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 1855 |
|
---|
| 1856 | if( mbedtls_mpi_cmp_int( E, 0 ) < 0 )
|
---|
| 1857 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 1858 |
|
---|
| 1859 | /*
|
---|
| 1860 | * Init temps and window size
|
---|
| 1861 | */
|
---|
| 1862 | mpi_montg_init( &mm, N );
|
---|
| 1863 | mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &T );
|
---|
| 1864 | mbedtls_mpi_init( &Apos );
|
---|
| 1865 | memset( W, 0, sizeof( W ) );
|
---|
| 1866 |
|
---|
| 1867 | i = mbedtls_mpi_bitlen( E );
|
---|
| 1868 |
|
---|
| 1869 | wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
|
---|
| 1870 | ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
|
---|
| 1871 |
|
---|
| 1872 | if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
|
---|
| 1873 | wsize = MBEDTLS_MPI_WINDOW_SIZE;
|
---|
| 1874 |
|
---|
| 1875 | j = N->n + 1;
|
---|
| 1876 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
|
---|
| 1877 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[1], j ) );
|
---|
| 1878 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &T, j * 2 ) );
|
---|
| 1879 |
|
---|
| 1880 | /*
|
---|
| 1881 | * Compensate for negative A (and correct at the end)
|
---|
| 1882 | */
|
---|
| 1883 | neg = ( A->s == -1 );
|
---|
| 1884 | if( neg )
|
---|
| 1885 | {
|
---|
| 1886 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Apos, A ) );
|
---|
| 1887 | Apos.s = 1;
|
---|
| 1888 | A = &Apos;
|
---|
| 1889 | }
|
---|
| 1890 |
|
---|
| 1891 | /*
|
---|
| 1892 | * If 1st call, pre-compute R^2 mod N
|
---|
| 1893 | */
|
---|
| 1894 | if( _RR == NULL || _RR->p == NULL )
|
---|
| 1895 | {
|
---|
| 1896 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &RR, 1 ) );
|
---|
| 1897 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &RR, N->n * 2 * biL ) );
|
---|
| 1898 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &RR, &RR, N ) );
|
---|
| 1899 |
|
---|
| 1900 | if( _RR != NULL )
|
---|
| 1901 | memcpy( _RR, &RR, sizeof( mbedtls_mpi ) );
|
---|
| 1902 | }
|
---|
| 1903 | else
|
---|
| 1904 | memcpy( &RR, _RR, sizeof( mbedtls_mpi ) );
|
---|
| 1905 |
|
---|
| 1906 | /*
|
---|
| 1907 | * W[1] = A * R^2 * R^-1 mod N = A * R mod N
|
---|
| 1908 | */
|
---|
| 1909 | if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 )
|
---|
| 1910 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) );
|
---|
| 1911 | else
|
---|
| 1912 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );
|
---|
| 1913 |
|
---|
| 1914 | MBEDTLS_MPI_CHK( mpi_montmul( &W[1], &RR, N, mm, &T ) );
|
---|
| 1915 |
|
---|
| 1916 | /*
|
---|
| 1917 | * X = R^2 * R^-1 mod N = R mod N
|
---|
| 1918 | */
|
---|
| 1919 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) );
|
---|
| 1920 | MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
|
---|
| 1921 |
|
---|
| 1922 | if( wsize > 1 )
|
---|
| 1923 | {
|
---|
| 1924 | /*
|
---|
| 1925 | * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
|
---|
| 1926 | */
|
---|
| 1927 | j = one << ( wsize - 1 );
|
---|
| 1928 |
|
---|
| 1929 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[j], N->n + 1 ) );
|
---|
| 1930 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) );
|
---|
| 1931 |
|
---|
| 1932 | for( i = 0; i < wsize - 1; i++ )
|
---|
| 1933 | MBEDTLS_MPI_CHK( mpi_montmul( &W[j], &W[j], N, mm, &T ) );
|
---|
| 1934 |
|
---|
| 1935 | /*
|
---|
| 1936 | * W[i] = W[i - 1] * W[1]
|
---|
| 1937 | */
|
---|
| 1938 | for( i = j + 1; i < ( one << wsize ); i++ )
|
---|
| 1939 | {
|
---|
| 1940 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) );
|
---|
| 1941 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) );
|
---|
| 1942 |
|
---|
| 1943 | MBEDTLS_MPI_CHK( mpi_montmul( &W[i], &W[1], N, mm, &T ) );
|
---|
| 1944 | }
|
---|
| 1945 | }
|
---|
| 1946 |
|
---|
| 1947 | nblimbs = E->n;
|
---|
| 1948 | bufsize = 0;
|
---|
| 1949 | nbits = 0;
|
---|
| 1950 | wbits = 0;
|
---|
| 1951 | state = 0;
|
---|
| 1952 |
|
---|
| 1953 | while( 1 )
|
---|
| 1954 | {
|
---|
| 1955 | if( bufsize == 0 )
|
---|
| 1956 | {
|
---|
| 1957 | if( nblimbs == 0 )
|
---|
| 1958 | break;
|
---|
| 1959 |
|
---|
| 1960 | nblimbs--;
|
---|
| 1961 |
|
---|
| 1962 | bufsize = sizeof( mbedtls_mpi_uint ) << 3;
|
---|
| 1963 | }
|
---|
| 1964 |
|
---|
| 1965 | bufsize--;
|
---|
| 1966 |
|
---|
| 1967 | ei = (E->p[nblimbs] >> bufsize) & 1;
|
---|
| 1968 |
|
---|
| 1969 | /*
|
---|
| 1970 | * skip leading 0s
|
---|
| 1971 | */
|
---|
| 1972 | if( ei == 0 && state == 0 )
|
---|
| 1973 | continue;
|
---|
| 1974 |
|
---|
| 1975 | if( ei == 0 && state == 1 )
|
---|
| 1976 | {
|
---|
| 1977 | /*
|
---|
| 1978 | * out of window, square X
|
---|
| 1979 | */
|
---|
| 1980 | MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
|
---|
| 1981 | continue;
|
---|
| 1982 | }
|
---|
| 1983 |
|
---|
| 1984 | /*
|
---|
| 1985 | * add ei to current window
|
---|
| 1986 | */
|
---|
| 1987 | state = 2;
|
---|
| 1988 |
|
---|
| 1989 | nbits++;
|
---|
| 1990 | wbits |= ( ei << ( wsize - nbits ) );
|
---|
| 1991 |
|
---|
| 1992 | if( nbits == wsize )
|
---|
| 1993 | {
|
---|
| 1994 | /*
|
---|
| 1995 | * X = X^wsize R^-1 mod N
|
---|
| 1996 | */
|
---|
| 1997 | for( i = 0; i < wsize; i++ )
|
---|
| 1998 | MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
|
---|
| 1999 |
|
---|
| 2000 | /*
|
---|
| 2001 | * X = X * W[wbits] R^-1 mod N
|
---|
| 2002 | */
|
---|
| 2003 | MBEDTLS_MPI_CHK( mpi_montmul( X, &W[wbits], N, mm, &T ) );
|
---|
| 2004 |
|
---|
| 2005 | state--;
|
---|
| 2006 | nbits = 0;
|
---|
| 2007 | wbits = 0;
|
---|
| 2008 | }
|
---|
| 2009 | }
|
---|
| 2010 |
|
---|
| 2011 | /*
|
---|
| 2012 | * process the remaining bits
|
---|
| 2013 | */
|
---|
| 2014 | for( i = 0; i < nbits; i++ )
|
---|
| 2015 | {
|
---|
| 2016 | MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
|
---|
| 2017 |
|
---|
| 2018 | wbits <<= 1;
|
---|
| 2019 |
|
---|
| 2020 | if( ( wbits & ( one << wsize ) ) != 0 )
|
---|
| 2021 | MBEDTLS_MPI_CHK( mpi_montmul( X, &W[1], N, mm, &T ) );
|
---|
| 2022 | }
|
---|
| 2023 |
|
---|
| 2024 | /*
|
---|
| 2025 | * X = A^E * R * R^-1 mod N = A^E mod N
|
---|
| 2026 | */
|
---|
| 2027 | MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
|
---|
| 2028 |
|
---|
| 2029 | if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 )
|
---|
| 2030 | {
|
---|
| 2031 | X->s = -1;
|
---|
| 2032 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
|
---|
| 2033 | }
|
---|
| 2034 |
|
---|
| 2035 | cleanup:
|
---|
| 2036 |
|
---|
| 2037 | for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
|
---|
| 2038 | mbedtls_mpi_free( &W[i] );
|
---|
| 2039 |
|
---|
| 2040 | mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
|
---|
| 2041 |
|
---|
| 2042 | if( _RR == NULL || _RR->p == NULL )
|
---|
| 2043 | mbedtls_mpi_free( &RR );
|
---|
| 2044 |
|
---|
| 2045 | return( ret );
|
---|
| 2046 | }
|
---|
| 2047 |
|
---|
| 2048 | /*
|
---|
| 2049 | * Greatest common divisor: G = gcd(A, B) (HAC 14.54)
|
---|
| 2050 | */
|
---|
| 2051 | int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B )
|
---|
| 2052 | {
|
---|
| 2053 | int ret;
|
---|
| 2054 | size_t lz, lzt;
|
---|
| 2055 | mbedtls_mpi TG, TA, TB;
|
---|
| 2056 |
|
---|
| 2057 | MPI_VALIDATE_RET( G != NULL );
|
---|
| 2058 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 2059 | MPI_VALIDATE_RET( B != NULL );
|
---|
| 2060 |
|
---|
| 2061 | mbedtls_mpi_init( &TG ); mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
|
---|
| 2062 |
|
---|
| 2063 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) );
|
---|
| 2064 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
|
---|
| 2065 |
|
---|
| 2066 | lz = mbedtls_mpi_lsb( &TA );
|
---|
| 2067 | lzt = mbedtls_mpi_lsb( &TB );
|
---|
| 2068 |
|
---|
| 2069 | if( lzt < lz )
|
---|
| 2070 | lz = lzt;
|
---|
| 2071 |
|
---|
| 2072 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, lz ) );
|
---|
| 2073 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, lz ) );
|
---|
| 2074 |
|
---|
| 2075 | TA.s = TB.s = 1;
|
---|
| 2076 |
|
---|
| 2077 | while( mbedtls_mpi_cmp_int( &TA, 0 ) != 0 )
|
---|
| 2078 | {
|
---|
| 2079 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) );
|
---|
| 2080 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) );
|
---|
| 2081 |
|
---|
| 2082 | if( mbedtls_mpi_cmp_mpi( &TA, &TB ) >= 0 )
|
---|
| 2083 | {
|
---|
| 2084 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TA, &TA, &TB ) );
|
---|
| 2085 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, 1 ) );
|
---|
| 2086 | }
|
---|
| 2087 | else
|
---|
| 2088 | {
|
---|
| 2089 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TB, &TB, &TA ) );
|
---|
| 2090 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, 1 ) );
|
---|
| 2091 | }
|
---|
| 2092 | }
|
---|
| 2093 |
|
---|
| 2094 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) );
|
---|
| 2095 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) );
|
---|
| 2096 |
|
---|
| 2097 | cleanup:
|
---|
| 2098 |
|
---|
| 2099 | mbedtls_mpi_free( &TG ); mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB );
|
---|
| 2100 |
|
---|
| 2101 | return( ret );
|
---|
| 2102 | }
|
---|
| 2103 |
|
---|
| 2104 | /*
|
---|
| 2105 | * Fill X with size bytes of random.
|
---|
| 2106 | *
|
---|
| 2107 | * Use a temporary bytes representation to make sure the result is the same
|
---|
| 2108 | * regardless of the platform endianness (useful when f_rng is actually
|
---|
| 2109 | * deterministic, eg for tests).
|
---|
| 2110 | */
|
---|
| 2111 | int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
|
---|
| 2112 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2113 | void *p_rng )
|
---|
| 2114 | {
|
---|
| 2115 | int ret;
|
---|
| 2116 | size_t const limbs = CHARS_TO_LIMBS( size );
|
---|
| 2117 | size_t const overhead = ( limbs * ciL ) - size;
|
---|
| 2118 | unsigned char *Xp;
|
---|
| 2119 |
|
---|
| 2120 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 2121 | MPI_VALIDATE_RET( f_rng != NULL );
|
---|
| 2122 |
|
---|
| 2123 | /* Ensure that target MPI has exactly the necessary number of limbs */
|
---|
| 2124 | if( X->n != limbs )
|
---|
| 2125 | {
|
---|
| 2126 | mbedtls_mpi_free( X );
|
---|
| 2127 | mbedtls_mpi_init( X );
|
---|
| 2128 | MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
|
---|
| 2129 | }
|
---|
| 2130 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
|
---|
| 2131 |
|
---|
| 2132 | Xp = (unsigned char*) X->p;
|
---|
| 2133 | f_rng( p_rng, Xp + overhead, size );
|
---|
| 2134 |
|
---|
| 2135 | mpi_bigendian_to_host( X->p, limbs );
|
---|
| 2136 |
|
---|
| 2137 | cleanup:
|
---|
| 2138 | return( ret );
|
---|
| 2139 | }
|
---|
| 2140 |
|
---|
| 2141 | /*
|
---|
| 2142 | * Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64)
|
---|
| 2143 | */
|
---|
| 2144 | int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N )
|
---|
| 2145 | {
|
---|
| 2146 | int ret;
|
---|
| 2147 | mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
|
---|
| 2148 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 2149 | MPI_VALIDATE_RET( A != NULL );
|
---|
| 2150 | MPI_VALIDATE_RET( N != NULL );
|
---|
| 2151 |
|
---|
| 2152 | if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 )
|
---|
| 2153 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 2154 |
|
---|
| 2155 | mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TU ); mbedtls_mpi_init( &U1 ); mbedtls_mpi_init( &U2 );
|
---|
| 2156 | mbedtls_mpi_init( &G ); mbedtls_mpi_init( &TB ); mbedtls_mpi_init( &TV );
|
---|
| 2157 | mbedtls_mpi_init( &V1 ); mbedtls_mpi_init( &V2 );
|
---|
| 2158 |
|
---|
| 2159 | MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, A, N ) );
|
---|
| 2160 |
|
---|
| 2161 | if( mbedtls_mpi_cmp_int( &G, 1 ) != 0 )
|
---|
| 2162 | {
|
---|
| 2163 | ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
|
---|
| 2164 | goto cleanup;
|
---|
| 2165 | }
|
---|
| 2166 |
|
---|
| 2167 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &TA, A, N ) );
|
---|
| 2168 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TU, &TA ) );
|
---|
| 2169 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, N ) );
|
---|
| 2170 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TV, N ) );
|
---|
| 2171 |
|
---|
| 2172 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U1, 1 ) );
|
---|
| 2173 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U2, 0 ) );
|
---|
| 2174 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V1, 0 ) );
|
---|
| 2175 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V2, 1 ) );
|
---|
| 2176 |
|
---|
| 2177 | do
|
---|
| 2178 | {
|
---|
| 2179 | while( ( TU.p[0] & 1 ) == 0 )
|
---|
| 2180 | {
|
---|
| 2181 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TU, 1 ) );
|
---|
| 2182 |
|
---|
| 2183 | if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 )
|
---|
| 2184 | {
|
---|
| 2185 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &U1, &U1, &TB ) );
|
---|
| 2186 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &TA ) );
|
---|
| 2187 | }
|
---|
| 2188 |
|
---|
| 2189 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U1, 1 ) );
|
---|
| 2190 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U2, 1 ) );
|
---|
| 2191 | }
|
---|
| 2192 |
|
---|
| 2193 | while( ( TV.p[0] & 1 ) == 0 )
|
---|
| 2194 | {
|
---|
| 2195 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TV, 1 ) );
|
---|
| 2196 |
|
---|
| 2197 | if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 )
|
---|
| 2198 | {
|
---|
| 2199 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, &TB ) );
|
---|
| 2200 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &TA ) );
|
---|
| 2201 | }
|
---|
| 2202 |
|
---|
| 2203 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V1, 1 ) );
|
---|
| 2204 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V2, 1 ) );
|
---|
| 2205 | }
|
---|
| 2206 |
|
---|
| 2207 | if( mbedtls_mpi_cmp_mpi( &TU, &TV ) >= 0 )
|
---|
| 2208 | {
|
---|
| 2209 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TU, &TU, &TV ) );
|
---|
| 2210 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U1, &U1, &V1 ) );
|
---|
| 2211 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &V2 ) );
|
---|
| 2212 | }
|
---|
| 2213 | else
|
---|
| 2214 | {
|
---|
| 2215 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TV, &TV, &TU ) );
|
---|
| 2216 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, &U1 ) );
|
---|
| 2217 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &U2 ) );
|
---|
| 2218 | }
|
---|
| 2219 | }
|
---|
| 2220 | while( mbedtls_mpi_cmp_int( &TU, 0 ) != 0 );
|
---|
| 2221 |
|
---|
| 2222 | while( mbedtls_mpi_cmp_int( &V1, 0 ) < 0 )
|
---|
| 2223 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, N ) );
|
---|
| 2224 |
|
---|
| 2225 | while( mbedtls_mpi_cmp_mpi( &V1, N ) >= 0 )
|
---|
| 2226 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, N ) );
|
---|
| 2227 |
|
---|
| 2228 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &V1 ) );
|
---|
| 2229 |
|
---|
| 2230 | cleanup:
|
---|
| 2231 |
|
---|
| 2232 | mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TU ); mbedtls_mpi_free( &U1 ); mbedtls_mpi_free( &U2 );
|
---|
| 2233 | mbedtls_mpi_free( &G ); mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TV );
|
---|
| 2234 | mbedtls_mpi_free( &V1 ); mbedtls_mpi_free( &V2 );
|
---|
| 2235 |
|
---|
| 2236 | return( ret );
|
---|
| 2237 | }
|
---|
| 2238 |
|
---|
| 2239 | #if defined(MBEDTLS_GENPRIME)
|
---|
| 2240 |
|
---|
| 2241 | static const int small_prime[] =
|
---|
| 2242 | {
|
---|
| 2243 | 3, 5, 7, 11, 13, 17, 19, 23,
|
---|
| 2244 | 29, 31, 37, 41, 43, 47, 53, 59,
|
---|
| 2245 | 61, 67, 71, 73, 79, 83, 89, 97,
|
---|
| 2246 | 101, 103, 107, 109, 113, 127, 131, 137,
|
---|
| 2247 | 139, 149, 151, 157, 163, 167, 173, 179,
|
---|
| 2248 | 181, 191, 193, 197, 199, 211, 223, 227,
|
---|
| 2249 | 229, 233, 239, 241, 251, 257, 263, 269,
|
---|
| 2250 | 271, 277, 281, 283, 293, 307, 311, 313,
|
---|
| 2251 | 317, 331, 337, 347, 349, 353, 359, 367,
|
---|
| 2252 | 373, 379, 383, 389, 397, 401, 409, 419,
|
---|
| 2253 | 421, 431, 433, 439, 443, 449, 457, 461,
|
---|
| 2254 | 463, 467, 479, 487, 491, 499, 503, 509,
|
---|
| 2255 | 521, 523, 541, 547, 557, 563, 569, 571,
|
---|
| 2256 | 577, 587, 593, 599, 601, 607, 613, 617,
|
---|
| 2257 | 619, 631, 641, 643, 647, 653, 659, 661,
|
---|
| 2258 | 673, 677, 683, 691, 701, 709, 719, 727,
|
---|
| 2259 | 733, 739, 743, 751, 757, 761, 769, 773,
|
---|
| 2260 | 787, 797, 809, 811, 821, 823, 827, 829,
|
---|
| 2261 | 839, 853, 857, 859, 863, 877, 881, 883,
|
---|
| 2262 | 887, 907, 911, 919, 929, 937, 941, 947,
|
---|
| 2263 | 953, 967, 971, 977, 983, 991, 997, -103
|
---|
| 2264 | };
|
---|
| 2265 |
|
---|
| 2266 | /*
|
---|
| 2267 | * Small divisors test (X must be positive)
|
---|
| 2268 | *
|
---|
| 2269 | * Return values:
|
---|
| 2270 | * 0: no small factor (possible prime, more tests needed)
|
---|
| 2271 | * 1: certain prime
|
---|
| 2272 | * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
|
---|
| 2273 | * other negative: error
|
---|
| 2274 | */
|
---|
| 2275 | static int mpi_check_small_factors( const mbedtls_mpi *X )
|
---|
| 2276 | {
|
---|
| 2277 | int ret = 0;
|
---|
| 2278 | size_t i;
|
---|
| 2279 | mbedtls_mpi_uint r;
|
---|
| 2280 |
|
---|
| 2281 | if( ( X->p[0] & 1 ) == 0 )
|
---|
| 2282 | return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
|
---|
| 2283 |
|
---|
| 2284 | for( i = 0; small_prime[i] > 0; i++ )
|
---|
| 2285 | {
|
---|
| 2286 | if( mbedtls_mpi_cmp_int( X, small_prime[i] ) <= 0 )
|
---|
| 2287 | return( 1 );
|
---|
| 2288 |
|
---|
| 2289 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, small_prime[i] ) );
|
---|
| 2290 |
|
---|
| 2291 | if( r == 0 )
|
---|
| 2292 | return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
|
---|
| 2293 | }
|
---|
| 2294 |
|
---|
| 2295 | cleanup:
|
---|
| 2296 | return( ret );
|
---|
| 2297 | }
|
---|
| 2298 |
|
---|
| 2299 | /*
|
---|
| 2300 | * Miller-Rabin pseudo-primality test (HAC 4.24)
|
---|
| 2301 | */
|
---|
| 2302 | static int mpi_miller_rabin( const mbedtls_mpi *X, size_t rounds,
|
---|
| 2303 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2304 | void *p_rng )
|
---|
| 2305 | {
|
---|
| 2306 | int ret, count;
|
---|
| 2307 | size_t i, j, k, s;
|
---|
| 2308 | mbedtls_mpi W, R, T, A, RR;
|
---|
| 2309 |
|
---|
| 2310 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 2311 | MPI_VALIDATE_RET( f_rng != NULL );
|
---|
| 2312 |
|
---|
| 2313 | mbedtls_mpi_init( &W ); mbedtls_mpi_init( &R );
|
---|
| 2314 | mbedtls_mpi_init( &T ); mbedtls_mpi_init( &A );
|
---|
| 2315 | mbedtls_mpi_init( &RR );
|
---|
| 2316 |
|
---|
| 2317 | /*
|
---|
| 2318 | * W = |X| - 1
|
---|
| 2319 | * R = W >> lsb( W )
|
---|
| 2320 | */
|
---|
| 2321 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &W, X, 1 ) );
|
---|
| 2322 | s = mbedtls_mpi_lsb( &W );
|
---|
| 2323 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R, &W ) );
|
---|
| 2324 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &R, s ) );
|
---|
| 2325 |
|
---|
| 2326 | i = mbedtls_mpi_bitlen( X );
|
---|
| 2327 |
|
---|
| 2328 | for( i = 0; i < rounds; i++ )
|
---|
| 2329 | {
|
---|
| 2330 | /*
|
---|
| 2331 | * pick a random A, 1 < A < |X| - 1
|
---|
| 2332 | */
|
---|
| 2333 | count = 0;
|
---|
| 2334 | do {
|
---|
| 2335 | MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
|
---|
| 2336 |
|
---|
| 2337 | j = mbedtls_mpi_bitlen( &A );
|
---|
| 2338 | k = mbedtls_mpi_bitlen( &W );
|
---|
| 2339 | if (j > k) {
|
---|
| 2340 | A.p[A.n - 1] &= ( (mbedtls_mpi_uint) 1 << ( k - ( A.n - 1 ) * biL - 1 ) ) - 1;
|
---|
| 2341 | }
|
---|
| 2342 |
|
---|
| 2343 | if (count++ > 30) {
|
---|
| 2344 | return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
|
---|
| 2345 | }
|
---|
| 2346 |
|
---|
| 2347 | } while ( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 ||
|
---|
| 2348 | mbedtls_mpi_cmp_int( &A, 1 ) <= 0 );
|
---|
| 2349 |
|
---|
| 2350 | /*
|
---|
| 2351 | * A = A^R mod |X|
|
---|
| 2352 | */
|
---|
| 2353 | MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &A, &A, &R, X, &RR ) );
|
---|
| 2354 |
|
---|
| 2355 | if( mbedtls_mpi_cmp_mpi( &A, &W ) == 0 ||
|
---|
| 2356 | mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
|
---|
| 2357 | continue;
|
---|
| 2358 |
|
---|
| 2359 | j = 1;
|
---|
| 2360 | while( j < s && mbedtls_mpi_cmp_mpi( &A, &W ) != 0 )
|
---|
| 2361 | {
|
---|
| 2362 | /*
|
---|
| 2363 | * A = A * A mod |X|
|
---|
| 2364 | */
|
---|
| 2365 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &A, &A ) );
|
---|
| 2366 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &A, &T, X ) );
|
---|
| 2367 |
|
---|
| 2368 | if( mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
|
---|
| 2369 | break;
|
---|
| 2370 |
|
---|
| 2371 | j++;
|
---|
| 2372 | }
|
---|
| 2373 |
|
---|
| 2374 | /*
|
---|
| 2375 | * not prime if A != |X| - 1 or A == 1
|
---|
| 2376 | */
|
---|
| 2377 | if( mbedtls_mpi_cmp_mpi( &A, &W ) != 0 ||
|
---|
| 2378 | mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
|
---|
| 2379 | {
|
---|
| 2380 | ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
|
---|
| 2381 | break;
|
---|
| 2382 | }
|
---|
| 2383 | }
|
---|
| 2384 |
|
---|
| 2385 | cleanup:
|
---|
| 2386 | mbedtls_mpi_free( &W ); mbedtls_mpi_free( &R );
|
---|
| 2387 | mbedtls_mpi_free( &T ); mbedtls_mpi_free( &A );
|
---|
| 2388 | mbedtls_mpi_free( &RR );
|
---|
| 2389 |
|
---|
| 2390 | return( ret );
|
---|
| 2391 | }
|
---|
| 2392 |
|
---|
| 2393 | /*
|
---|
| 2394 | * Pseudo-primality test: small factors, then Miller-Rabin
|
---|
| 2395 | */
|
---|
| 2396 | int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
|
---|
| 2397 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2398 | void *p_rng )
|
---|
| 2399 | {
|
---|
| 2400 | int ret;
|
---|
| 2401 | mbedtls_mpi XX;
|
---|
| 2402 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 2403 | MPI_VALIDATE_RET( f_rng != NULL );
|
---|
| 2404 |
|
---|
| 2405 | XX.s = 1;
|
---|
| 2406 | XX.n = X->n;
|
---|
| 2407 | XX.p = X->p;
|
---|
| 2408 |
|
---|
| 2409 | if( mbedtls_mpi_cmp_int( &XX, 0 ) == 0 ||
|
---|
| 2410 | mbedtls_mpi_cmp_int( &XX, 1 ) == 0 )
|
---|
| 2411 | return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
|
---|
| 2412 |
|
---|
| 2413 | if( mbedtls_mpi_cmp_int( &XX, 2 ) == 0 )
|
---|
| 2414 | return( 0 );
|
---|
| 2415 |
|
---|
| 2416 | if( ( ret = mpi_check_small_factors( &XX ) ) != 0 )
|
---|
| 2417 | {
|
---|
| 2418 | if( ret == 1 )
|
---|
| 2419 | return( 0 );
|
---|
| 2420 |
|
---|
| 2421 | return( ret );
|
---|
| 2422 | }
|
---|
| 2423 |
|
---|
| 2424 | return( mpi_miller_rabin( &XX, rounds, f_rng, p_rng ) );
|
---|
| 2425 | }
|
---|
| 2426 |
|
---|
| 2427 | #if !defined(MBEDTLS_DEPRECATED_REMOVED)
|
---|
| 2428 | /*
|
---|
| 2429 | * Pseudo-primality test, error probability 2^-80
|
---|
| 2430 | */
|
---|
| 2431 | int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
|
---|
| 2432 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2433 | void *p_rng )
|
---|
| 2434 | {
|
---|
| 2435 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 2436 | MPI_VALIDATE_RET( f_rng != NULL );
|
---|
| 2437 |
|
---|
| 2438 | /*
|
---|
| 2439 | * In the past our key generation aimed for an error rate of at most
|
---|
| 2440 | * 2^-80. Since this function is deprecated, aim for the same certainty
|
---|
| 2441 | * here as well.
|
---|
| 2442 | */
|
---|
| 2443 | return( mbedtls_mpi_is_prime_ext( X, 40, f_rng, p_rng ) );
|
---|
| 2444 | }
|
---|
| 2445 | #endif
|
---|
| 2446 |
|
---|
| 2447 | /*
|
---|
| 2448 | * Prime number generation
|
---|
| 2449 | *
|
---|
| 2450 | * To generate an RSA key in a way recommended by FIPS 186-4, both primes must
|
---|
| 2451 | * be either 1024 bits or 1536 bits long, and flags must contain
|
---|
| 2452 | * MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR.
|
---|
| 2453 | */
|
---|
| 2454 | int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
|
---|
| 2455 | int (*f_rng)(void *, unsigned char *, size_t),
|
---|
| 2456 | void *p_rng )
|
---|
| 2457 | {
|
---|
| 2458 | #ifdef MBEDTLS_HAVE_INT64
|
---|
| 2459 | // ceil(2^63.5)
|
---|
| 2460 | #define CEIL_MAXUINT_DIV_SQRT2 0xb504f333f9de6485ULL
|
---|
| 2461 | #else
|
---|
| 2462 | // ceil(2^31.5)
|
---|
| 2463 | #define CEIL_MAXUINT_DIV_SQRT2 0xb504f334U
|
---|
| 2464 | #endif
|
---|
| 2465 | int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
|
---|
| 2466 | size_t k, n;
|
---|
| 2467 | int rounds;
|
---|
| 2468 | mbedtls_mpi_uint r;
|
---|
| 2469 | mbedtls_mpi Y;
|
---|
| 2470 |
|
---|
| 2471 | MPI_VALIDATE_RET( X != NULL );
|
---|
| 2472 | MPI_VALIDATE_RET( f_rng != NULL );
|
---|
| 2473 |
|
---|
| 2474 | if( nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS )
|
---|
| 2475 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
|
---|
| 2476 |
|
---|
| 2477 | mbedtls_mpi_init( &Y );
|
---|
| 2478 |
|
---|
| 2479 | n = BITS_TO_LIMBS( nbits );
|
---|
| 2480 |
|
---|
| 2481 | if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR ) == 0 )
|
---|
| 2482 | {
|
---|
| 2483 | /*
|
---|
| 2484 | * 2^-80 error probability, number of rounds chosen per HAC, table 4.4
|
---|
| 2485 | */
|
---|
| 2486 | rounds = ( ( nbits >= 1300 ) ? 2 : ( nbits >= 850 ) ? 3 :
|
---|
| 2487 | ( nbits >= 650 ) ? 4 : ( nbits >= 350 ) ? 8 :
|
---|
| 2488 | ( nbits >= 250 ) ? 12 : ( nbits >= 150 ) ? 18 : 27 );
|
---|
| 2489 | }
|
---|
| 2490 | else
|
---|
| 2491 | {
|
---|
| 2492 | /*
|
---|
| 2493 | * 2^-100 error probability, number of rounds computed based on HAC,
|
---|
| 2494 | * fact 4.48
|
---|
| 2495 | */
|
---|
| 2496 | rounds = ( ( nbits >= 1450 ) ? 4 : ( nbits >= 1150 ) ? 5 :
|
---|
| 2497 | ( nbits >= 1000 ) ? 6 : ( nbits >= 850 ) ? 7 :
|
---|
| 2498 | ( nbits >= 750 ) ? 8 : ( nbits >= 500 ) ? 13 :
|
---|
| 2499 | ( nbits >= 250 ) ? 28 : ( nbits >= 150 ) ? 40 : 51 );
|
---|
| 2500 | }
|
---|
| 2501 |
|
---|
| 2502 | while( 1 )
|
---|
| 2503 | {
|
---|
| 2504 | MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
|
---|
| 2505 | /* make sure generated number is at least (nbits-1)+0.5 bits (FIPS 186-4 §B.3.3 steps 4.4, 5.5) */
|
---|
| 2506 | if( X->p[n-1] < CEIL_MAXUINT_DIV_SQRT2 ) continue;
|
---|
| 2507 |
|
---|
| 2508 | k = n * biL;
|
---|
| 2509 | if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits ) );
|
---|
| 2510 | X->p[0] |= 1;
|
---|
| 2511 |
|
---|
| 2512 | if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH ) == 0 )
|
---|
| 2513 | {
|
---|
| 2514 | ret = mbedtls_mpi_is_prime_ext( X, rounds, f_rng, p_rng );
|
---|
| 2515 |
|
---|
| 2516 | if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
|
---|
| 2517 | goto cleanup;
|
---|
| 2518 | }
|
---|
| 2519 | else
|
---|
| 2520 | {
|
---|
| 2521 | /*
|
---|
| 2522 | * An necessary condition for Y and X = 2Y + 1 to be prime
|
---|
| 2523 | * is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
|
---|
| 2524 | * Make sure it is satisfied, while keeping X = 3 mod 4
|
---|
| 2525 | */
|
---|
| 2526 |
|
---|
| 2527 | X->p[0] |= 2;
|
---|
| 2528 |
|
---|
| 2529 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, 3 ) );
|
---|
| 2530 | if( r == 0 )
|
---|
| 2531 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 8 ) );
|
---|
| 2532 | else if( r == 1 )
|
---|
| 2533 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 4 ) );
|
---|
| 2534 |
|
---|
| 2535 | /* Set Y = (X-1) / 2, which is X / 2 because X is odd */
|
---|
| 2536 | MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, X ) );
|
---|
| 2537 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, 1 ) );
|
---|
| 2538 |
|
---|
| 2539 | while( 1 )
|
---|
| 2540 | {
|
---|
| 2541 | /*
|
---|
| 2542 | * First, check small factors for X and Y
|
---|
| 2543 | * before doing Miller-Rabin on any of them
|
---|
| 2544 | */
|
---|
| 2545 | if( ( ret = mpi_check_small_factors( X ) ) == 0 &&
|
---|
| 2546 | ( ret = mpi_check_small_factors( &Y ) ) == 0 &&
|
---|
| 2547 | ( ret = mpi_miller_rabin( X, rounds, f_rng, p_rng ) )
|
---|
| 2548 | == 0 &&
|
---|
| 2549 | ( ret = mpi_miller_rabin( &Y, rounds, f_rng, p_rng ) )
|
---|
| 2550 | == 0 )
|
---|
| 2551 | goto cleanup;
|
---|
| 2552 |
|
---|
| 2553 | if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
|
---|
| 2554 | goto cleanup;
|
---|
| 2555 |
|
---|
| 2556 | /*
|
---|
| 2557 | * Next candidates. We want to preserve Y = (X-1) / 2 and
|
---|
| 2558 | * Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3)
|
---|
| 2559 | * so up Y by 6 and X by 12.
|
---|
| 2560 | */
|
---|
| 2561 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 12 ) );
|
---|
| 2562 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &Y, &Y, 6 ) );
|
---|
| 2563 | }
|
---|
| 2564 | }
|
---|
| 2565 | }
|
---|
| 2566 |
|
---|
| 2567 | cleanup:
|
---|
| 2568 |
|
---|
| 2569 | mbedtls_mpi_free( &Y );
|
---|
| 2570 |
|
---|
| 2571 | return( ret );
|
---|
| 2572 | }
|
---|
| 2573 |
|
---|
| 2574 | #endif /* MBEDTLS_GENPRIME */
|
---|
| 2575 |
|
---|
| 2576 | #if defined(MBEDTLS_SELF_TEST)
|
---|
| 2577 |
|
---|
| 2578 | #define GCD_PAIR_COUNT 3
|
---|
| 2579 |
|
---|
| 2580 | static const int gcd_pairs[GCD_PAIR_COUNT][3] =
|
---|
| 2581 | {
|
---|
| 2582 | { 693, 609, 21 },
|
---|
| 2583 | { 1764, 868, 28 },
|
---|
| 2584 | { 768454923, 542167814, 1 }
|
---|
| 2585 | };
|
---|
| 2586 |
|
---|
| 2587 | /*
|
---|
| 2588 | * Checkup routine
|
---|
| 2589 | */
|
---|
| 2590 | int mbedtls_mpi_self_test( int verbose )
|
---|
| 2591 | {
|
---|
| 2592 | int ret, i;
|
---|
| 2593 | mbedtls_mpi A, E, N, X, Y, U, V;
|
---|
| 2594 |
|
---|
| 2595 | mbedtls_mpi_init( &A ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &N ); mbedtls_mpi_init( &X );
|
---|
| 2596 | mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &U ); mbedtls_mpi_init( &V );
|
---|
| 2597 |
|
---|
| 2598 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &A, 16,
|
---|
| 2599 | "EFE021C2645FD1DC586E69184AF4A31E" \
|
---|
| 2600 | "D5F53E93B5F123FA41680867BA110131" \
|
---|
| 2601 | "944FE7952E2517337780CB0DB80E61AA" \
|
---|
| 2602 | "E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) );
|
---|
| 2603 |
|
---|
| 2604 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &E, 16,
|
---|
| 2605 | "B2E7EFD37075B9F03FF989C7C5051C20" \
|
---|
| 2606 | "34D2A323810251127E7BF8625A4F49A5" \
|
---|
| 2607 | "F3E27F4DA8BD59C47D6DAABA4C8127BD" \
|
---|
| 2608 | "5B5C25763222FEFCCFC38B832366C29E" ) );
|
---|
| 2609 |
|
---|
| 2610 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &N, 16,
|
---|
| 2611 | "0066A198186C18C10B2F5ED9B522752A" \
|
---|
| 2612 | "9830B69916E535C8F047518A889A43A5" \
|
---|
| 2613 | "94B6BED27A168D31D4A52F88925AA8F5" ) );
|
---|
| 2614 |
|
---|
| 2615 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &A, &N ) );
|
---|
| 2616 |
|
---|
| 2617 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
|
---|
| 2618 | "602AB7ECA597A3D6B56FF9829A5E8B85" \
|
---|
| 2619 | "9E857EA95A03512E2BAE7391688D264A" \
|
---|
| 2620 | "A5663B0341DB9CCFD2C4C5F421FEC814" \
|
---|
| 2621 | "8001B72E848A38CAE1C65F78E56ABDEF" \
|
---|
| 2622 | "E12D3C039B8A02D6BE593F0BBBDA56F1" \
|
---|
| 2623 | "ECF677152EF804370C1A305CAF3B5BF1" \
|
---|
| 2624 | "30879B56C61DE584A0F53A2447A51E" ) );
|
---|
| 2625 |
|
---|
| 2626 | if( verbose != 0 )
|
---|
| 2627 | mbedtls_printf( " MPI test #1 (mul_mpi): " );
|
---|
| 2628 |
|
---|
| 2629 | if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
|
---|
| 2630 | {
|
---|
| 2631 | if( verbose != 0 )
|
---|
| 2632 | mbedtls_printf( "failed\n" );
|
---|
| 2633 |
|
---|
| 2634 | ret = 1;
|
---|
| 2635 | goto cleanup;
|
---|
| 2636 | }
|
---|
| 2637 |
|
---|
| 2638 | if( verbose != 0 )
|
---|
| 2639 | mbedtls_printf( "passed\n" );
|
---|
| 2640 |
|
---|
| 2641 | MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &X, &Y, &A, &N ) );
|
---|
| 2642 |
|
---|
| 2643 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
|
---|
| 2644 | "256567336059E52CAE22925474705F39A94" ) );
|
---|
| 2645 |
|
---|
| 2646 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &V, 16,
|
---|
| 2647 | "6613F26162223DF488E9CD48CC132C7A" \
|
---|
| 2648 | "0AC93C701B001B092E4E5B9F73BCD27B" \
|
---|
| 2649 | "9EE50D0657C77F374E903CDFA4C642" ) );
|
---|
| 2650 |
|
---|
| 2651 | if( verbose != 0 )
|
---|
| 2652 | mbedtls_printf( " MPI test #2 (div_mpi): " );
|
---|
| 2653 |
|
---|
| 2654 | if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 ||
|
---|
| 2655 | mbedtls_mpi_cmp_mpi( &Y, &V ) != 0 )
|
---|
| 2656 | {
|
---|
| 2657 | if( verbose != 0 )
|
---|
| 2658 | mbedtls_printf( "failed\n" );
|
---|
| 2659 |
|
---|
| 2660 | ret = 1;
|
---|
| 2661 | goto cleanup;
|
---|
| 2662 | }
|
---|
| 2663 |
|
---|
| 2664 | if( verbose != 0 )
|
---|
| 2665 | mbedtls_printf( "passed\n" );
|
---|
| 2666 |
|
---|
| 2667 | MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &X, &A, &E, &N, NULL ) );
|
---|
| 2668 |
|
---|
| 2669 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
|
---|
| 2670 | "36E139AEA55215609D2816998ED020BB" \
|
---|
| 2671 | "BD96C37890F65171D948E9BC7CBAA4D9" \
|
---|
| 2672 | "325D24D6A3C12710F10A09FA08AB87" ) );
|
---|
| 2673 |
|
---|
| 2674 | if( verbose != 0 )
|
---|
| 2675 | mbedtls_printf( " MPI test #3 (exp_mod): " );
|
---|
| 2676 |
|
---|
| 2677 | if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
|
---|
| 2678 | {
|
---|
| 2679 | if( verbose != 0 )
|
---|
| 2680 | mbedtls_printf( "failed\n" );
|
---|
| 2681 |
|
---|
| 2682 | ret = 1;
|
---|
| 2683 | goto cleanup;
|
---|
| 2684 | }
|
---|
| 2685 |
|
---|
| 2686 | if( verbose != 0 )
|
---|
| 2687 | mbedtls_printf( "passed\n" );
|
---|
| 2688 |
|
---|
| 2689 | MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &X, &A, &N ) );
|
---|
| 2690 |
|
---|
| 2691 | MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
|
---|
| 2692 | "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
|
---|
| 2693 | "C3DBA76456363A10869622EAC2DD84EC" \
|
---|
| 2694 | "C5B8A74DAC4D09E03B5E0BE779F2DF61" ) );
|
---|
| 2695 |
|
---|
| 2696 | if( verbose != 0 )
|
---|
| 2697 | mbedtls_printf( " MPI test #4 (inv_mod): " );
|
---|
| 2698 |
|
---|
| 2699 | if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
|
---|
| 2700 | {
|
---|
| 2701 | if( verbose != 0 )
|
---|
| 2702 | mbedtls_printf( "failed\n" );
|
---|
| 2703 |
|
---|
| 2704 | ret = 1;
|
---|
| 2705 | goto cleanup;
|
---|
| 2706 | }
|
---|
| 2707 |
|
---|
| 2708 | if( verbose != 0 )
|
---|
| 2709 | mbedtls_printf( "passed\n" );
|
---|
| 2710 |
|
---|
| 2711 | if( verbose != 0 )
|
---|
| 2712 | mbedtls_printf( " MPI test #5 (simple gcd): " );
|
---|
| 2713 |
|
---|
| 2714 | for( i = 0; i < GCD_PAIR_COUNT; i++ )
|
---|
| 2715 | {
|
---|
| 2716 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &X, gcd_pairs[i][0] ) );
|
---|
| 2717 | MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Y, gcd_pairs[i][1] ) );
|
---|
| 2718 |
|
---|
| 2719 | MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &A, &X, &Y ) );
|
---|
| 2720 |
|
---|
| 2721 | if( mbedtls_mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 )
|
---|
| 2722 | {
|
---|
| 2723 | if( verbose != 0 )
|
---|
| 2724 | mbedtls_printf( "failed at %d\n", i );
|
---|
| 2725 |
|
---|
| 2726 | ret = 1;
|
---|
| 2727 | goto cleanup;
|
---|
| 2728 | }
|
---|
| 2729 | }
|
---|
| 2730 |
|
---|
| 2731 | if( verbose != 0 )
|
---|
| 2732 | mbedtls_printf( "passed\n" );
|
---|
| 2733 |
|
---|
| 2734 | cleanup:
|
---|
| 2735 |
|
---|
| 2736 | if( ret != 0 && verbose != 0 )
|
---|
| 2737 | mbedtls_printf( "Unexpected error, return code = %08X\n", ret );
|
---|
| 2738 |
|
---|
| 2739 | mbedtls_mpi_free( &A ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &N ); mbedtls_mpi_free( &X );
|
---|
| 2740 | mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &U ); mbedtls_mpi_free( &V );
|
---|
| 2741 |
|
---|
| 2742 | if( verbose != 0 )
|
---|
| 2743 | mbedtls_printf( "\n" );
|
---|
| 2744 |
|
---|
| 2745 | return( ret );
|
---|
| 2746 | }
|
---|
| 2747 |
|
---|
| 2748 | #endif /* MBEDTLS_SELF_TEST */
|
---|
| 2749 |
|
---|
| 2750 | #endif /* MBEDTLS_BIGNUM_C */
|
---|