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/* |
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* Copyright (c) 2017 Thomas Pornin |
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* |
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* Permission is hereby granted, free of charge, to any person obtaining |
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* a copy of this software and associated documentation files (the |
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* "Software"), to deal in the Software without restriction, including |
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* without limitation the rights to use, copy, modify, merge, publish, |
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* distribute, sublicense, and/or sell copies of the Software, and to |
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* permit persons to whom the Software is furnished to do so, subject to |
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* the following conditions: |
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* |
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* The above copyright notice and this permission notice shall be |
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* included in all copies or substantial portions of the Software. |
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* |
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, |
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF |
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND |
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS |
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* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN |
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* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN |
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* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
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* SOFTWARE. |
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*/ |
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#include "inner.h" |
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27
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/* obsolete |
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#include |
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#include |
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static void |
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print_int(const char *name, const uint32_t *x) |
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32
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{ |
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33
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size_t u; |
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34
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unsigned char tmp[40]; |
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35
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36
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printf("%s = ", name); |
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37
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for (u = 0; u < 9; u ++) { |
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38
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if (x[u] > 0x3FFFFFFF) { |
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39
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printf("INVALID:"); |
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40
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for (u = 0; u < 9; u ++) { |
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printf(" %08X", x[u]); |
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} |
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printf("\n"); |
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44
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return; |
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} |
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46
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} |
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47
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memset(tmp, 0, sizeof tmp); |
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48
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for (u = 0; u < 9; u ++) { |
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49
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uint64_t w; |
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50
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int j, k; |
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51
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52
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w = x[u]; |
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53
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j = 30 * (int)u; |
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54
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k = j & 7; |
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55
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if (k != 0) { |
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56
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w <<= k; |
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57
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j -= k; |
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58
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} |
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59
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k = j >> 3; |
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60
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for (j = 0; j < 8; j ++) { |
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61
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tmp[39 - k - j] |= (unsigned char)w; |
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62
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w >>= 8; |
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63
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} |
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64
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} |
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65
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for (u = 8; u < 40; u ++) { |
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66
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printf("%02X", tmp[u]); |
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67
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} |
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68
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printf("\n"); |
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69
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} |
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70
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*/ |
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71
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72
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/* |
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73
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* If BR_NO_ARITH_SHIFT is undefined, or defined to 0, then we _assume_ |
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74
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* that right-shifting a signed negative integer copies the sign bit |
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75
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* (arithmetic right-shift). This is "implementation-defined behaviour", |
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76
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* i.e. it is not undefined, but it may differ between compilers. Each |
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77
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* compiler is supposed to document its behaviour in that respect. GCC |
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78
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* explicitly defines that an arithmetic right shift is used. We expect |
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79
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* all other compilers to do the same, because underlying CPU offer an |
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80
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* arithmetic right shift opcode that could not be used otherwise. |
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81
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*/ |
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82
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#if BR_NO_ARITH_SHIFT |
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83
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#define ARSH(x, n) (((uint32_t)(x) >> (n)) \ |
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84
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| ((-((uint32_t)(x) >> 31)) << (32 - (n)))) |
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85
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#else |
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86
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#define ARSH(x, n) ((*(int32_t *)&(x)) >> (n)) |
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87
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#endif |
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88
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89
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/* |
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90
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* Convert an integer from unsigned little-endian encoding to a sequence of |
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91
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* 30-bit words in little-endian order. The final "partial" word is |
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92
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* returned. |
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93
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*/ |
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94
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static uint32_t |
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95
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0
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le8_to_le30(uint32_t *dst, const unsigned char *src, size_t len) |
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96
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{ |
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97
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uint32_t acc; |
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98
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int acc_len; |
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99
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100
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0
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acc = 0; |
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101
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0
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acc_len = 0; |
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102
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0
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0
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while (len -- > 0) { |
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103
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uint32_t b; |
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104
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105
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0
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b = *src ++; |
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106
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0
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0
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if (acc_len < 22) { |
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107
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0
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acc |= b << acc_len; |
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108
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0
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acc_len += 8; |
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109
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} else { |
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110
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0
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*dst ++ = (acc | (b << acc_len)) & 0x3FFFFFFF; |
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111
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0
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acc = b >> (30 - acc_len); |
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112
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0
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acc_len -= 22; |
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113
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} |
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114
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} |
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115
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0
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return acc; |
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116
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} |
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117
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118
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/* |
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119
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* Convert an integer (30-bit words, little-endian) to unsigned |
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120
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* little-endian encoding. The total encoding length is provided; all |
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121
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* the destination bytes will be filled. |
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122
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*/ |
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123
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static void |
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124
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0
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le30_to_le8(unsigned char *dst, size_t len, const uint32_t *src) |
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125
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{ |
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126
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uint32_t acc; |
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127
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int acc_len; |
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128
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129
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0
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acc = 0; |
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130
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0
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acc_len = 0; |
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131
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0
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0
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while (len -- > 0) { |
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132
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0
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0
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if (acc_len < 8) { |
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133
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uint32_t w; |
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134
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135
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0
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w = *src ++; |
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136
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0
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*dst ++ = (unsigned char)(acc | (w << acc_len)); |
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137
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0
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acc = w >> (8 - acc_len); |
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138
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0
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acc_len += 22; |
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139
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} else { |
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140
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0
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*dst ++ = (unsigned char)acc; |
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141
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0
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acc >>= 8; |
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142
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0
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acc_len -= 8; |
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143
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} |
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144
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} |
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145
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0
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} |
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146
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147
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/* |
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148
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* Multiply two integers. Source integers are represented as arrays of |
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149
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* nine 30-bit words, for values up to 2^270-1. Result is encoded over |
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150
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* 18 words of 30 bits each. |
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151
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*/ |
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152
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static void |
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153
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0
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mul9(uint32_t *d, const uint32_t *a, const uint32_t *b) |
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154
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{ |
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155
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/* |
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156
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* Maximum intermediate result is no more than |
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157
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* 10376293531797946367, which fits in 64 bits. Reason: |
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158
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* |
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159
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* 10376293531797946367 = 9 * (2^30-1)^2 + 9663676406 |
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160
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* 10376293531797946367 < 9663676407 * 2^30 |
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161
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* |
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162
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* Thus, adding together 9 products of 30-bit integers, with |
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163
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* a carry of at most 9663676406, yields an integer that fits |
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164
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* on 64 bits and generates a carry of at most 9663676406. |
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165
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*/ |
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166
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uint64_t t[17]; |
|
167
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uint64_t cc; |
|
168
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int i; |
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169
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170
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0
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t[ 0] = MUL31(a[0], b[0]); |
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171
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0
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t[ 1] = MUL31(a[0], b[1]) |
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172
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0
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+ MUL31(a[1], b[0]); |
|
173
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0
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t[ 2] = MUL31(a[0], b[2]) |
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174
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0
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+ MUL31(a[1], b[1]) |
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175
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0
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+ MUL31(a[2], b[0]); |
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176
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0
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t[ 3] = MUL31(a[0], b[3]) |
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177
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0
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+ MUL31(a[1], b[2]) |
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178
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0
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+ MUL31(a[2], b[1]) |
|
179
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0
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+ MUL31(a[3], b[0]); |
|
180
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0
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t[ 4] = MUL31(a[0], b[4]) |
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181
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0
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+ MUL31(a[1], b[3]) |
|
182
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0
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+ MUL31(a[2], b[2]) |
|
183
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0
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+ MUL31(a[3], b[1]) |
|
184
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0
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+ MUL31(a[4], b[0]); |
|
185
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0
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t[ 5] = MUL31(a[0], b[5]) |
|
186
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0
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+ MUL31(a[1], b[4]) |
|
187
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0
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+ MUL31(a[2], b[3]) |
|
188
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0
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+ MUL31(a[3], b[2]) |
|
189
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0
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+ MUL31(a[4], b[1]) |
|
190
|
0
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+ MUL31(a[5], b[0]); |
|
191
|
0
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t[ 6] = MUL31(a[0], b[6]) |
|
192
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0
|
|
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+ MUL31(a[1], b[5]) |
|
193
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0
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+ MUL31(a[2], b[4]) |
|
194
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0
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+ MUL31(a[3], b[3]) |
|
195
|
0
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+ MUL31(a[4], b[2]) |
|
196
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0
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+ MUL31(a[5], b[1]) |
|
197
|
0
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+ MUL31(a[6], b[0]); |
|
198
|
0
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|
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t[ 7] = MUL31(a[0], b[7]) |
|
199
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0
|
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+ MUL31(a[1], b[6]) |
|
200
|
0
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+ MUL31(a[2], b[5]) |
|
201
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0
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+ MUL31(a[3], b[4]) |
|
202
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0
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+ MUL31(a[4], b[3]) |
|
203
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0
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+ MUL31(a[5], b[2]) |
|
204
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0
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+ MUL31(a[6], b[1]) |
|
205
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0
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+ MUL31(a[7], b[0]); |
|
206
|
0
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|
|
|
t[ 8] = MUL31(a[0], b[8]) |
|
207
|
0
|
|
|
|
|
|
+ MUL31(a[1], b[7]) |
|
208
|
0
|
|
|
|
|
|
+ MUL31(a[2], b[6]) |
|
209
|
0
|
|
|
|
|
|
+ MUL31(a[3], b[5]) |
|
210
|
0
|
|
|
|
|
|
+ MUL31(a[4], b[4]) |
|
211
|
0
|
|
|
|
|
|
+ MUL31(a[5], b[3]) |
|
212
|
0
|
|
|
|
|
|
+ MUL31(a[6], b[2]) |
|
213
|
0
|
|
|
|
|
|
+ MUL31(a[7], b[1]) |
|
214
|
0
|
|
|
|
|
|
+ MUL31(a[8], b[0]); |
|
215
|
0
|
|
|
|
|
|
t[ 9] = MUL31(a[1], b[8]) |
|
216
|
0
|
|
|
|
|
|
+ MUL31(a[2], b[7]) |
|
217
|
0
|
|
|
|
|
|
+ MUL31(a[3], b[6]) |
|
218
|
0
|
|
|
|
|
|
+ MUL31(a[4], b[5]) |
|
219
|
0
|
|
|
|
|
|
+ MUL31(a[5], b[4]) |
|
220
|
0
|
|
|
|
|
|
+ MUL31(a[6], b[3]) |
|
221
|
0
|
|
|
|
|
|
+ MUL31(a[7], b[2]) |
|
222
|
0
|
|
|
|
|
|
+ MUL31(a[8], b[1]); |
|
223
|
0
|
|
|
|
|
|
t[10] = MUL31(a[2], b[8]) |
|
224
|
0
|
|
|
|
|
|
+ MUL31(a[3], b[7]) |
|
225
|
0
|
|
|
|
|
|
+ MUL31(a[4], b[6]) |
|
226
|
0
|
|
|
|
|
|
+ MUL31(a[5], b[5]) |
|
227
|
0
|
|
|
|
|
|
+ MUL31(a[6], b[4]) |
|
228
|
0
|
|
|
|
|
|
+ MUL31(a[7], b[3]) |
|
229
|
0
|
|
|
|
|
|
+ MUL31(a[8], b[2]); |
|
230
|
0
|
|
|
|
|
|
t[11] = MUL31(a[3], b[8]) |
|
231
|
0
|
|
|
|
|
|
+ MUL31(a[4], b[7]) |
|
232
|
0
|
|
|
|
|
|
+ MUL31(a[5], b[6]) |
|
233
|
0
|
|
|
|
|
|
+ MUL31(a[6], b[5]) |
|
234
|
0
|
|
|
|
|
|
+ MUL31(a[7], b[4]) |
|
235
|
0
|
|
|
|
|
|
+ MUL31(a[8], b[3]); |
|
236
|
0
|
|
|
|
|
|
t[12] = MUL31(a[4], b[8]) |
|
237
|
0
|
|
|
|
|
|
+ MUL31(a[5], b[7]) |
|
238
|
0
|
|
|
|
|
|
+ MUL31(a[6], b[6]) |
|
239
|
0
|
|
|
|
|
|
+ MUL31(a[7], b[5]) |
|
240
|
0
|
|
|
|
|
|
+ MUL31(a[8], b[4]); |
|
241
|
0
|
|
|
|
|
|
t[13] = MUL31(a[5], b[8]) |
|
242
|
0
|
|
|
|
|
|
+ MUL31(a[6], b[7]) |
|
243
|
0
|
|
|
|
|
|
+ MUL31(a[7], b[6]) |
|
244
|
0
|
|
|
|
|
|
+ MUL31(a[8], b[5]); |
|
245
|
0
|
|
|
|
|
|
t[14] = MUL31(a[6], b[8]) |
|
246
|
0
|
|
|
|
|
|
+ MUL31(a[7], b[7]) |
|
247
|
0
|
|
|
|
|
|
+ MUL31(a[8], b[6]); |
|
248
|
0
|
|
|
|
|
|
t[15] = MUL31(a[7], b[8]) |
|
249
|
0
|
|
|
|
|
|
+ MUL31(a[8], b[7]); |
|
250
|
0
|
|
|
|
|
|
t[16] = MUL31(a[8], b[8]); |
|
251
|
|
|
|
|
|
|
|
|
252
|
|
|
|
|
|
|
/* |
|
253
|
|
|
|
|
|
|
* Propagate carries. |
|
254
|
|
|
|
|
|
|
*/ |
|
255
|
0
|
|
|
|
|
|
cc = 0; |
|
256
|
0
|
0
|
|
|
|
|
for (i = 0; i < 17; i ++) { |
|
257
|
|
|
|
|
|
|
uint64_t w; |
|
258
|
|
|
|
|
|
|
|
|
259
|
0
|
|
|
|
|
|
w = t[i] + cc; |
|
260
|
0
|
|
|
|
|
|
d[i] = (uint32_t)w & 0x3FFFFFFF; |
|
261
|
0
|
|
|
|
|
|
cc = w >> 30; |
|
262
|
|
|
|
|
|
|
} |
|
263
|
0
|
|
|
|
|
|
d[17] = (uint32_t)cc; |
|
264
|
0
|
|
|
|
|
|
} |
|
265
|
|
|
|
|
|
|
|
|
266
|
|
|
|
|
|
|
/* |
|
267
|
|
|
|
|
|
|
* Square a 270-bit integer, represented as an array of nine 30-bit words. |
|
268
|
|
|
|
|
|
|
* Result uses 18 words of 30 bits each. |
|
269
|
|
|
|
|
|
|
*/ |
|
270
|
|
|
|
|
|
|
static void |
|
271
|
0
|
|
|
|
|
|
square9(uint32_t *d, const uint32_t *a) |
|
272
|
|
|
|
|
|
|
{ |
|
273
|
|
|
|
|
|
|
uint64_t t[17]; |
|
274
|
|
|
|
|
|
|
uint64_t cc; |
|
275
|
|
|
|
|
|
|
int i; |
|
276
|
|
|
|
|
|
|
|
|
277
|
0
|
|
|
|
|
|
t[ 0] = MUL31(a[0], a[0]); |
|
278
|
0
|
|
|
|
|
|
t[ 1] = ((MUL31(a[0], a[1])) << 1); |
|
279
|
0
|
|
|
|
|
|
t[ 2] = MUL31(a[1], a[1]) |
|
280
|
0
|
|
|
|
|
|
+ ((MUL31(a[0], a[2])) << 1); |
|
281
|
0
|
|
|
|
|
|
t[ 3] = ((MUL31(a[0], a[3]) |
|
282
|
0
|
|
|
|
|
|
+ MUL31(a[1], a[2])) << 1); |
|
283
|
0
|
|
|
|
|
|
t[ 4] = MUL31(a[2], a[2]) |
|
284
|
0
|
|
|
|
|
|
+ ((MUL31(a[0], a[4]) |
|
285
|
0
|
|
|
|
|
|
+ MUL31(a[1], a[3])) << 1); |
|
286
|
0
|
|
|
|
|
|
t[ 5] = ((MUL31(a[0], a[5]) |
|
287
|
0
|
|
|
|
|
|
+ MUL31(a[1], a[4]) |
|
288
|
0
|
|
|
|
|
|
+ MUL31(a[2], a[3])) << 1); |
|
289
|
0
|
|
|
|
|
|
t[ 6] = MUL31(a[3], a[3]) |
|
290
|
0
|
|
|
|
|
|
+ ((MUL31(a[0], a[6]) |
|
291
|
0
|
|
|
|
|
|
+ MUL31(a[1], a[5]) |
|
292
|
0
|
|
|
|
|
|
+ MUL31(a[2], a[4])) << 1); |
|
293
|
0
|
|
|
|
|
|
t[ 7] = ((MUL31(a[0], a[7]) |
|
294
|
0
|
|
|
|
|
|
+ MUL31(a[1], a[6]) |
|
295
|
0
|
|
|
|
|
|
+ MUL31(a[2], a[5]) |
|
296
|
0
|
|
|
|
|
|
+ MUL31(a[3], a[4])) << 1); |
|
297
|
0
|
|
|
|
|
|
t[ 8] = MUL31(a[4], a[4]) |
|
298
|
0
|
|
|
|
|
|
+ ((MUL31(a[0], a[8]) |
|
299
|
0
|
|
|
|
|
|
+ MUL31(a[1], a[7]) |
|
300
|
0
|
|
|
|
|
|
+ MUL31(a[2], a[6]) |
|
301
|
0
|
|
|
|
|
|
+ MUL31(a[3], a[5])) << 1); |
|
302
|
0
|
|
|
|
|
|
t[ 9] = ((MUL31(a[1], a[8]) |
|
303
|
0
|
|
|
|
|
|
+ MUL31(a[2], a[7]) |
|
304
|
0
|
|
|
|
|
|
+ MUL31(a[3], a[6]) |
|
305
|
0
|
|
|
|
|
|
+ MUL31(a[4], a[5])) << 1); |
|
306
|
0
|
|
|
|
|
|
t[10] = MUL31(a[5], a[5]) |
|
307
|
0
|
|
|
|
|
|
+ ((MUL31(a[2], a[8]) |
|
308
|
0
|
|
|
|
|
|
+ MUL31(a[3], a[7]) |
|
309
|
0
|
|
|
|
|
|
+ MUL31(a[4], a[6])) << 1); |
|
310
|
0
|
|
|
|
|
|
t[11] = ((MUL31(a[3], a[8]) |
|
311
|
0
|
|
|
|
|
|
+ MUL31(a[4], a[7]) |
|
312
|
0
|
|
|
|
|
|
+ MUL31(a[5], a[6])) << 1); |
|
313
|
0
|
|
|
|
|
|
t[12] = MUL31(a[6], a[6]) |
|
314
|
0
|
|
|
|
|
|
+ ((MUL31(a[4], a[8]) |
|
315
|
0
|
|
|
|
|
|
+ MUL31(a[5], a[7])) << 1); |
|
316
|
0
|
|
|
|
|
|
t[13] = ((MUL31(a[5], a[8]) |
|
317
|
0
|
|
|
|
|
|
+ MUL31(a[6], a[7])) << 1); |
|
318
|
0
|
|
|
|
|
|
t[14] = MUL31(a[7], a[7]) |
|
319
|
0
|
|
|
|
|
|
+ ((MUL31(a[6], a[8])) << 1); |
|
320
|
0
|
|
|
|
|
|
t[15] = ((MUL31(a[7], a[8])) << 1); |
|
321
|
0
|
|
|
|
|
|
t[16] = MUL31(a[8], a[8]); |
|
322
|
|
|
|
|
|
|
|
|
323
|
|
|
|
|
|
|
/* |
|
324
|
|
|
|
|
|
|
* Propagate carries. |
|
325
|
|
|
|
|
|
|
*/ |
|
326
|
0
|
|
|
|
|
|
cc = 0; |
|
327
|
0
|
0
|
|
|
|
|
for (i = 0; i < 17; i ++) { |
|
328
|
|
|
|
|
|
|
uint64_t w; |
|
329
|
|
|
|
|
|
|
|
|
330
|
0
|
|
|
|
|
|
w = t[i] + cc; |
|
331
|
0
|
|
|
|
|
|
d[i] = (uint32_t)w & 0x3FFFFFFF; |
|
332
|
0
|
|
|
|
|
|
cc = w >> 30; |
|
333
|
|
|
|
|
|
|
} |
|
334
|
0
|
|
|
|
|
|
d[17] = (uint32_t)cc; |
|
335
|
0
|
|
|
|
|
|
} |
|
336
|
|
|
|
|
|
|
|
|
337
|
|
|
|
|
|
|
/* |
|
338
|
|
|
|
|
|
|
* Perform a "final reduction" in field F255 (field for Curve25519) |
|
339
|
|
|
|
|
|
|
* The source value must be less than twice the modulus. If the value |
|
340
|
|
|
|
|
|
|
* is not lower than the modulus, then the modulus is subtracted and |
|
341
|
|
|
|
|
|
|
* this function returns 1; otherwise, it leaves it untouched and it |
|
342
|
|
|
|
|
|
|
* returns 0. |
|
343
|
|
|
|
|
|
|
*/ |
|
344
|
|
|
|
|
|
|
static uint32_t |
|
345
|
0
|
|
|
|
|
|
reduce_final_f255(uint32_t *d) |
|
346
|
|
|
|
|
|
|
{ |
|
347
|
|
|
|
|
|
|
uint32_t t[9]; |
|
348
|
|
|
|
|
|
|
uint32_t cc; |
|
349
|
|
|
|
|
|
|
int i; |
|
350
|
|
|
|
|
|
|
|
|
351
|
0
|
|
|
|
|
|
memcpy(t, d, sizeof t); |
|
352
|
0
|
|
|
|
|
|
cc = 19; |
|
353
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
354
|
|
|
|
|
|
|
uint32_t w; |
|
355
|
|
|
|
|
|
|
|
|
356
|
0
|
|
|
|
|
|
w = t[i] + cc; |
|
357
|
0
|
|
|
|
|
|
cc = w >> 30; |
|
358
|
0
|
|
|
|
|
|
t[i] = w & 0x3FFFFFFF; |
|
359
|
|
|
|
|
|
|
} |
|
360
|
0
|
|
|
|
|
|
cc = t[8] >> 15; |
|
361
|
0
|
|
|
|
|
|
t[8] &= 0x7FFF; |
|
362
|
0
|
|
|
|
|
|
CCOPY(cc, d, t, sizeof t); |
|
363
|
0
|
|
|
|
|
|
return cc; |
|
364
|
|
|
|
|
|
|
} |
|
365
|
|
|
|
|
|
|
|
|
366
|
|
|
|
|
|
|
/* |
|
367
|
|
|
|
|
|
|
* Perform a multiplication of two integers modulo 2^255-19. |
|
368
|
|
|
|
|
|
|
* Operands are arrays of 9 words, each containing 30 bits of data, in |
|
369
|
|
|
|
|
|
|
* little-endian order. Input value may be up to 2^256-1; on output, value |
|
370
|
|
|
|
|
|
|
* fits on 256 bits and is lower than twice the modulus. |
|
371
|
|
|
|
|
|
|
*/ |
|
372
|
|
|
|
|
|
|
static void |
|
373
|
0
|
|
|
|
|
|
f255_mul(uint32_t *d, const uint32_t *a, const uint32_t *b) |
|
374
|
|
|
|
|
|
|
{ |
|
375
|
|
|
|
|
|
|
uint32_t t[18], cc; |
|
376
|
|
|
|
|
|
|
int i; |
|
377
|
|
|
|
|
|
|
|
|
378
|
|
|
|
|
|
|
/* |
|
379
|
|
|
|
|
|
|
* Compute raw multiplication. All result words fit in 30 bits |
|
380
|
|
|
|
|
|
|
* each; upper word (t[17]) must fit on 2 bits, since the product |
|
381
|
|
|
|
|
|
|
* of two 256-bit integers must fit on 512 bits. |
|
382
|
|
|
|
|
|
|
*/ |
|
383
|
0
|
|
|
|
|
|
mul9(t, a, b); |
|
384
|
|
|
|
|
|
|
|
|
385
|
|
|
|
|
|
|
/* |
|
386
|
|
|
|
|
|
|
* Modular reduction: each high word is added where necessary. |
|
387
|
|
|
|
|
|
|
* Since the modulus is 2^255-19 and word 9 corresponds to |
|
388
|
|
|
|
|
|
|
* offset 9*30 = 270, word 9+k must be added to word k with |
|
389
|
|
|
|
|
|
|
* a factor of 19*2^15 = 622592. The extra bits in word 8 are also |
|
390
|
|
|
|
|
|
|
* added that way. |
|
391
|
|
|
|
|
|
|
* |
|
392
|
|
|
|
|
|
|
* Keeping the carry on 32 bits helps with 32-bit architectures, |
|
393
|
|
|
|
|
|
|
* and does not noticeably impact performance on 64-bit systems. |
|
394
|
|
|
|
|
|
|
*/ |
|
395
|
0
|
|
|
|
|
|
cc = MUL15(t[8] >> 15, 19); /* at most 19*(2^15-1) = 622573 */ |
|
396
|
0
|
|
|
|
|
|
t[8] &= 0x7FFF; |
|
397
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
398
|
|
|
|
|
|
|
uint64_t w; |
|
399
|
|
|
|
|
|
|
|
|
400
|
0
|
|
|
|
|
|
w = (uint64_t)t[i] + (uint64_t)cc + MUL31(t[i + 9], 622592); |
|
401
|
0
|
|
|
|
|
|
t[i] = (uint32_t)w & 0x3FFFFFFF; |
|
402
|
0
|
|
|
|
|
|
cc = (uint32_t)(w >> 30); /* at most 622592 */ |
|
403
|
|
|
|
|
|
|
} |
|
404
|
|
|
|
|
|
|
|
|
405
|
|
|
|
|
|
|
/* |
|
406
|
|
|
|
|
|
|
* Original product was up to (2^256-1)^2, i.e. a 512-bit integer. |
|
407
|
|
|
|
|
|
|
* This was split into two parts (upper of 257 bits, lower of 255 |
|
408
|
|
|
|
|
|
|
* bits), and the upper was added to the lower with a factor 19, |
|
409
|
|
|
|
|
|
|
* which means that the intermediate value is less than 77*2^255 |
|
410
|
|
|
|
|
|
|
* (19*2^257 + 2^255). Therefore, the extra bits "t[8] >> 15" are |
|
411
|
|
|
|
|
|
|
* less than 77, and the initial carry cc is at most 76*19 = 1444. |
|
412
|
|
|
|
|
|
|
*/ |
|
413
|
0
|
|
|
|
|
|
cc = MUL15(t[8] >> 15, 19); |
|
414
|
0
|
|
|
|
|
|
t[8] &= 0x7FFF; |
|
415
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
416
|
|
|
|
|
|
|
uint32_t z; |
|
417
|
|
|
|
|
|
|
|
|
418
|
0
|
|
|
|
|
|
z = t[i] + cc; |
|
419
|
0
|
|
|
|
|
|
d[i] = z & 0x3FFFFFFF; |
|
420
|
0
|
|
|
|
|
|
cc = z >> 30; |
|
421
|
|
|
|
|
|
|
} |
|
422
|
|
|
|
|
|
|
|
|
423
|
|
|
|
|
|
|
/* |
|
424
|
|
|
|
|
|
|
* Final result is at most 2^255 + 1443. In particular, the last |
|
425
|
|
|
|
|
|
|
* carry is necessarily 0, since t[8] was truncated to 15 bits. |
|
426
|
|
|
|
|
|
|
*/ |
|
427
|
0
|
|
|
|
|
|
} |
|
428
|
|
|
|
|
|
|
|
|
429
|
|
|
|
|
|
|
/* |
|
430
|
|
|
|
|
|
|
* Perform a squaring of an integer modulo 2^255-19. |
|
431
|
|
|
|
|
|
|
* Operands are arrays of 9 words, each containing 30 bits of data, in |
|
432
|
|
|
|
|
|
|
* little-endian order. Input value may be up to 2^256-1; on output, value |
|
433
|
|
|
|
|
|
|
* fits on 256 bits and is lower than twice the modulus. |
|
434
|
|
|
|
|
|
|
*/ |
|
435
|
|
|
|
|
|
|
static void |
|
436
|
0
|
|
|
|
|
|
f255_square(uint32_t *d, const uint32_t *a) |
|
437
|
|
|
|
|
|
|
{ |
|
438
|
|
|
|
|
|
|
uint32_t t[18], cc; |
|
439
|
|
|
|
|
|
|
int i; |
|
440
|
|
|
|
|
|
|
|
|
441
|
|
|
|
|
|
|
/* |
|
442
|
|
|
|
|
|
|
* Compute raw squaring. All result words fit in 30 bits |
|
443
|
|
|
|
|
|
|
* each; upper word (t[17]) must fit on 2 bits, since the square |
|
444
|
|
|
|
|
|
|
* of a 256-bit integers must fit on 512 bits. |
|
445
|
|
|
|
|
|
|
*/ |
|
446
|
0
|
|
|
|
|
|
square9(t, a); |
|
447
|
|
|
|
|
|
|
|
|
448
|
|
|
|
|
|
|
/* |
|
449
|
|
|
|
|
|
|
* Modular reduction: each high word is added where necessary. |
|
450
|
|
|
|
|
|
|
* See f255_mul() for details on the reduction and carry limits. |
|
451
|
|
|
|
|
|
|
*/ |
|
452
|
0
|
|
|
|
|
|
cc = MUL15(t[8] >> 15, 19); |
|
453
|
0
|
|
|
|
|
|
t[8] &= 0x7FFF; |
|
454
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
455
|
|
|
|
|
|
|
uint64_t w; |
|
456
|
|
|
|
|
|
|
|
|
457
|
0
|
|
|
|
|
|
w = (uint64_t)t[i] + (uint64_t)cc + MUL31(t[i + 9], 622592); |
|
458
|
0
|
|
|
|
|
|
t[i] = (uint32_t)w & 0x3FFFFFFF; |
|
459
|
0
|
|
|
|
|
|
cc = (uint32_t)(w >> 30); |
|
460
|
|
|
|
|
|
|
} |
|
461
|
0
|
|
|
|
|
|
cc = MUL15(t[8] >> 15, 19); |
|
462
|
0
|
|
|
|
|
|
t[8] &= 0x7FFF; |
|
463
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
464
|
|
|
|
|
|
|
uint32_t z; |
|
465
|
|
|
|
|
|
|
|
|
466
|
0
|
|
|
|
|
|
z = t[i] + cc; |
|
467
|
0
|
|
|
|
|
|
d[i] = z & 0x3FFFFFFF; |
|
468
|
0
|
|
|
|
|
|
cc = z >> 30; |
|
469
|
|
|
|
|
|
|
} |
|
470
|
0
|
|
|
|
|
|
} |
|
471
|
|
|
|
|
|
|
|
|
472
|
|
|
|
|
|
|
/* |
|
473
|
|
|
|
|
|
|
* Add two values in F255. Partial reduction is performed (down to less |
|
474
|
|
|
|
|
|
|
* than twice the modulus). |
|
475
|
|
|
|
|
|
|
*/ |
|
476
|
|
|
|
|
|
|
static void |
|
477
|
0
|
|
|
|
|
|
f255_add(uint32_t *d, const uint32_t *a, const uint32_t *b) |
|
478
|
|
|
|
|
|
|
{ |
|
479
|
|
|
|
|
|
|
/* |
|
480
|
|
|
|
|
|
|
* Since operand words fit on 30 bits, we can use 32-bit |
|
481
|
|
|
|
|
|
|
* variables throughout. |
|
482
|
|
|
|
|
|
|
*/ |
|
483
|
|
|
|
|
|
|
int i; |
|
484
|
|
|
|
|
|
|
uint32_t cc, w; |
|
485
|
|
|
|
|
|
|
|
|
486
|
0
|
|
|
|
|
|
cc = 0; |
|
487
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
488
|
0
|
|
|
|
|
|
w = a[i] + b[i] + cc; |
|
489
|
0
|
|
|
|
|
|
d[i] = w & 0x3FFFFFFF; |
|
490
|
0
|
|
|
|
|
|
cc = w >> 30; |
|
491
|
|
|
|
|
|
|
} |
|
492
|
0
|
|
|
|
|
|
cc = MUL15(w >> 15, 19); |
|
493
|
0
|
|
|
|
|
|
d[8] &= 0x7FFF; |
|
494
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
495
|
0
|
|
|
|
|
|
w = d[i] + cc; |
|
496
|
0
|
|
|
|
|
|
d[i] = w & 0x3FFFFFFF; |
|
497
|
0
|
|
|
|
|
|
cc = w >> 30; |
|
498
|
|
|
|
|
|
|
} |
|
499
|
0
|
|
|
|
|
|
} |
|
500
|
|
|
|
|
|
|
|
|
501
|
|
|
|
|
|
|
/* |
|
502
|
|
|
|
|
|
|
* Subtract one value from another in F255. Partial reduction is |
|
503
|
|
|
|
|
|
|
* performed (down to less than twice the modulus). |
|
504
|
|
|
|
|
|
|
*/ |
|
505
|
|
|
|
|
|
|
static void |
|
506
|
0
|
|
|
|
|
|
f255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b) |
|
507
|
|
|
|
|
|
|
{ |
|
508
|
|
|
|
|
|
|
/* |
|
509
|
|
|
|
|
|
|
* We actually compute a - b + 2*p, so that the final value is |
|
510
|
|
|
|
|
|
|
* necessarily positive. |
|
511
|
|
|
|
|
|
|
*/ |
|
512
|
|
|
|
|
|
|
int i; |
|
513
|
|
|
|
|
|
|
uint32_t cc, w; |
|
514
|
|
|
|
|
|
|
|
|
515
|
0
|
|
|
|
|
|
cc = (uint32_t)-38; |
|
516
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
517
|
0
|
|
|
|
|
|
w = a[i] - b[i] + cc; |
|
518
|
0
|
|
|
|
|
|
d[i] = w & 0x3FFFFFFF; |
|
519
|
0
|
|
|
|
|
|
cc = ARSH(w, 30); |
|
520
|
|
|
|
|
|
|
} |
|
521
|
0
|
|
|
|
|
|
cc = MUL15((w + 0x10000) >> 15, 19); |
|
522
|
0
|
|
|
|
|
|
d[8] &= 0x7FFF; |
|
523
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
524
|
0
|
|
|
|
|
|
w = d[i] + cc; |
|
525
|
0
|
|
|
|
|
|
d[i] = w & 0x3FFFFFFF; |
|
526
|
0
|
|
|
|
|
|
cc = w >> 30; |
|
527
|
|
|
|
|
|
|
} |
|
528
|
0
|
|
|
|
|
|
} |
|
529
|
|
|
|
|
|
|
|
|
530
|
|
|
|
|
|
|
/* |
|
531
|
|
|
|
|
|
|
* Multiply an integer by the 'A24' constant (121665). Partial reduction |
|
532
|
|
|
|
|
|
|
* is performed (down to less than twice the modulus). |
|
533
|
|
|
|
|
|
|
*/ |
|
534
|
|
|
|
|
|
|
static void |
|
535
|
0
|
|
|
|
|
|
f255_mul_a24(uint32_t *d, const uint32_t *a) |
|
536
|
|
|
|
|
|
|
{ |
|
537
|
|
|
|
|
|
|
int i; |
|
538
|
|
|
|
|
|
|
uint64_t w; |
|
539
|
|
|
|
|
|
|
uint32_t cc; |
|
540
|
|
|
|
|
|
|
|
|
541
|
|
|
|
|
|
|
/* |
|
542
|
|
|
|
|
|
|
* a[] is over 256 bits, thus a[8] has length at most 16 bits. |
|
543
|
|
|
|
|
|
|
* We single out the processing of the last word: intermediate |
|
544
|
|
|
|
|
|
|
* value w is up to 121665*2^16, yielding a carry for the next |
|
545
|
|
|
|
|
|
|
* loop of at most 19*(121665*2^16/2^15) = 4623289. |
|
546
|
|
|
|
|
|
|
*/ |
|
547
|
0
|
|
|
|
|
|
cc = 0; |
|
548
|
0
|
0
|
|
|
|
|
for (i = 0; i < 8; i ++) { |
|
549
|
0
|
|
|
|
|
|
w = MUL31(a[i], 121665) + (uint64_t)cc; |
|
550
|
0
|
|
|
|
|
|
d[i] = (uint32_t)w & 0x3FFFFFFF; |
|
551
|
0
|
|
|
|
|
|
cc = (uint32_t)(w >> 30); |
|
552
|
|
|
|
|
|
|
} |
|
553
|
0
|
|
|
|
|
|
w = MUL31(a[8], 121665) + (uint64_t)cc; |
|
554
|
0
|
|
|
|
|
|
d[8] = (uint32_t)w & 0x7FFF; |
|
555
|
0
|
|
|
|
|
|
cc = MUL15((uint32_t)(w >> 15), 19); |
|
556
|
|
|
|
|
|
|
|
|
557
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
558
|
|
|
|
|
|
|
uint32_t z; |
|
559
|
|
|
|
|
|
|
|
|
560
|
0
|
|
|
|
|
|
z = d[i] + cc; |
|
561
|
0
|
|
|
|
|
|
d[i] = z & 0x3FFFFFFF; |
|
562
|
0
|
|
|
|
|
|
cc = z >> 30; |
|
563
|
|
|
|
|
|
|
} |
|
564
|
0
|
|
|
|
|
|
} |
|
565
|
|
|
|
|
|
|
|
|
566
|
|
|
|
|
|
|
static const unsigned char GEN[] = { |
|
567
|
|
|
|
|
|
|
0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
|
568
|
|
|
|
|
|
|
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
|
569
|
|
|
|
|
|
|
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
|
570
|
|
|
|
|
|
|
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 |
|
571
|
|
|
|
|
|
|
}; |
|
572
|
|
|
|
|
|
|
|
|
573
|
|
|
|
|
|
|
static const unsigned char ORDER[] = { |
|
574
|
|
|
|
|
|
|
0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, |
|
575
|
|
|
|
|
|
|
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, |
|
576
|
|
|
|
|
|
|
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, |
|
577
|
|
|
|
|
|
|
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF |
|
578
|
|
|
|
|
|
|
}; |
|
579
|
|
|
|
|
|
|
|
|
580
|
|
|
|
|
|
|
static const unsigned char * |
|
581
|
0
|
|
|
|
|
|
api_generator(int curve, size_t *len) |
|
582
|
|
|
|
|
|
|
{ |
|
583
|
|
|
|
|
|
|
(void)curve; |
|
584
|
0
|
|
|
|
|
|
*len = 32; |
|
585
|
0
|
|
|
|
|
|
return GEN; |
|
586
|
|
|
|
|
|
|
} |
|
587
|
|
|
|
|
|
|
|
|
588
|
|
|
|
|
|
|
static const unsigned char * |
|
589
|
0
|
|
|
|
|
|
api_order(int curve, size_t *len) |
|
590
|
|
|
|
|
|
|
{ |
|
591
|
|
|
|
|
|
|
(void)curve; |
|
592
|
0
|
|
|
|
|
|
*len = 32; |
|
593
|
0
|
|
|
|
|
|
return ORDER; |
|
594
|
|
|
|
|
|
|
} |
|
595
|
|
|
|
|
|
|
|
|
596
|
|
|
|
|
|
|
static size_t |
|
597
|
0
|
|
|
|
|
|
api_xoff(int curve, size_t *len) |
|
598
|
|
|
|
|
|
|
{ |
|
599
|
|
|
|
|
|
|
(void)curve; |
|
600
|
0
|
|
|
|
|
|
*len = 32; |
|
601
|
0
|
|
|
|
|
|
return 0; |
|
602
|
|
|
|
|
|
|
} |
|
603
|
|
|
|
|
|
|
|
|
604
|
|
|
|
|
|
|
static void |
|
605
|
0
|
|
|
|
|
|
cswap(uint32_t *a, uint32_t *b, uint32_t ctl) |
|
606
|
|
|
|
|
|
|
{ |
|
607
|
|
|
|
|
|
|
int i; |
|
608
|
|
|
|
|
|
|
|
|
609
|
0
|
|
|
|
|
|
ctl = -ctl; |
|
610
|
0
|
0
|
|
|
|
|
for (i = 0; i < 9; i ++) { |
|
611
|
|
|
|
|
|
|
uint32_t aw, bw, tw; |
|
612
|
|
|
|
|
|
|
|
|
613
|
0
|
|
|
|
|
|
aw = a[i]; |
|
614
|
0
|
|
|
|
|
|
bw = b[i]; |
|
615
|
0
|
|
|
|
|
|
tw = ctl & (aw ^ bw); |
|
616
|
0
|
|
|
|
|
|
a[i] = aw ^ tw; |
|
617
|
0
|
|
|
|
|
|
b[i] = bw ^ tw; |
|
618
|
|
|
|
|
|
|
} |
|
619
|
0
|
|
|
|
|
|
} |
|
620
|
|
|
|
|
|
|
|
|
621
|
|
|
|
|
|
|
static uint32_t |
|
622
|
0
|
|
|
|
|
|
api_mul(unsigned char *G, size_t Glen, |
|
623
|
|
|
|
|
|
|
const unsigned char *kb, size_t kblen, int curve) |
|
624
|
|
|
|
|
|
|
{ |
|
625
|
|
|
|
|
|
|
uint32_t x1[9], x2[9], x3[9], z2[9], z3[9]; |
|
626
|
|
|
|
|
|
|
uint32_t a[9], aa[9], b[9], bb[9]; |
|
627
|
|
|
|
|
|
|
uint32_t c[9], d[9], e[9], da[9], cb[9]; |
|
628
|
|
|
|
|
|
|
unsigned char k[32]; |
|
629
|
|
|
|
|
|
|
uint32_t swap; |
|
630
|
|
|
|
|
|
|
int i; |
|
631
|
|
|
|
|
|
|
|
|
632
|
|
|
|
|
|
|
(void)curve; |
|
633
|
|
|
|
|
|
|
|
|
634
|
|
|
|
|
|
|
/* |
|
635
|
|
|
|
|
|
|
* Points are encoded over exactly 32 bytes. Multipliers must fit |
|
636
|
|
|
|
|
|
|
* in 32 bytes as well. |
|
637
|
|
|
|
|
|
|
* RFC 7748 mandates that the high bit of the last point byte must |
|
638
|
|
|
|
|
|
|
* be ignored/cleared. |
|
639
|
|
|
|
|
|
|
*/ |
|
640
|
0
|
0
|
|
|
|
|
if (Glen != 32 || kblen > 32) { |
|
|
|
0
|
|
|
|
|
|
|
641
|
0
|
|
|
|
|
|
return 0; |
|
642
|
|
|
|
|
|
|
} |
|
643
|
0
|
|
|
|
|
|
G[31] &= 0x7F; |
|
644
|
|
|
|
|
|
|
|
|
645
|
|
|
|
|
|
|
/* |
|
646
|
|
|
|
|
|
|
* Initialise variables x1, x2, z2, x3 and z3. We set all of them |
|
647
|
|
|
|
|
|
|
* into Montgomery representation. |
|
648
|
|
|
|
|
|
|
*/ |
|
649
|
0
|
|
|
|
|
|
x1[8] = le8_to_le30(x1, G, 32); |
|
650
|
0
|
|
|
|
|
|
memcpy(x3, x1, sizeof x1); |
|
651
|
0
|
|
|
|
|
|
memset(z2, 0, sizeof z2); |
|
652
|
0
|
|
|
|
|
|
memset(x2, 0, sizeof x2); |
|
653
|
0
|
|
|
|
|
|
x2[0] = 1; |
|
654
|
0
|
|
|
|
|
|
memset(z3, 0, sizeof z3); |
|
655
|
0
|
|
|
|
|
|
z3[0] = 1; |
|
656
|
|
|
|
|
|
|
|
|
657
|
0
|
|
|
|
|
|
memset(k, 0, (sizeof k) - kblen); |
|
658
|
0
|
|
|
|
|
|
memcpy(k + (sizeof k) - kblen, kb, kblen); |
|
659
|
0
|
|
|
|
|
|
k[31] &= 0xF8; |
|
660
|
0
|
|
|
|
|
|
k[0] &= 0x7F; |
|
661
|
0
|
|
|
|
|
|
k[0] |= 0x40; |
|
662
|
|
|
|
|
|
|
|
|
663
|
|
|
|
|
|
|
/* obsolete |
|
664
|
|
|
|
|
|
|
print_int("x1", x1); |
|
665
|
|
|
|
|
|
|
*/ |
|
666
|
|
|
|
|
|
|
|
|
667
|
0
|
|
|
|
|
|
swap = 0; |
|
668
|
0
|
0
|
|
|
|
|
for (i = 254; i >= 0; i --) { |
|
669
|
|
|
|
|
|
|
uint32_t kt; |
|
670
|
|
|
|
|
|
|
|
|
671
|
0
|
|
|
|
|
|
kt = (k[31 - (i >> 3)] >> (i & 7)) & 1; |
|
672
|
0
|
|
|
|
|
|
swap ^= kt; |
|
673
|
0
|
|
|
|
|
|
cswap(x2, x3, swap); |
|
674
|
0
|
|
|
|
|
|
cswap(z2, z3, swap); |
|
675
|
0
|
|
|
|
|
|
swap = kt; |
|
676
|
|
|
|
|
|
|
|
|
677
|
|
|
|
|
|
|
/* obsolete |
|
678
|
|
|
|
|
|
|
print_int("x2", x2); |
|
679
|
|
|
|
|
|
|
print_int("z2", z2); |
|
680
|
|
|
|
|
|
|
print_int("x3", x3); |
|
681
|
|
|
|
|
|
|
print_int("z3", z3); |
|
682
|
|
|
|
|
|
|
*/ |
|
683
|
|
|
|
|
|
|
|
|
684
|
0
|
|
|
|
|
|
f255_add(a, x2, z2); |
|
685
|
0
|
|
|
|
|
|
f255_square(aa, a); |
|
686
|
0
|
|
|
|
|
|
f255_sub(b, x2, z2); |
|
687
|
0
|
|
|
|
|
|
f255_square(bb, b); |
|
688
|
0
|
|
|
|
|
|
f255_sub(e, aa, bb); |
|
689
|
0
|
|
|
|
|
|
f255_add(c, x3, z3); |
|
690
|
0
|
|
|
|
|
|
f255_sub(d, x3, z3); |
|
691
|
0
|
|
|
|
|
|
f255_mul(da, d, a); |
|
692
|
0
|
|
|
|
|
|
f255_mul(cb, c, b); |
|
693
|
|
|
|
|
|
|
|
|
694
|
|
|
|
|
|
|
/* obsolete |
|
695
|
|
|
|
|
|
|
print_int("a ", a); |
|
696
|
|
|
|
|
|
|
print_int("aa", aa); |
|
697
|
|
|
|
|
|
|
print_int("b ", b); |
|
698
|
|
|
|
|
|
|
print_int("bb", bb); |
|
699
|
|
|
|
|
|
|
print_int("e ", e); |
|
700
|
|
|
|
|
|
|
print_int("c ", c); |
|
701
|
|
|
|
|
|
|
print_int("d ", d); |
|
702
|
|
|
|
|
|
|
print_int("da", da); |
|
703
|
|
|
|
|
|
|
print_int("cb", cb); |
|
704
|
|
|
|
|
|
|
*/ |
|
705
|
|
|
|
|
|
|
|
|
706
|
0
|
|
|
|
|
|
f255_add(x3, da, cb); |
|
707
|
0
|
|
|
|
|
|
f255_square(x3, x3); |
|
708
|
0
|
|
|
|
|
|
f255_sub(z3, da, cb); |
|
709
|
0
|
|
|
|
|
|
f255_square(z3, z3); |
|
710
|
0
|
|
|
|
|
|
f255_mul(z3, z3, x1); |
|
711
|
0
|
|
|
|
|
|
f255_mul(x2, aa, bb); |
|
712
|
0
|
|
|
|
|
|
f255_mul_a24(z2, e); |
|
713
|
0
|
|
|
|
|
|
f255_add(z2, z2, aa); |
|
714
|
0
|
|
|
|
|
|
f255_mul(z2, e, z2); |
|
715
|
|
|
|
|
|
|
|
|
716
|
|
|
|
|
|
|
/* obsolete |
|
717
|
|
|
|
|
|
|
print_int("x2", x2); |
|
718
|
|
|
|
|
|
|
print_int("z2", z2); |
|
719
|
|
|
|
|
|
|
print_int("x3", x3); |
|
720
|
|
|
|
|
|
|
print_int("z3", z3); |
|
721
|
|
|
|
|
|
|
*/ |
|
722
|
|
|
|
|
|
|
} |
|
723
|
0
|
|
|
|
|
|
cswap(x2, x3, swap); |
|
724
|
0
|
|
|
|
|
|
cswap(z2, z3, swap); |
|
725
|
|
|
|
|
|
|
|
|
726
|
|
|
|
|
|
|
/* |
|
727
|
|
|
|
|
|
|
* Inverse z2 with a modular exponentiation. This is a simple |
|
728
|
|
|
|
|
|
|
* square-and-multiply algorithm; we mutualise most non-squarings |
|
729
|
|
|
|
|
|
|
* since the exponent contains almost only ones. |
|
730
|
|
|
|
|
|
|
*/ |
|
731
|
0
|
|
|
|
|
|
memcpy(a, z2, sizeof z2); |
|
732
|
0
|
0
|
|
|
|
|
for (i = 0; i < 15; i ++) { |
|
733
|
0
|
|
|
|
|
|
f255_square(a, a); |
|
734
|
0
|
|
|
|
|
|
f255_mul(a, a, z2); |
|
735
|
|
|
|
|
|
|
} |
|
736
|
0
|
|
|
|
|
|
memcpy(b, a, sizeof a); |
|
737
|
0
|
0
|
|
|
|
|
for (i = 0; i < 14; i ++) { |
|
738
|
|
|
|
|
|
|
int j; |
|
739
|
|
|
|
|
|
|
|
|
740
|
0
|
0
|
|
|
|
|
for (j = 0; j < 16; j ++) { |
|
741
|
0
|
|
|
|
|
|
f255_square(b, b); |
|
742
|
|
|
|
|
|
|
} |
|
743
|
0
|
|
|
|
|
|
f255_mul(b, b, a); |
|
744
|
|
|
|
|
|
|
} |
|
745
|
0
|
0
|
|
|
|
|
for (i = 14; i >= 0; i --) { |
|
746
|
0
|
|
|
|
|
|
f255_square(b, b); |
|
747
|
0
|
0
|
|
|
|
|
if ((0xFFEB >> i) & 1) { |
|
748
|
0
|
|
|
|
|
|
f255_mul(b, z2, b); |
|
749
|
|
|
|
|
|
|
} |
|
750
|
|
|
|
|
|
|
} |
|
751
|
0
|
|
|
|
|
|
f255_mul(x2, x2, b); |
|
752
|
0
|
|
|
|
|
|
reduce_final_f255(x2); |
|
753
|
0
|
|
|
|
|
|
le30_to_le8(G, 32, x2); |
|
754
|
0
|
|
|
|
|
|
return 1; |
|
755
|
|
|
|
|
|
|
} |
|
756
|
|
|
|
|
|
|
|
|
757
|
|
|
|
|
|
|
static size_t |
|
758
|
0
|
|
|
|
|
|
api_mulgen(unsigned char *R, |
|
759
|
|
|
|
|
|
|
const unsigned char *x, size_t xlen, int curve) |
|
760
|
|
|
|
|
|
|
{ |
|
761
|
|
|
|
|
|
|
const unsigned char *G; |
|
762
|
|
|
|
|
|
|
size_t Glen; |
|
763
|
|
|
|
|
|
|
|
|
764
|
0
|
|
|
|
|
|
G = api_generator(curve, &Glen); |
|
765
|
0
|
|
|
|
|
|
memcpy(R, G, Glen); |
|
766
|
0
|
|
|
|
|
|
api_mul(R, Glen, x, xlen, curve); |
|
767
|
0
|
|
|
|
|
|
return Glen; |
|
768
|
|
|
|
|
|
|
} |
|
769
|
|
|
|
|
|
|
|
|
770
|
|
|
|
|
|
|
static uint32_t |
|
771
|
0
|
|
|
|
|
|
api_muladd(unsigned char *A, const unsigned char *B, size_t len, |
|
772
|
|
|
|
|
|
|
const unsigned char *x, size_t xlen, |
|
773
|
|
|
|
|
|
|
const unsigned char *y, size_t ylen, int curve) |
|
774
|
|
|
|
|
|
|
{ |
|
775
|
|
|
|
|
|
|
/* |
|
776
|
|
|
|
|
|
|
* We don't implement this method, since it is used for ECDSA |
|
777
|
|
|
|
|
|
|
* only, and there is no ECDSA over Curve25519 (which instead |
|
778
|
|
|
|
|
|
|
* uses EdDSA). |
|
779
|
|
|
|
|
|
|
*/ |
|
780
|
|
|
|
|
|
|
(void)A; |
|
781
|
|
|
|
|
|
|
(void)B; |
|
782
|
|
|
|
|
|
|
(void)len; |
|
783
|
|
|
|
|
|
|
(void)x; |
|
784
|
|
|
|
|
|
|
(void)xlen; |
|
785
|
|
|
|
|
|
|
(void)y; |
|
786
|
|
|
|
|
|
|
(void)ylen; |
|
787
|
|
|
|
|
|
|
(void)curve; |
|
788
|
0
|
|
|
|
|
|
return 0; |
|
789
|
|
|
|
|
|
|
} |
|
790
|
|
|
|
|
|
|
|
|
791
|
|
|
|
|
|
|
/* see bearssl_ec.h */ |
|
792
|
|
|
|
|
|
|
const br_ec_impl br_ec_c25519_m31 = { |
|
793
|
|
|
|
|
|
|
(uint32_t)0x20000000, |
|
794
|
|
|
|
|
|
|
&api_generator, |
|
795
|
|
|
|
|
|
|
&api_order, |
|
796
|
|
|
|
|
|
|
&api_xoff, |
|
797
|
|
|
|
|
|
|
&api_mul, |
|
798
|
|
|
|
|
|
|
&api_mulgen, |
|
799
|
|
|
|
|
|
|
&api_muladd |
|
800
|
|
|
|
|
|
|
}; |