[331] | 1 | /*
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| 2 | * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
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| 3 | *
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| 4 | * Licensed under the OpenSSL license (the "License"). You may not use
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| 5 | * this file except in compliance with the License. You can obtain a copy
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| 6 | * in the file LICENSE in the source distribution or at
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| 7 | * https://www.openssl.org/source/license.html
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| 8 | */
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| 9 |
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| 10 | /* ====================================================================
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| 11 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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| 12 | *
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| 13 | * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
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| 14 | * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
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| 15 | * to the OpenSSL project.
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| 16 | *
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| 17 | * The ECC Code is licensed pursuant to the OpenSSL open source
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| 18 | * license provided below.
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| 19 | */
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| 20 |
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| 21 | #include <assert.h>
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| 22 | #include <limits.h>
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| 23 | #include <stdio.h>
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| 24 | #include "internal/cryptlib.h"
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| 25 | #include "bn_lcl.h"
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| 26 |
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| 27 | #ifndef OPENSSL_NO_EC2M
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| 28 |
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| 29 | /*
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| 30 | * Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should
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| 31 | * fail.
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| 32 | */
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| 33 | # define MAX_ITERATIONS 50
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| 34 |
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| 35 | static const BN_ULONG SQR_tb[16] = { 0, 1, 4, 5, 16, 17, 20, 21,
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| 36 | 64, 65, 68, 69, 80, 81, 84, 85
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| 37 | };
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| 38 |
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| 39 | /* Platform-specific macros to accelerate squaring. */
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| 40 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
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| 41 | # define SQR1(w) \
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| 42 | SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
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| 43 | SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
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| 44 | SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
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| 45 | SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF]
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| 46 | # define SQR0(w) \
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| 47 | SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
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| 48 | SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
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| 49 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
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| 50 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
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| 51 | # endif
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| 52 | # ifdef THIRTY_TWO_BIT
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| 53 | # define SQR1(w) \
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| 54 | SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
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| 55 | SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF]
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| 56 | # define SQR0(w) \
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| 57 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
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| 58 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
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| 59 | # endif
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| 60 |
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| 61 | # if !defined(OPENSSL_BN_ASM_GF2m)
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| 62 | /*
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| 63 | * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is
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| 64 | * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that
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| 65 | * the variables have the right amount of space allocated.
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| 66 | */
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| 67 | # ifdef THIRTY_TWO_BIT
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| 68 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
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| 69 | const BN_ULONG b)
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| 70 | {
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| 71 | register BN_ULONG h, l, s;
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| 72 | BN_ULONG tab[8], top2b = a >> 30;
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| 73 | register BN_ULONG a1, a2, a4;
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| 74 |
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| 75 | a1 = a & (0x3FFFFFFF);
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| 76 | a2 = a1 << 1;
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| 77 | a4 = a2 << 1;
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| 78 |
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| 79 | tab[0] = 0;
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| 80 | tab[1] = a1;
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| 81 | tab[2] = a2;
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| 82 | tab[3] = a1 ^ a2;
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| 83 | tab[4] = a4;
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| 84 | tab[5] = a1 ^ a4;
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| 85 | tab[6] = a2 ^ a4;
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| 86 | tab[7] = a1 ^ a2 ^ a4;
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| 87 |
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| 88 | s = tab[b & 0x7];
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| 89 | l = s;
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| 90 | s = tab[b >> 3 & 0x7];
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| 91 | l ^= s << 3;
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| 92 | h = s >> 29;
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| 93 | s = tab[b >> 6 & 0x7];
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| 94 | l ^= s << 6;
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| 95 | h ^= s >> 26;
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| 96 | s = tab[b >> 9 & 0x7];
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| 97 | l ^= s << 9;
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| 98 | h ^= s >> 23;
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| 99 | s = tab[b >> 12 & 0x7];
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| 100 | l ^= s << 12;
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| 101 | h ^= s >> 20;
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| 102 | s = tab[b >> 15 & 0x7];
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| 103 | l ^= s << 15;
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| 104 | h ^= s >> 17;
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| 105 | s = tab[b >> 18 & 0x7];
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| 106 | l ^= s << 18;
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| 107 | h ^= s >> 14;
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| 108 | s = tab[b >> 21 & 0x7];
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| 109 | l ^= s << 21;
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| 110 | h ^= s >> 11;
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| 111 | s = tab[b >> 24 & 0x7];
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| 112 | l ^= s << 24;
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| 113 | h ^= s >> 8;
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| 114 | s = tab[b >> 27 & 0x7];
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| 115 | l ^= s << 27;
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| 116 | h ^= s >> 5;
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| 117 | s = tab[b >> 30];
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| 118 | l ^= s << 30;
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| 119 | h ^= s >> 2;
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| 120 |
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| 121 | /* compensate for the top two bits of a */
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| 122 |
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| 123 | if (top2b & 01) {
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| 124 | l ^= b << 30;
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| 125 | h ^= b >> 2;
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| 126 | }
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| 127 | if (top2b & 02) {
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| 128 | l ^= b << 31;
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| 129 | h ^= b >> 1;
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| 130 | }
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| 131 |
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| 132 | *r1 = h;
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| 133 | *r0 = l;
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| 134 | }
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| 135 | # endif
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| 136 | # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
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| 137 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
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| 138 | const BN_ULONG b)
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| 139 | {
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| 140 | register BN_ULONG h, l, s;
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| 141 | BN_ULONG tab[16], top3b = a >> 61;
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| 142 | register BN_ULONG a1, a2, a4, a8;
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| 143 |
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| 144 | a1 = a & (0x1FFFFFFFFFFFFFFFULL);
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| 145 | a2 = a1 << 1;
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| 146 | a4 = a2 << 1;
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| 147 | a8 = a4 << 1;
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| 148 |
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| 149 | tab[0] = 0;
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| 150 | tab[1] = a1;
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| 151 | tab[2] = a2;
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| 152 | tab[3] = a1 ^ a2;
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| 153 | tab[4] = a4;
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| 154 | tab[5] = a1 ^ a4;
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| 155 | tab[6] = a2 ^ a4;
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| 156 | tab[7] = a1 ^ a2 ^ a4;
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| 157 | tab[8] = a8;
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| 158 | tab[9] = a1 ^ a8;
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| 159 | tab[10] = a2 ^ a8;
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| 160 | tab[11] = a1 ^ a2 ^ a8;
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| 161 | tab[12] = a4 ^ a8;
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| 162 | tab[13] = a1 ^ a4 ^ a8;
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| 163 | tab[14] = a2 ^ a4 ^ a8;
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| 164 | tab[15] = a1 ^ a2 ^ a4 ^ a8;
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| 165 |
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| 166 | s = tab[b & 0xF];
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| 167 | l = s;
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| 168 | s = tab[b >> 4 & 0xF];
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| 169 | l ^= s << 4;
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| 170 | h = s >> 60;
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| 171 | s = tab[b >> 8 & 0xF];
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| 172 | l ^= s << 8;
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| 173 | h ^= s >> 56;
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| 174 | s = tab[b >> 12 & 0xF];
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| 175 | l ^= s << 12;
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| 176 | h ^= s >> 52;
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| 177 | s = tab[b >> 16 & 0xF];
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| 178 | l ^= s << 16;
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| 179 | h ^= s >> 48;
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| 180 | s = tab[b >> 20 & 0xF];
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| 181 | l ^= s << 20;
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| 182 | h ^= s >> 44;
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| 183 | s = tab[b >> 24 & 0xF];
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| 184 | l ^= s << 24;
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| 185 | h ^= s >> 40;
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| 186 | s = tab[b >> 28 & 0xF];
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| 187 | l ^= s << 28;
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| 188 | h ^= s >> 36;
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| 189 | s = tab[b >> 32 & 0xF];
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| 190 | l ^= s << 32;
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| 191 | h ^= s >> 32;
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| 192 | s = tab[b >> 36 & 0xF];
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| 193 | l ^= s << 36;
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| 194 | h ^= s >> 28;
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| 195 | s = tab[b >> 40 & 0xF];
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| 196 | l ^= s << 40;
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| 197 | h ^= s >> 24;
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| 198 | s = tab[b >> 44 & 0xF];
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| 199 | l ^= s << 44;
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| 200 | h ^= s >> 20;
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| 201 | s = tab[b >> 48 & 0xF];
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| 202 | l ^= s << 48;
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| 203 | h ^= s >> 16;
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| 204 | s = tab[b >> 52 & 0xF];
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| 205 | l ^= s << 52;
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| 206 | h ^= s >> 12;
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| 207 | s = tab[b >> 56 & 0xF];
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| 208 | l ^= s << 56;
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| 209 | h ^= s >> 8;
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| 210 | s = tab[b >> 60];
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| 211 | l ^= s << 60;
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| 212 | h ^= s >> 4;
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| 213 |
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| 214 | /* compensate for the top three bits of a */
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| 215 |
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| 216 | if (top3b & 01) {
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| 217 | l ^= b << 61;
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| 218 | h ^= b >> 3;
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| 219 | }
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| 220 | if (top3b & 02) {
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| 221 | l ^= b << 62;
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| 222 | h ^= b >> 2;
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| 223 | }
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| 224 | if (top3b & 04) {
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| 225 | l ^= b << 63;
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| 226 | h ^= b >> 1;
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| 227 | }
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| 228 |
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| 229 | *r1 = h;
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| 230 | *r0 = l;
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| 231 | }
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| 232 | # endif
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| 233 |
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| 234 | /*
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| 235 | * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
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| 236 | * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST
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| 237 | * ensure that the variables have the right amount of space allocated.
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| 238 | */
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| 239 | static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0,
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| 240 | const BN_ULONG b1, const BN_ULONG b0)
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| 241 | {
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| 242 | BN_ULONG m1, m0;
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| 243 | /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
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| 244 | bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1);
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| 245 | bn_GF2m_mul_1x1(r + 1, r, a0, b0);
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| 246 | bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
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| 247 | /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
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| 248 | r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */
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| 249 | r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */
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| 250 | }
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| 251 | # else
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| 252 | void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1,
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| 253 | BN_ULONG b0);
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| 254 | # endif
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| 255 |
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| 256 | /*
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| 257 | * Add polynomials a and b and store result in r; r could be a or b, a and b
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| 258 | * could be equal; r is the bitwise XOR of a and b.
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| 259 | */
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| 260 | int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
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| 261 | {
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| 262 | int i;
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| 263 | const BIGNUM *at, *bt;
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| 264 |
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| 265 | bn_check_top(a);
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| 266 | bn_check_top(b);
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| 267 |
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| 268 | if (a->top < b->top) {
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| 269 | at = b;
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| 270 | bt = a;
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| 271 | } else {
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| 272 | at = a;
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| 273 | bt = b;
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| 274 | }
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| 275 |
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| 276 | if (bn_wexpand(r, at->top) == NULL)
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| 277 | return 0;
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| 278 |
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| 279 | for (i = 0; i < bt->top; i++) {
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| 280 | r->d[i] = at->d[i] ^ bt->d[i];
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| 281 | }
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| 282 | for (; i < at->top; i++) {
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| 283 | r->d[i] = at->d[i];
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| 284 | }
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| 285 |
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| 286 | r->top = at->top;
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| 287 | bn_correct_top(r);
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| 288 |
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| 289 | return 1;
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| 290 | }
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| 291 |
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| 292 | /*-
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| 293 | * Some functions allow for representation of the irreducible polynomials
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| 294 | * as an int[], say p. The irreducible f(t) is then of the form:
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| 295 | * t^p[0] + t^p[1] + ... + t^p[k]
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| 296 | * where m = p[0] > p[1] > ... > p[k] = 0.
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| 297 | */
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| 298 |
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| 299 | /* Performs modular reduction of a and store result in r. r could be a. */
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| 300 | int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])
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| 301 | {
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| 302 | int j, k;
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| 303 | int n, dN, d0, d1;
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| 304 | BN_ULONG zz, *z;
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| 305 |
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| 306 | bn_check_top(a);
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| 307 |
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| 308 | if (!p[0]) {
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| 309 | /* reduction mod 1 => return 0 */
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| 310 | BN_zero(r);
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| 311 | return 1;
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| 312 | }
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| 313 |
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| 314 | /*
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| 315 | * Since the algorithm does reduction in the r value, if a != r, copy the
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| 316 | * contents of a into r so we can do reduction in r.
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| 317 | */
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| 318 | if (a != r) {
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| 319 | if (!bn_wexpand(r, a->top))
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| 320 | return 0;
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| 321 | for (j = 0; j < a->top; j++) {
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| 322 | r->d[j] = a->d[j];
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| 323 | }
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| 324 | r->top = a->top;
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| 325 | }
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| 326 | z = r->d;
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| 327 |
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| 328 | /* start reduction */
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| 329 | dN = p[0] / BN_BITS2;
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| 330 | for (j = r->top - 1; j > dN;) {
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| 331 | zz = z[j];
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| 332 | if (z[j] == 0) {
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| 333 | j--;
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| 334 | continue;
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| 335 | }
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| 336 | z[j] = 0;
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| 337 |
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| 338 | for (k = 1; p[k] != 0; k++) {
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| 339 | /* reducing component t^p[k] */
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| 340 | n = p[0] - p[k];
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| 341 | d0 = n % BN_BITS2;
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| 342 | d1 = BN_BITS2 - d0;
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| 343 | n /= BN_BITS2;
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| 344 | z[j - n] ^= (zz >> d0);
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| 345 | if (d0)
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| 346 | z[j - n - 1] ^= (zz << d1);
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| 347 | }
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| 348 |
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| 349 | /* reducing component t^0 */
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| 350 | n = dN;
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| 351 | d0 = p[0] % BN_BITS2;
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| 352 | d1 = BN_BITS2 - d0;
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| 353 | z[j - n] ^= (zz >> d0);
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| 354 | if (d0)
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| 355 | z[j - n - 1] ^= (zz << d1);
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| 356 | }
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| 357 |
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| 358 | /* final round of reduction */
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| 359 | while (j == dN) {
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| 360 |
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| 361 | d0 = p[0] % BN_BITS2;
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| 362 | zz = z[dN] >> d0;
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| 363 | if (zz == 0)
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| 364 | break;
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| 365 | d1 = BN_BITS2 - d0;
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| 366 |
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| 367 | /* clear up the top d1 bits */
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| 368 | if (d0)
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| 369 | z[dN] = (z[dN] << d1) >> d1;
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| 370 | else
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| 371 | z[dN] = 0;
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| 372 | z[0] ^= zz; /* reduction t^0 component */
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| 373 |
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| 374 | for (k = 1; p[k] != 0; k++) {
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| 375 | BN_ULONG tmp_ulong;
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| 376 |
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| 377 | /* reducing component t^p[k] */
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| 378 | n = p[k] / BN_BITS2;
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| 379 | d0 = p[k] % BN_BITS2;
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| 380 | d1 = BN_BITS2 - d0;
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| 381 | z[n] ^= (zz << d0);
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| 382 | if (d0 && (tmp_ulong = zz >> d1))
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| 383 | z[n + 1] ^= tmp_ulong;
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| 384 | }
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| 385 |
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| 386 | }
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| 387 |
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| 388 | bn_correct_top(r);
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| 389 | return 1;
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| 390 | }
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| 391 |
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| 392 | /*
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| 393 | * Performs modular reduction of a by p and store result in r. r could be a.
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| 394 | * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
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| 395 | * function is only provided for convenience; for best performance, use the
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| 396 | * BN_GF2m_mod_arr function.
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| 397 | */
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| 398 | int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
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| 399 | {
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| 400 | int ret = 0;
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| 401 | int arr[6];
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| 402 | bn_check_top(a);
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| 403 | bn_check_top(p);
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| 404 | ret = BN_GF2m_poly2arr(p, arr, OSSL_NELEM(arr));
|
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| 405 | if (!ret || ret > (int)OSSL_NELEM(arr)) {
|
---|
| 406 | BNerr(BN_F_BN_GF2M_MOD, BN_R_INVALID_LENGTH);
|
---|
| 407 | return 0;
|
---|
| 408 | }
|
---|
| 409 | ret = BN_GF2m_mod_arr(r, a, arr);
|
---|
| 410 | bn_check_top(r);
|
---|
| 411 | return ret;
|
---|
| 412 | }
|
---|
| 413 |
|
---|
| 414 | /*
|
---|
| 415 | * Compute the product of two polynomials a and b, reduce modulo p, and store
|
---|
| 416 | * the result in r. r could be a or b; a could be b.
|
---|
| 417 | */
|
---|
| 418 | int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
|
---|
| 419 | const int p[], BN_CTX *ctx)
|
---|
| 420 | {
|
---|
| 421 | int zlen, i, j, k, ret = 0;
|
---|
| 422 | BIGNUM *s;
|
---|
| 423 | BN_ULONG x1, x0, y1, y0, zz[4];
|
---|
| 424 |
|
---|
| 425 | bn_check_top(a);
|
---|
| 426 | bn_check_top(b);
|
---|
| 427 |
|
---|
| 428 | if (a == b) {
|
---|
| 429 | return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
|
---|
| 430 | }
|
---|
| 431 |
|
---|
| 432 | BN_CTX_start(ctx);
|
---|
| 433 | if ((s = BN_CTX_get(ctx)) == NULL)
|
---|
| 434 | goto err;
|
---|
| 435 |
|
---|
| 436 | zlen = a->top + b->top + 4;
|
---|
| 437 | if (!bn_wexpand(s, zlen))
|
---|
| 438 | goto err;
|
---|
| 439 | s->top = zlen;
|
---|
| 440 |
|
---|
| 441 | for (i = 0; i < zlen; i++)
|
---|
| 442 | s->d[i] = 0;
|
---|
| 443 |
|
---|
| 444 | for (j = 0; j < b->top; j += 2) {
|
---|
| 445 | y0 = b->d[j];
|
---|
| 446 | y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1];
|
---|
| 447 | for (i = 0; i < a->top; i += 2) {
|
---|
| 448 | x0 = a->d[i];
|
---|
| 449 | x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1];
|
---|
| 450 | bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
|
---|
| 451 | for (k = 0; k < 4; k++)
|
---|
| 452 | s->d[i + j + k] ^= zz[k];
|
---|
| 453 | }
|
---|
| 454 | }
|
---|
| 455 |
|
---|
| 456 | bn_correct_top(s);
|
---|
| 457 | if (BN_GF2m_mod_arr(r, s, p))
|
---|
| 458 | ret = 1;
|
---|
| 459 | bn_check_top(r);
|
---|
| 460 |
|
---|
| 461 | err:
|
---|
| 462 | BN_CTX_end(ctx);
|
---|
| 463 | return ret;
|
---|
| 464 | }
|
---|
| 465 |
|
---|
| 466 | /*
|
---|
| 467 | * Compute the product of two polynomials a and b, reduce modulo p, and store
|
---|
| 468 | * the result in r. r could be a or b; a could equal b. This function calls
|
---|
| 469 | * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is
|
---|
| 470 | * only provided for convenience; for best performance, use the
|
---|
| 471 | * BN_GF2m_mod_mul_arr function.
|
---|
| 472 | */
|
---|
| 473 | int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
|
---|
| 474 | const BIGNUM *p, BN_CTX *ctx)
|
---|
| 475 | {
|
---|
| 476 | int ret = 0;
|
---|
| 477 | const int max = BN_num_bits(p) + 1;
|
---|
| 478 | int *arr = NULL;
|
---|
| 479 | bn_check_top(a);
|
---|
| 480 | bn_check_top(b);
|
---|
| 481 | bn_check_top(p);
|
---|
| 482 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
| 483 | goto err;
|
---|
| 484 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
| 485 | if (!ret || ret > max) {
|
---|
| 486 | BNerr(BN_F_BN_GF2M_MOD_MUL, BN_R_INVALID_LENGTH);
|
---|
| 487 | goto err;
|
---|
| 488 | }
|
---|
| 489 | ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
|
---|
| 490 | bn_check_top(r);
|
---|
| 491 | err:
|
---|
| 492 | OPENSSL_free(arr);
|
---|
| 493 | return ret;
|
---|
| 494 | }
|
---|
| 495 |
|
---|
| 496 | /* Square a, reduce the result mod p, and store it in a. r could be a. */
|
---|
| 497 | int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
|
---|
| 498 | BN_CTX *ctx)
|
---|
| 499 | {
|
---|
| 500 | int i, ret = 0;
|
---|
| 501 | BIGNUM *s;
|
---|
| 502 |
|
---|
| 503 | bn_check_top(a);
|
---|
| 504 | BN_CTX_start(ctx);
|
---|
| 505 | if ((s = BN_CTX_get(ctx)) == NULL)
|
---|
| 506 | goto err;
|
---|
| 507 | if (!bn_wexpand(s, 2 * a->top))
|
---|
| 508 | goto err;
|
---|
| 509 |
|
---|
| 510 | for (i = a->top - 1; i >= 0; i--) {
|
---|
| 511 | s->d[2 * i + 1] = SQR1(a->d[i]);
|
---|
| 512 | s->d[2 * i] = SQR0(a->d[i]);
|
---|
| 513 | }
|
---|
| 514 |
|
---|
| 515 | s->top = 2 * a->top;
|
---|
| 516 | bn_correct_top(s);
|
---|
| 517 | if (!BN_GF2m_mod_arr(r, s, p))
|
---|
| 518 | goto err;
|
---|
| 519 | bn_check_top(r);
|
---|
| 520 | ret = 1;
|
---|
| 521 | err:
|
---|
| 522 | BN_CTX_end(ctx);
|
---|
| 523 | return ret;
|
---|
| 524 | }
|
---|
| 525 |
|
---|
| 526 | /*
|
---|
| 527 | * Square a, reduce the result mod p, and store it in a. r could be a. This
|
---|
| 528 | * function calls down to the BN_GF2m_mod_sqr_arr implementation; this
|
---|
| 529 | * wrapper function is only provided for convenience; for best performance,
|
---|
| 530 | * use the BN_GF2m_mod_sqr_arr function.
|
---|
| 531 | */
|
---|
| 532 | int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
|
---|
| 533 | {
|
---|
| 534 | int ret = 0;
|
---|
| 535 | const int max = BN_num_bits(p) + 1;
|
---|
| 536 | int *arr = NULL;
|
---|
| 537 |
|
---|
| 538 | bn_check_top(a);
|
---|
| 539 | bn_check_top(p);
|
---|
| 540 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
| 541 | goto err;
|
---|
| 542 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
| 543 | if (!ret || ret > max) {
|
---|
| 544 | BNerr(BN_F_BN_GF2M_MOD_SQR, BN_R_INVALID_LENGTH);
|
---|
| 545 | goto err;
|
---|
| 546 | }
|
---|
| 547 | ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
|
---|
| 548 | bn_check_top(r);
|
---|
| 549 | err:
|
---|
| 550 | OPENSSL_free(arr);
|
---|
| 551 | return ret;
|
---|
| 552 | }
|
---|
| 553 |
|
---|
| 554 | /*
|
---|
| 555 | * Invert a, reduce modulo p, and store the result in r. r could be a. Uses
|
---|
| 556 | * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D.,
|
---|
| 557 | * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic
|
---|
| 558 | * Curve Cryptography Over Binary Fields".
|
---|
| 559 | */
|
---|
| 560 | int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
|
---|
| 561 | {
|
---|
| 562 | BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp;
|
---|
| 563 | int ret = 0;
|
---|
| 564 |
|
---|
| 565 | bn_check_top(a);
|
---|
| 566 | bn_check_top(p);
|
---|
| 567 |
|
---|
| 568 | BN_CTX_start(ctx);
|
---|
| 569 |
|
---|
| 570 | if ((b = BN_CTX_get(ctx)) == NULL)
|
---|
| 571 | goto err;
|
---|
| 572 | if ((c = BN_CTX_get(ctx)) == NULL)
|
---|
| 573 | goto err;
|
---|
| 574 | if ((u = BN_CTX_get(ctx)) == NULL)
|
---|
| 575 | goto err;
|
---|
| 576 | if ((v = BN_CTX_get(ctx)) == NULL)
|
---|
| 577 | goto err;
|
---|
| 578 |
|
---|
| 579 | if (!BN_GF2m_mod(u, a, p))
|
---|
| 580 | goto err;
|
---|
| 581 | if (BN_is_zero(u))
|
---|
| 582 | goto err;
|
---|
| 583 |
|
---|
| 584 | if (!BN_copy(v, p))
|
---|
| 585 | goto err;
|
---|
| 586 | # if 0
|
---|
| 587 | if (!BN_one(b))
|
---|
| 588 | goto err;
|
---|
| 589 |
|
---|
| 590 | while (1) {
|
---|
| 591 | while (!BN_is_odd(u)) {
|
---|
| 592 | if (BN_is_zero(u))
|
---|
| 593 | goto err;
|
---|
| 594 | if (!BN_rshift1(u, u))
|
---|
| 595 | goto err;
|
---|
| 596 | if (BN_is_odd(b)) {
|
---|
| 597 | if (!BN_GF2m_add(b, b, p))
|
---|
| 598 | goto err;
|
---|
| 599 | }
|
---|
| 600 | if (!BN_rshift1(b, b))
|
---|
| 601 | goto err;
|
---|
| 602 | }
|
---|
| 603 |
|
---|
| 604 | if (BN_abs_is_word(u, 1))
|
---|
| 605 | break;
|
---|
| 606 |
|
---|
| 607 | if (BN_num_bits(u) < BN_num_bits(v)) {
|
---|
| 608 | tmp = u;
|
---|
| 609 | u = v;
|
---|
| 610 | v = tmp;
|
---|
| 611 | tmp = b;
|
---|
| 612 | b = c;
|
---|
| 613 | c = tmp;
|
---|
| 614 | }
|
---|
| 615 |
|
---|
| 616 | if (!BN_GF2m_add(u, u, v))
|
---|
| 617 | goto err;
|
---|
| 618 | if (!BN_GF2m_add(b, b, c))
|
---|
| 619 | goto err;
|
---|
| 620 | }
|
---|
| 621 | # else
|
---|
| 622 | {
|
---|
| 623 | int i;
|
---|
| 624 | int ubits = BN_num_bits(u);
|
---|
| 625 | int vbits = BN_num_bits(v); /* v is copy of p */
|
---|
| 626 | int top = p->top;
|
---|
| 627 | BN_ULONG *udp, *bdp, *vdp, *cdp;
|
---|
| 628 |
|
---|
| 629 | if (!bn_wexpand(u, top))
|
---|
| 630 | goto err;
|
---|
| 631 | udp = u->d;
|
---|
| 632 | for (i = u->top; i < top; i++)
|
---|
| 633 | udp[i] = 0;
|
---|
| 634 | u->top = top;
|
---|
| 635 | if (!bn_wexpand(b, top))
|
---|
| 636 | goto err;
|
---|
| 637 | bdp = b->d;
|
---|
| 638 | bdp[0] = 1;
|
---|
| 639 | for (i = 1; i < top; i++)
|
---|
| 640 | bdp[i] = 0;
|
---|
| 641 | b->top = top;
|
---|
| 642 | if (!bn_wexpand(c, top))
|
---|
| 643 | goto err;
|
---|
| 644 | cdp = c->d;
|
---|
| 645 | for (i = 0; i < top; i++)
|
---|
| 646 | cdp[i] = 0;
|
---|
| 647 | c->top = top;
|
---|
| 648 | vdp = v->d; /* It pays off to "cache" *->d pointers,
|
---|
| 649 | * because it allows optimizer to be more
|
---|
| 650 | * aggressive. But we don't have to "cache"
|
---|
| 651 | * p->d, because *p is declared 'const'... */
|
---|
| 652 | while (1) {
|
---|
| 653 | while (ubits && !(udp[0] & 1)) {
|
---|
| 654 | BN_ULONG u0, u1, b0, b1, mask;
|
---|
| 655 |
|
---|
| 656 | u0 = udp[0];
|
---|
| 657 | b0 = bdp[0];
|
---|
| 658 | mask = (BN_ULONG)0 - (b0 & 1);
|
---|
| 659 | b0 ^= p->d[0] & mask;
|
---|
| 660 | for (i = 0; i < top - 1; i++) {
|
---|
| 661 | u1 = udp[i + 1];
|
---|
| 662 | udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2;
|
---|
| 663 | u0 = u1;
|
---|
| 664 | b1 = bdp[i + 1] ^ (p->d[i + 1] & mask);
|
---|
| 665 | bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2;
|
---|
| 666 | b0 = b1;
|
---|
| 667 | }
|
---|
| 668 | udp[i] = u0 >> 1;
|
---|
| 669 | bdp[i] = b0 >> 1;
|
---|
| 670 | ubits--;
|
---|
| 671 | }
|
---|
| 672 |
|
---|
| 673 | if (ubits <= BN_BITS2) {
|
---|
| 674 | if (udp[0] == 0) /* poly was reducible */
|
---|
| 675 | goto err;
|
---|
| 676 | if (udp[0] == 1)
|
---|
| 677 | break;
|
---|
| 678 | }
|
---|
| 679 |
|
---|
| 680 | if (ubits < vbits) {
|
---|
| 681 | i = ubits;
|
---|
| 682 | ubits = vbits;
|
---|
| 683 | vbits = i;
|
---|
| 684 | tmp = u;
|
---|
| 685 | u = v;
|
---|
| 686 | v = tmp;
|
---|
| 687 | tmp = b;
|
---|
| 688 | b = c;
|
---|
| 689 | c = tmp;
|
---|
| 690 | udp = vdp;
|
---|
| 691 | vdp = v->d;
|
---|
| 692 | bdp = cdp;
|
---|
| 693 | cdp = c->d;
|
---|
| 694 | }
|
---|
| 695 | for (i = 0; i < top; i++) {
|
---|
| 696 | udp[i] ^= vdp[i];
|
---|
| 697 | bdp[i] ^= cdp[i];
|
---|
| 698 | }
|
---|
| 699 | if (ubits == vbits) {
|
---|
| 700 | BN_ULONG ul;
|
---|
| 701 | int utop = (ubits - 1) / BN_BITS2;
|
---|
| 702 |
|
---|
| 703 | while ((ul = udp[utop]) == 0 && utop)
|
---|
| 704 | utop--;
|
---|
| 705 | ubits = utop * BN_BITS2 + BN_num_bits_word(ul);
|
---|
| 706 | }
|
---|
| 707 | }
|
---|
| 708 | bn_correct_top(b);
|
---|
| 709 | }
|
---|
| 710 | # endif
|
---|
| 711 |
|
---|
| 712 | if (!BN_copy(r, b))
|
---|
| 713 | goto err;
|
---|
| 714 | bn_check_top(r);
|
---|
| 715 | ret = 1;
|
---|
| 716 |
|
---|
| 717 | err:
|
---|
| 718 | # ifdef BN_DEBUG /* BN_CTX_end would complain about the
|
---|
| 719 | * expanded form */
|
---|
| 720 | bn_correct_top(c);
|
---|
| 721 | bn_correct_top(u);
|
---|
| 722 | bn_correct_top(v);
|
---|
| 723 | # endif
|
---|
| 724 | BN_CTX_end(ctx);
|
---|
| 725 | return ret;
|
---|
| 726 | }
|
---|
| 727 |
|
---|
| 728 | /*
|
---|
| 729 | * Invert xx, reduce modulo p, and store the result in r. r could be xx.
|
---|
| 730 | * This function calls down to the BN_GF2m_mod_inv implementation; this
|
---|
| 731 | * wrapper function is only provided for convenience; for best performance,
|
---|
| 732 | * use the BN_GF2m_mod_inv function.
|
---|
| 733 | */
|
---|
| 734 | int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[],
|
---|
| 735 | BN_CTX *ctx)
|
---|
| 736 | {
|
---|
| 737 | BIGNUM *field;
|
---|
| 738 | int ret = 0;
|
---|
| 739 |
|
---|
| 740 | bn_check_top(xx);
|
---|
| 741 | BN_CTX_start(ctx);
|
---|
| 742 | if ((field = BN_CTX_get(ctx)) == NULL)
|
---|
| 743 | goto err;
|
---|
| 744 | if (!BN_GF2m_arr2poly(p, field))
|
---|
| 745 | goto err;
|
---|
| 746 |
|
---|
| 747 | ret = BN_GF2m_mod_inv(r, xx, field, ctx);
|
---|
| 748 | bn_check_top(r);
|
---|
| 749 |
|
---|
| 750 | err:
|
---|
| 751 | BN_CTX_end(ctx);
|
---|
| 752 | return ret;
|
---|
| 753 | }
|
---|
| 754 |
|
---|
| 755 | # ifndef OPENSSL_SUN_GF2M_DIV
|
---|
| 756 | /*
|
---|
| 757 | * Divide y by x, reduce modulo p, and store the result in r. r could be x
|
---|
| 758 | * or y, x could equal y.
|
---|
| 759 | */
|
---|
| 760 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
|
---|
| 761 | const BIGNUM *p, BN_CTX *ctx)
|
---|
| 762 | {
|
---|
| 763 | BIGNUM *xinv = NULL;
|
---|
| 764 | int ret = 0;
|
---|
| 765 |
|
---|
| 766 | bn_check_top(y);
|
---|
| 767 | bn_check_top(x);
|
---|
| 768 | bn_check_top(p);
|
---|
| 769 |
|
---|
| 770 | BN_CTX_start(ctx);
|
---|
| 771 | xinv = BN_CTX_get(ctx);
|
---|
| 772 | if (xinv == NULL)
|
---|
| 773 | goto err;
|
---|
| 774 |
|
---|
| 775 | if (!BN_GF2m_mod_inv(xinv, x, p, ctx))
|
---|
| 776 | goto err;
|
---|
| 777 | if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx))
|
---|
| 778 | goto err;
|
---|
| 779 | bn_check_top(r);
|
---|
| 780 | ret = 1;
|
---|
| 781 |
|
---|
| 782 | err:
|
---|
| 783 | BN_CTX_end(ctx);
|
---|
| 784 | return ret;
|
---|
| 785 | }
|
---|
| 786 | # else
|
---|
| 787 | /*
|
---|
| 788 | * Divide y by x, reduce modulo p, and store the result in r. r could be x
|
---|
| 789 | * or y, x could equal y. Uses algorithm Modular_Division_GF(2^m) from
|
---|
| 790 | * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to the
|
---|
| 791 | * Great Divide".
|
---|
| 792 | */
|
---|
| 793 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
|
---|
| 794 | const BIGNUM *p, BN_CTX *ctx)
|
---|
| 795 | {
|
---|
| 796 | BIGNUM *a, *b, *u, *v;
|
---|
| 797 | int ret = 0;
|
---|
| 798 |
|
---|
| 799 | bn_check_top(y);
|
---|
| 800 | bn_check_top(x);
|
---|
| 801 | bn_check_top(p);
|
---|
| 802 |
|
---|
| 803 | BN_CTX_start(ctx);
|
---|
| 804 |
|
---|
| 805 | a = BN_CTX_get(ctx);
|
---|
| 806 | b = BN_CTX_get(ctx);
|
---|
| 807 | u = BN_CTX_get(ctx);
|
---|
| 808 | v = BN_CTX_get(ctx);
|
---|
| 809 | if (v == NULL)
|
---|
| 810 | goto err;
|
---|
| 811 |
|
---|
| 812 | /* reduce x and y mod p */
|
---|
| 813 | if (!BN_GF2m_mod(u, y, p))
|
---|
| 814 | goto err;
|
---|
| 815 | if (!BN_GF2m_mod(a, x, p))
|
---|
| 816 | goto err;
|
---|
| 817 | if (!BN_copy(b, p))
|
---|
| 818 | goto err;
|
---|
| 819 |
|
---|
| 820 | while (!BN_is_odd(a)) {
|
---|
| 821 | if (!BN_rshift1(a, a))
|
---|
| 822 | goto err;
|
---|
| 823 | if (BN_is_odd(u))
|
---|
| 824 | if (!BN_GF2m_add(u, u, p))
|
---|
| 825 | goto err;
|
---|
| 826 | if (!BN_rshift1(u, u))
|
---|
| 827 | goto err;
|
---|
| 828 | }
|
---|
| 829 |
|
---|
| 830 | do {
|
---|
| 831 | if (BN_GF2m_cmp(b, a) > 0) {
|
---|
| 832 | if (!BN_GF2m_add(b, b, a))
|
---|
| 833 | goto err;
|
---|
| 834 | if (!BN_GF2m_add(v, v, u))
|
---|
| 835 | goto err;
|
---|
| 836 | do {
|
---|
| 837 | if (!BN_rshift1(b, b))
|
---|
| 838 | goto err;
|
---|
| 839 | if (BN_is_odd(v))
|
---|
| 840 | if (!BN_GF2m_add(v, v, p))
|
---|
| 841 | goto err;
|
---|
| 842 | if (!BN_rshift1(v, v))
|
---|
| 843 | goto err;
|
---|
| 844 | } while (!BN_is_odd(b));
|
---|
| 845 | } else if (BN_abs_is_word(a, 1))
|
---|
| 846 | break;
|
---|
| 847 | else {
|
---|
| 848 | if (!BN_GF2m_add(a, a, b))
|
---|
| 849 | goto err;
|
---|
| 850 | if (!BN_GF2m_add(u, u, v))
|
---|
| 851 | goto err;
|
---|
| 852 | do {
|
---|
| 853 | if (!BN_rshift1(a, a))
|
---|
| 854 | goto err;
|
---|
| 855 | if (BN_is_odd(u))
|
---|
| 856 | if (!BN_GF2m_add(u, u, p))
|
---|
| 857 | goto err;
|
---|
| 858 | if (!BN_rshift1(u, u))
|
---|
| 859 | goto err;
|
---|
| 860 | } while (!BN_is_odd(a));
|
---|
| 861 | }
|
---|
| 862 | } while (1);
|
---|
| 863 |
|
---|
| 864 | if (!BN_copy(r, u))
|
---|
| 865 | goto err;
|
---|
| 866 | bn_check_top(r);
|
---|
| 867 | ret = 1;
|
---|
| 868 |
|
---|
| 869 | err:
|
---|
| 870 | BN_CTX_end(ctx);
|
---|
| 871 | return ret;
|
---|
| 872 | }
|
---|
| 873 | # endif
|
---|
| 874 |
|
---|
| 875 | /*
|
---|
| 876 | * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
|
---|
| 877 | * * or yy, xx could equal yy. This function calls down to the
|
---|
| 878 | * BN_GF2m_mod_div implementation; this wrapper function is only provided for
|
---|
| 879 | * convenience; for best performance, use the BN_GF2m_mod_div function.
|
---|
| 880 | */
|
---|
| 881 | int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx,
|
---|
| 882 | const int p[], BN_CTX *ctx)
|
---|
| 883 | {
|
---|
| 884 | BIGNUM *field;
|
---|
| 885 | int ret = 0;
|
---|
| 886 |
|
---|
| 887 | bn_check_top(yy);
|
---|
| 888 | bn_check_top(xx);
|
---|
| 889 |
|
---|
| 890 | BN_CTX_start(ctx);
|
---|
| 891 | if ((field = BN_CTX_get(ctx)) == NULL)
|
---|
| 892 | goto err;
|
---|
| 893 | if (!BN_GF2m_arr2poly(p, field))
|
---|
| 894 | goto err;
|
---|
| 895 |
|
---|
| 896 | ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
|
---|
| 897 | bn_check_top(r);
|
---|
| 898 |
|
---|
| 899 | err:
|
---|
| 900 | BN_CTX_end(ctx);
|
---|
| 901 | return ret;
|
---|
| 902 | }
|
---|
| 903 |
|
---|
| 904 | /*
|
---|
| 905 | * Compute the bth power of a, reduce modulo p, and store the result in r. r
|
---|
| 906 | * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE
|
---|
| 907 | * P1363.
|
---|
| 908 | */
|
---|
| 909 | int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
|
---|
| 910 | const int p[], BN_CTX *ctx)
|
---|
| 911 | {
|
---|
| 912 | int ret = 0, i, n;
|
---|
| 913 | BIGNUM *u;
|
---|
| 914 |
|
---|
| 915 | bn_check_top(a);
|
---|
| 916 | bn_check_top(b);
|
---|
| 917 |
|
---|
| 918 | if (BN_is_zero(b))
|
---|
| 919 | return (BN_one(r));
|
---|
| 920 |
|
---|
| 921 | if (BN_abs_is_word(b, 1))
|
---|
| 922 | return (BN_copy(r, a) != NULL);
|
---|
| 923 |
|
---|
| 924 | BN_CTX_start(ctx);
|
---|
| 925 | if ((u = BN_CTX_get(ctx)) == NULL)
|
---|
| 926 | goto err;
|
---|
| 927 |
|
---|
| 928 | if (!BN_GF2m_mod_arr(u, a, p))
|
---|
| 929 | goto err;
|
---|
| 930 |
|
---|
| 931 | n = BN_num_bits(b) - 1;
|
---|
| 932 | for (i = n - 1; i >= 0; i--) {
|
---|
| 933 | if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx))
|
---|
| 934 | goto err;
|
---|
| 935 | if (BN_is_bit_set(b, i)) {
|
---|
| 936 | if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx))
|
---|
| 937 | goto err;
|
---|
| 938 | }
|
---|
| 939 | }
|
---|
| 940 | if (!BN_copy(r, u))
|
---|
| 941 | goto err;
|
---|
| 942 | bn_check_top(r);
|
---|
| 943 | ret = 1;
|
---|
| 944 | err:
|
---|
| 945 | BN_CTX_end(ctx);
|
---|
| 946 | return ret;
|
---|
| 947 | }
|
---|
| 948 |
|
---|
| 949 | /*
|
---|
| 950 | * Compute the bth power of a, reduce modulo p, and store the result in r. r
|
---|
| 951 | * could be a. This function calls down to the BN_GF2m_mod_exp_arr
|
---|
| 952 | * implementation; this wrapper function is only provided for convenience;
|
---|
| 953 | * for best performance, use the BN_GF2m_mod_exp_arr function.
|
---|
| 954 | */
|
---|
| 955 | int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
|
---|
| 956 | const BIGNUM *p, BN_CTX *ctx)
|
---|
| 957 | {
|
---|
| 958 | int ret = 0;
|
---|
| 959 | const int max = BN_num_bits(p) + 1;
|
---|
| 960 | int *arr = NULL;
|
---|
| 961 | bn_check_top(a);
|
---|
| 962 | bn_check_top(b);
|
---|
| 963 | bn_check_top(p);
|
---|
| 964 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
| 965 | goto err;
|
---|
| 966 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
| 967 | if (!ret || ret > max) {
|
---|
| 968 | BNerr(BN_F_BN_GF2M_MOD_EXP, BN_R_INVALID_LENGTH);
|
---|
| 969 | goto err;
|
---|
| 970 | }
|
---|
| 971 | ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
|
---|
| 972 | bn_check_top(r);
|
---|
| 973 | err:
|
---|
| 974 | OPENSSL_free(arr);
|
---|
| 975 | return ret;
|
---|
| 976 | }
|
---|
| 977 |
|
---|
| 978 | /*
|
---|
| 979 | * Compute the square root of a, reduce modulo p, and store the result in r.
|
---|
| 980 | * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
|
---|
| 981 | */
|
---|
| 982 | int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[],
|
---|
| 983 | BN_CTX *ctx)
|
---|
| 984 | {
|
---|
| 985 | int ret = 0;
|
---|
| 986 | BIGNUM *u;
|
---|
| 987 |
|
---|
| 988 | bn_check_top(a);
|
---|
| 989 |
|
---|
| 990 | if (!p[0]) {
|
---|
| 991 | /* reduction mod 1 => return 0 */
|
---|
| 992 | BN_zero(r);
|
---|
| 993 | return 1;
|
---|
| 994 | }
|
---|
| 995 |
|
---|
| 996 | BN_CTX_start(ctx);
|
---|
| 997 | if ((u = BN_CTX_get(ctx)) == NULL)
|
---|
| 998 | goto err;
|
---|
| 999 |
|
---|
| 1000 | if (!BN_set_bit(u, p[0] - 1))
|
---|
| 1001 | goto err;
|
---|
| 1002 | ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
|
---|
| 1003 | bn_check_top(r);
|
---|
| 1004 |
|
---|
| 1005 | err:
|
---|
| 1006 | BN_CTX_end(ctx);
|
---|
| 1007 | return ret;
|
---|
| 1008 | }
|
---|
| 1009 |
|
---|
| 1010 | /*
|
---|
| 1011 | * Compute the square root of a, reduce modulo p, and store the result in r.
|
---|
| 1012 | * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr
|
---|
| 1013 | * implementation; this wrapper function is only provided for convenience;
|
---|
| 1014 | * for best performance, use the BN_GF2m_mod_sqrt_arr function.
|
---|
| 1015 | */
|
---|
| 1016 | int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
|
---|
| 1017 | {
|
---|
| 1018 | int ret = 0;
|
---|
| 1019 | const int max = BN_num_bits(p) + 1;
|
---|
| 1020 | int *arr = NULL;
|
---|
| 1021 | bn_check_top(a);
|
---|
| 1022 | bn_check_top(p);
|
---|
| 1023 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
| 1024 | goto err;
|
---|
| 1025 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
| 1026 | if (!ret || ret > max) {
|
---|
| 1027 | BNerr(BN_F_BN_GF2M_MOD_SQRT, BN_R_INVALID_LENGTH);
|
---|
| 1028 | goto err;
|
---|
| 1029 | }
|
---|
| 1030 | ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
|
---|
| 1031 | bn_check_top(r);
|
---|
| 1032 | err:
|
---|
| 1033 | OPENSSL_free(arr);
|
---|
| 1034 | return ret;
|
---|
| 1035 | }
|
---|
| 1036 |
|
---|
| 1037 | /*
|
---|
| 1038 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
|
---|
| 1039 | * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
|
---|
| 1040 | */
|
---|
| 1041 | int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[],
|
---|
| 1042 | BN_CTX *ctx)
|
---|
| 1043 | {
|
---|
| 1044 | int ret = 0, count = 0, j;
|
---|
| 1045 | BIGNUM *a, *z, *rho, *w, *w2, *tmp;
|
---|
| 1046 |
|
---|
| 1047 | bn_check_top(a_);
|
---|
| 1048 |
|
---|
| 1049 | if (!p[0]) {
|
---|
| 1050 | /* reduction mod 1 => return 0 */
|
---|
| 1051 | BN_zero(r);
|
---|
| 1052 | return 1;
|
---|
| 1053 | }
|
---|
| 1054 |
|
---|
| 1055 | BN_CTX_start(ctx);
|
---|
| 1056 | a = BN_CTX_get(ctx);
|
---|
| 1057 | z = BN_CTX_get(ctx);
|
---|
| 1058 | w = BN_CTX_get(ctx);
|
---|
| 1059 | if (w == NULL)
|
---|
| 1060 | goto err;
|
---|
| 1061 |
|
---|
| 1062 | if (!BN_GF2m_mod_arr(a, a_, p))
|
---|
| 1063 | goto err;
|
---|
| 1064 |
|
---|
| 1065 | if (BN_is_zero(a)) {
|
---|
| 1066 | BN_zero(r);
|
---|
| 1067 | ret = 1;
|
---|
| 1068 | goto err;
|
---|
| 1069 | }
|
---|
| 1070 |
|
---|
| 1071 | if (p[0] & 0x1) { /* m is odd */
|
---|
| 1072 | /* compute half-trace of a */
|
---|
| 1073 | if (!BN_copy(z, a))
|
---|
| 1074 | goto err;
|
---|
| 1075 | for (j = 1; j <= (p[0] - 1) / 2; j++) {
|
---|
| 1076 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
|
---|
| 1077 | goto err;
|
---|
| 1078 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
|
---|
| 1079 | goto err;
|
---|
| 1080 | if (!BN_GF2m_add(z, z, a))
|
---|
| 1081 | goto err;
|
---|
| 1082 | }
|
---|
| 1083 |
|
---|
| 1084 | } else { /* m is even */
|
---|
| 1085 |
|
---|
| 1086 | rho = BN_CTX_get(ctx);
|
---|
| 1087 | w2 = BN_CTX_get(ctx);
|
---|
| 1088 | tmp = BN_CTX_get(ctx);
|
---|
| 1089 | if (tmp == NULL)
|
---|
| 1090 | goto err;
|
---|
| 1091 | do {
|
---|
| 1092 | if (!BN_rand(rho, p[0], BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
|
---|
| 1093 | goto err;
|
---|
| 1094 | if (!BN_GF2m_mod_arr(rho, rho, p))
|
---|
| 1095 | goto err;
|
---|
| 1096 | BN_zero(z);
|
---|
| 1097 | if (!BN_copy(w, rho))
|
---|
| 1098 | goto err;
|
---|
| 1099 | for (j = 1; j <= p[0] - 1; j++) {
|
---|
| 1100 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
|
---|
| 1101 | goto err;
|
---|
| 1102 | if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx))
|
---|
| 1103 | goto err;
|
---|
| 1104 | if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx))
|
---|
| 1105 | goto err;
|
---|
| 1106 | if (!BN_GF2m_add(z, z, tmp))
|
---|
| 1107 | goto err;
|
---|
| 1108 | if (!BN_GF2m_add(w, w2, rho))
|
---|
| 1109 | goto err;
|
---|
| 1110 | }
|
---|
| 1111 | count++;
|
---|
| 1112 | } while (BN_is_zero(w) && (count < MAX_ITERATIONS));
|
---|
| 1113 | if (BN_is_zero(w)) {
|
---|
| 1114 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_TOO_MANY_ITERATIONS);
|
---|
| 1115 | goto err;
|
---|
| 1116 | }
|
---|
| 1117 | }
|
---|
| 1118 |
|
---|
| 1119 | if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx))
|
---|
| 1120 | goto err;
|
---|
| 1121 | if (!BN_GF2m_add(w, z, w))
|
---|
| 1122 | goto err;
|
---|
| 1123 | if (BN_GF2m_cmp(w, a)) {
|
---|
| 1124 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION);
|
---|
| 1125 | goto err;
|
---|
| 1126 | }
|
---|
| 1127 |
|
---|
| 1128 | if (!BN_copy(r, z))
|
---|
| 1129 | goto err;
|
---|
| 1130 | bn_check_top(r);
|
---|
| 1131 |
|
---|
| 1132 | ret = 1;
|
---|
| 1133 |
|
---|
| 1134 | err:
|
---|
| 1135 | BN_CTX_end(ctx);
|
---|
| 1136 | return ret;
|
---|
| 1137 | }
|
---|
| 1138 |
|
---|
| 1139 | /*
|
---|
| 1140 | * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
|
---|
| 1141 | * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr
|
---|
| 1142 | * implementation; this wrapper function is only provided for convenience;
|
---|
| 1143 | * for best performance, use the BN_GF2m_mod_solve_quad_arr function.
|
---|
| 1144 | */
|
---|
| 1145 | int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
|
---|
| 1146 | BN_CTX *ctx)
|
---|
| 1147 | {
|
---|
| 1148 | int ret = 0;
|
---|
| 1149 | const int max = BN_num_bits(p) + 1;
|
---|
| 1150 | int *arr = NULL;
|
---|
| 1151 | bn_check_top(a);
|
---|
| 1152 | bn_check_top(p);
|
---|
| 1153 | if ((arr = OPENSSL_malloc(sizeof(*arr) * max)) == NULL)
|
---|
| 1154 | goto err;
|
---|
| 1155 | ret = BN_GF2m_poly2arr(p, arr, max);
|
---|
| 1156 | if (!ret || ret > max) {
|
---|
| 1157 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD, BN_R_INVALID_LENGTH);
|
---|
| 1158 | goto err;
|
---|
| 1159 | }
|
---|
| 1160 | ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
|
---|
| 1161 | bn_check_top(r);
|
---|
| 1162 | err:
|
---|
| 1163 | OPENSSL_free(arr);
|
---|
| 1164 | return ret;
|
---|
| 1165 | }
|
---|
| 1166 |
|
---|
| 1167 | /*
|
---|
| 1168 | * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i *
|
---|
| 1169 | * x^i) into an array of integers corresponding to the bits with non-zero
|
---|
| 1170 | * coefficient. Array is terminated with -1. Up to max elements of the array
|
---|
| 1171 | * will be filled. Return value is total number of array elements that would
|
---|
| 1172 | * be filled if array was large enough.
|
---|
| 1173 | */
|
---|
| 1174 | int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
|
---|
| 1175 | {
|
---|
| 1176 | int i, j, k = 0;
|
---|
| 1177 | BN_ULONG mask;
|
---|
| 1178 |
|
---|
| 1179 | if (BN_is_zero(a))
|
---|
| 1180 | return 0;
|
---|
| 1181 |
|
---|
| 1182 | for (i = a->top - 1; i >= 0; i--) {
|
---|
| 1183 | if (!a->d[i])
|
---|
| 1184 | /* skip word if a->d[i] == 0 */
|
---|
| 1185 | continue;
|
---|
| 1186 | mask = BN_TBIT;
|
---|
| 1187 | for (j = BN_BITS2 - 1; j >= 0; j--) {
|
---|
| 1188 | if (a->d[i] & mask) {
|
---|
| 1189 | if (k < max)
|
---|
| 1190 | p[k] = BN_BITS2 * i + j;
|
---|
| 1191 | k++;
|
---|
| 1192 | }
|
---|
| 1193 | mask >>= 1;
|
---|
| 1194 | }
|
---|
| 1195 | }
|
---|
| 1196 |
|
---|
| 1197 | if (k < max) {
|
---|
| 1198 | p[k] = -1;
|
---|
| 1199 | k++;
|
---|
| 1200 | }
|
---|
| 1201 |
|
---|
| 1202 | return k;
|
---|
| 1203 | }
|
---|
| 1204 |
|
---|
| 1205 | /*
|
---|
| 1206 | * Convert the coefficient array representation of a polynomial to a
|
---|
| 1207 | * bit-string. The array must be terminated by -1.
|
---|
| 1208 | */
|
---|
| 1209 | int BN_GF2m_arr2poly(const int p[], BIGNUM *a)
|
---|
| 1210 | {
|
---|
| 1211 | int i;
|
---|
| 1212 |
|
---|
| 1213 | bn_check_top(a);
|
---|
| 1214 | BN_zero(a);
|
---|
| 1215 | for (i = 0; p[i] != -1; i++) {
|
---|
| 1216 | if (BN_set_bit(a, p[i]) == 0)
|
---|
| 1217 | return 0;
|
---|
| 1218 | }
|
---|
| 1219 | bn_check_top(a);
|
---|
| 1220 |
|
---|
| 1221 | return 1;
|
---|
| 1222 | }
|
---|
| 1223 |
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| 1224 | #endif
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