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20
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1 ???using System; |
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2 using UCIS.NaCl; |
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3 using System.Runtime.InteropServices; |
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4 |
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5 namespace UCIS.NaCl.crypto_sign { |
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6 public static class edwards25519sha512batch { |
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7 public const int SECRETKEYBYTES = 64; |
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8 public const int PUBLICKEYBYTES = 32; |
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9 public const int CRYPTO_BYTES = 64; |
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10 |
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11 /*Arithmetic modulo the group order n = 2^252 + 27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 */ |
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12 |
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13 unsafe struct sc25519 { |
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14 public fixed UInt32 v[32]; //crypto_uint32 v[32]; |
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15 |
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16 static UInt32[] m = new UInt32[32] {0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, 0xDE, 0xF9, 0xDE, 0x14, |
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17 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10}; |
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18 |
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19 static UInt32[] mu = new UInt32[33] {0x1B, 0x13, 0x2C, 0x0A, 0xA3, 0xE5, 0x9C, 0xED, 0xA7, 0x29, 0x63, 0x08, 0x5D, 0x21, 0x06, 0x21, |
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20 0xEB, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0F}; |
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21 |
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22 /* Reduce coefficients of r before calling reduce_add_sub */ |
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23 static unsafe void reduce_add_sub(sc25519* r) { |
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24 int i, b = 0, pb = 0, nb; |
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25 Byte* t = stackalloc Byte[32]; |
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26 |
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27 for (i = 0; i < 32; i++) { |
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28 b = (r->v[i] < pb + m[i]) ? 1 : 0; |
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29 t[i] = (Byte)(r->v[i] - pb - m[i] + b * 256); |
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30 pb = b; |
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31 } |
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32 nb = 1 - b; |
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33 for (i = 0; i < 32; i++) r->v[i] = (uint)(r->v[i] * b + t[i] * nb); |
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34 } |
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35 |
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36 /* Reduce coefficients of x before calling barrett_reduce */ |
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37 static unsafe void barrett_reduce(sc25519* r, UInt32* x) { // const crypto_uint32 x[64] |
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38 /* See HAC, Alg. 14.42 */ |
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39 UInt32* q2 = stackalloc UInt32[66]; // { 0 }; |
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40 for (int z = 0; z < 66; z++) q2[z] = 0; |
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41 UInt32* q3 = q2 + 33; |
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42 UInt32* r1 = stackalloc UInt32[33]; |
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43 UInt32* r2 = stackalloc UInt32[33]; // { 0 }; |
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44 for (int z = 0; z < 33; z++) r2[z] = 0; |
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45 UInt32 carry; |
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46 int b, pb = 0; |
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47 |
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48 for (int i = 0; i < 33; i++) |
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49 for (int j = 0; j < 33; j++) |
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50 if (i + j >= 31) q2[i + j] += mu[i] * x[j + 31]; |
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51 carry = q2[31] >> 8; |
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52 q2[32] += carry; |
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53 carry = q2[32] >> 8; |
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54 q2[33] += carry; |
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55 |
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56 for (int i = 0; i < 33; i++) r1[i] = x[i]; |
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57 for (int i = 0; i < 32; i++) |
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58 for (int j = 0; j < 33; j++) |
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59 if (i + j < 33) r2[i + j] += m[i] * q3[j]; |
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60 |
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61 for (int i = 0; i < 32; i++) { |
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62 carry = r2[i] >> 8; |
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63 r2[i + 1] += carry; |
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64 r2[i] &= 0xff; |
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65 } |
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66 |
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67 for (int i = 0; i < 32; i++) { |
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68 b = (r1[i] < pb + r2[i]) ? 1 : 0; |
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69 r->v[i] = (uint)(r1[i] - pb - r2[i] + b * 256); |
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70 pb = b; |
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71 } |
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72 |
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73 /* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3 |
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74 * If so: Handle it here! |
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75 */ |
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76 |
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77 reduce_add_sub(r); |
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78 reduce_add_sub(r); |
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79 } |
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80 |
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81 /* |
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82 static int iszero(const sc25519 *x) |
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83 { |
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84 // Implement |
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85 return 0; |
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86 } |
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87 */ |
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88 |
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89 public static unsafe void sc25519_from32bytes(sc25519* r, Byte* x) { //const unsigned char x[32] |
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90 UInt32* t = stackalloc UInt32[64]; // { 0 }; |
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91 for (int i = 0; i < 32; i++) t[i] = x[i]; |
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92 for (int i = 32; i < 64; i++) t[i] = 0; |
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93 barrett_reduce(r, t); |
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94 } |
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95 |
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96 public static unsafe void sc25519_from64bytes(sc25519* r, Byte* x) { //const unsigned char x[64] |
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97 UInt32* t = stackalloc UInt32[64]; // { 0 }; |
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98 for (int i = 0; i < 64; i++) t[i] = x[i]; |
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99 barrett_reduce(r, t); |
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100 } |
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101 |
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102 /* XXX: What we actually want for crypto_group is probably just something like |
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103 * void sc25519_frombytes(sc25519 *r, const unsigned char *x, size_t xlen) |
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104 */ |
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105 |
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106 public static unsafe void sc25519_to32bytes(Byte* r, sc25519* x) { //unsigned char r[32] |
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107 for (int i = 0; i < 32; i++) r[i] = (Byte)x->v[i]; |
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108 } |
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109 |
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110 public static unsafe void sc25519_add(sc25519* r, sc25519* x, sc25519* y) { |
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111 for (int i = 0; i < 32; i++) r->v[i] = x->v[i] + y->v[i]; |
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112 for (int i = 0; i < 31; i++) { |
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113 uint carry = r->v[i] >> 8; |
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114 r->v[i + 1] += carry; |
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115 r->v[i] &= 0xff; |
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116 } |
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117 reduce_add_sub(r); |
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118 } |
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119 |
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120 public static unsafe void sc25519_mul(sc25519* r, sc25519* x, sc25519* y) { |
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121 UInt32* t = stackalloc UInt32[64]; |
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122 for (int i = 0; i < 64; i++) t[i] = 0; |
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123 |
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124 for (int i = 0; i < 32; i++) |
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125 for (int j = 0; j < 32; j++) |
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126 t[i + j] += x->v[i] * y->v[j]; |
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127 |
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128 /* Reduce coefficients */ |
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129 for (int i = 0; i < 63; i++) { |
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130 uint carry = t[i] >> 8; |
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131 t[i + 1] += carry; |
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132 t[i] &= 0xff; |
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133 } |
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134 |
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135 barrett_reduce(r, t); |
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136 } |
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137 |
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138 public static unsafe void sc25519_square(sc25519* r, sc25519* x) { |
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139 sc25519_mul(r, x, x); |
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140 } |
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141 } |
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142 struct ge25519 { |
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143 public fe25519 x; |
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144 public fe25519 y; |
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145 public fe25519 z; |
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146 public fe25519 t; |
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147 |
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148 struct ge25519_p1p1 { |
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149 public fe25519 x; |
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150 public fe25519 z; |
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151 public fe25519 y; |
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152 public fe25519 t; |
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153 } |
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154 struct ge25519_p2 { |
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155 public fe25519 x; |
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156 public fe25519 y; |
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157 public fe25519 z; |
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158 } |
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159 |
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160 /* Windowsize for fixed-window scalar multiplication */ |
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161 const int WINDOWSIZE = 2; //#define WINDOWSIZE 2 /* Should be 1,2, or 4 */ |
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162 const int WINDOWMASK = ((1 << WINDOWSIZE) - 1); //#define WINDOWMASK ((1<<WINDOWSIZE)-1) |
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163 |
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164 /* packed parameter d in the Edwards curve equation */ |
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165 static Byte[] ecd = new Byte[32] {0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00, |
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166 0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}; |
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167 |
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168 /* Packed coordinates of the base point */ |
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169 static Byte[] ge25519_base_x = new Byte[32] {0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69, |
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170 0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}; |
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171 static Byte[] ge25519_base_y = new Byte[32] {0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, |
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172 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}; |
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173 static Byte[] ge25519_base_z = new Byte[32] { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; |
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174 static Byte[] ge25519_base_t = new Byte[32] {0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20, |
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175 0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}; |
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176 |
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177 /* Packed coordinates of the neutral element */ |
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178 static Byte[] ge25519_neutral_x = new Byte[32]; // { 0 }; |
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179 static Byte[] ge25519_neutral_y = new Byte[32] { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; |
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180 static Byte[] ge25519_neutral_z = new Byte[32] { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; |
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181 static Byte[] ge25519_neutral_t = new Byte[32]; // { 0 }; |
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182 |
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183 static unsafe void p1p1_to_p2(ge25519_p2* r, ge25519_p1p1* p) { |
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184 fe25519.fe25519_mul(&r->x, &p->x, &p->t); |
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185 fe25519.fe25519_mul(&r->y, &p->y, &p->z); |
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186 fe25519.fe25519_mul(&r->z, &p->z, &p->t); |
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187 } |
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188 |
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189 static unsafe void p1p1_to_p3(ge25519* r, ge25519_p1p1* p) { |
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190 p1p1_to_p2((ge25519_p2*)r, p); |
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191 fe25519.fe25519_mul(&r->t, &p->x, &p->y); |
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192 } |
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193 |
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194 /* Constant-time version of: if(b) r = p */ |
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195 static unsafe void cmov_p3(ge25519* r, ge25519* p, Byte b) { |
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196 fe25519.fe25519_cmov(&r->x, &p->x, b); |
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197 fe25519.fe25519_cmov(&r->y, &p->y, b); |
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198 fe25519.fe25519_cmov(&r->z, &p->z, b); |
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199 fe25519.fe25519_cmov(&r->t, &p->t, b); |
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200 } |
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201 |
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202 /* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */ |
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203 static unsafe void dbl_p1p1(ge25519_p1p1* r, ge25519_p2* p) { |
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204 fe25519 a, b, c, d; |
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205 fe25519.fe25519_square(&a, &p->x); |
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206 fe25519.fe25519_square(&b, &p->y); |
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207 fe25519.fe25519_square(&c, &p->z); |
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208 fe25519.fe25519_add(&c, &c, &c); |
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209 fe25519.fe25519_neg(&d, &a); |
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210 |
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211 fe25519.fe25519_add(&r->x, &p->x, &p->y); |
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212 fe25519.fe25519_square(&r->x, &r->x); |
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213 fe25519.fe25519_sub(&r->x, &r->x, &a); |
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214 fe25519.fe25519_sub(&r->x, &r->x, &b); |
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215 fe25519.fe25519_add(&r->z, &d, &b); |
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216 fe25519.fe25519_sub(&r->t, &r->z, &c); |
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217 fe25519.fe25519_sub(&r->y, &d, &b); |
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218 } |
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219 |
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220 static unsafe void add_p1p1(ge25519_p1p1* r, ge25519* p, ge25519* q) { |
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221 fe25519 a, b, c, d, t, fd; |
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222 fixed (Byte* ecdp = ecd) fe25519.fe25519_unpack(&fd, ecdp); |
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223 |
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224 fe25519.fe25519_sub(&a, &p->y, &p->x); // A = (Y1-X1)*(Y2-X2) |
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225 fe25519.fe25519_sub(&t, &q->y, &q->x); |
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226 fe25519.fe25519_mul(&a, &a, &t); |
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227 fe25519.fe25519_add(&b, &p->x, &p->y); // B = (Y1+X1)*(Y2+X2) |
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228 fe25519.fe25519_add(&t, &q->x, &q->y); |
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229 fe25519.fe25519_mul(&b, &b, &t); |
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230 fe25519.fe25519_mul(&c, &p->t, &q->t); //C = T1*k*T2 |
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231 fe25519.fe25519_mul(&c, &c, &fd); |
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232 fe25519.fe25519_add(&c, &c, &c); //XXX: Can save this addition by precomputing 2*ecd |
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233 fe25519.fe25519_mul(&d, &p->z, &q->z); //D = Z1*2*Z2 |
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234 fe25519.fe25519_add(&d, &d, &d); |
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235 fe25519.fe25519_sub(&r->x, &b, &a); // E = B-A |
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236 fe25519.fe25519_sub(&r->t, &d, &c); // F = D-C |
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237 fe25519.fe25519_add(&r->z, &d, &c); // G = D+C |
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238 fe25519.fe25519_add(&r->y, &b, &a); // H = B+A |
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239 } |
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240 |
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241 /* ******************************************************************** |
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242 * EXPORTED FUNCTIONS |
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243 ******************************************************************** */ |
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244 |
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245 /* return 0 on success, -1 otherwise */ |
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246 public unsafe static Boolean ge25519_unpack_vartime(ge25519* r, Byte* p) { //const unsigned char p[32] |
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247 Boolean ret; |
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248 fe25519 t, fd; |
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249 fe25519.fe25519_setone(&r->z); |
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250 fixed (Byte* ecdp = ecd) fe25519.fe25519_unpack(&fd, ecdp); |
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251 Byte par = (Byte)(p[31] >> 7); |
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252 fe25519.fe25519_unpack(&r->y, p); |
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253 fe25519.fe25519_square(&r->x, &r->y); |
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254 fe25519.fe25519_mul(&t, &r->x, &fd); |
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255 fe25519.fe25519_sub(&r->x, &r->x, &r->z); |
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256 fe25519.fe25519_add(&t, &r->z, &t); |
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257 fe25519.fe25519_invert(&t, &t); |
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258 fe25519.fe25519_mul(&r->x, &r->x, &t); |
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259 ret = fe25519.fe25519_sqrt_vartime(&r->x, &r->x, par); |
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260 fe25519.fe25519_mul(&r->t, &r->x, &r->y); |
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261 return ret; |
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262 } |
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263 |
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264 public static unsafe void ge25519_pack(Byte* r, ge25519* p) { //unsigned char r[32] |
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265 fe25519 tx, ty, zi; |
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266 fe25519.fe25519_invert(&zi, &p->z); |
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267 fe25519.fe25519_mul(&tx, &p->x, &zi); |
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268 fe25519.fe25519_mul(&ty, &p->y, &zi); |
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269 fe25519.fe25519_pack(r, &ty); |
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270 r[31] ^= (Byte)(fe25519.fe25519_getparity(&tx) << 7); |
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271 } |
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272 |
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273 public static unsafe void ge25519_add(ge25519* r, ge25519* p, ge25519* q) { |
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274 ge25519_p1p1 grp1p1; |
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275 add_p1p1(&grp1p1, p, q); |
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276 p1p1_to_p3(r, &grp1p1); |
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277 } |
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278 |
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279 public static unsafe void ge25519_double(ge25519* r, ge25519* p) { |
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280 ge25519_p1p1 grp1p1; |
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281 dbl_p1p1(&grp1p1, (ge25519_p2*)p); |
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282 p1p1_to_p3(r, &grp1p1); |
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283 } |
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284 |
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285 public static unsafe void ge25519_scalarmult(ge25519* r, ge25519* p, sc25519* s) { |
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286 int i, j, k; |
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287 ge25519 g; |
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288 fixed (Byte* ge25519_neutral_xp = ge25519_neutral_x) fe25519.fe25519_unpack(&g.x, ge25519_neutral_xp); |
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289 fixed (Byte* ge25519_neutral_yp = ge25519_neutral_y) fe25519.fe25519_unpack(&g.y, ge25519_neutral_yp); |
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290 fixed (Byte* ge25519_neutral_zp = ge25519_neutral_z) fe25519.fe25519_unpack(&g.z, ge25519_neutral_zp); |
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291 fixed (Byte* ge25519_neutral_tp = ge25519_neutral_t) fe25519.fe25519_unpack(&g.t, ge25519_neutral_tp); |
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292 |
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293 ge25519[] pre = new ge25519[(1 << WINDOWSIZE)]; |
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294 ge25519 t; |
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295 ge25519_p1p1 tp1p1; |
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296 Byte w; |
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297 Byte* sb = stackalloc Byte[32]; |
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298 sc25519.sc25519_to32bytes(sb, s); |
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299 |
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300 // Precomputation |
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301 pre[0] = g; |
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302 pre[1] = *p; |
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303 for (i = 2; i < (1 << WINDOWSIZE); i += 2) { |
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304 fixed (ge25519* prep = pre) { |
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305 dbl_p1p1(&tp1p1, (ge25519_p2*)(prep + i / 2)); |
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306 p1p1_to_p3(prep + i, &tp1p1); |
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307 add_p1p1(&tp1p1, prep + i, prep + 1); |
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308 p1p1_to_p3(prep + i + 1, &tp1p1); |
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309 } |
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310 } |
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311 |
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312 // Fixed-window scalar multiplication |
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313 for (i = 32; i > 0; i--) { |
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314 for (j = 8 - WINDOWSIZE; j >= 0; j -= WINDOWSIZE) { |
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315 for (k = 0; k < WINDOWSIZE - 1; k++) { |
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316 dbl_p1p1(&tp1p1, (ge25519_p2*)&g); |
|
|
317 p1p1_to_p2((ge25519_p2*)&g, &tp1p1); |
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|
318 } |
|
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319 dbl_p1p1(&tp1p1, (ge25519_p2*)&g); |
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|
320 p1p1_to_p3(&g, &tp1p1); |
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321 // Cache-timing resistant loading of precomputed value: |
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322 w = (Byte)((sb[i - 1] >> j) & WINDOWMASK); |
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323 t = pre[0]; |
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|
324 for (k = 1; k < (1 << WINDOWSIZE); k++) |
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325 fixed (ge25519* prekp = &pre[k]) cmov_p3(&t, prekp, (k == w) ? (Byte)1 : (Byte)0); |
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|
326 |
|
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327 add_p1p1(&tp1p1, &g, &t); |
|
|
328 if (j != 0) p1p1_to_p2((ge25519_p2*)&g, &tp1p1); |
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329 else p1p1_to_p3(&g, &tp1p1); /* convert to p3 representation at the end */ |
|
|
330 } |
|
|
331 } |
|
|
332 r->x = g.x; |
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333 r->y = g.y; |
|
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334 r->z = g.z; |
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|
335 r->t = g.t; |
|
|
336 } |
|
|
337 |
|
|
338 public unsafe static void ge25519_scalarmult_base(ge25519* r, sc25519* s) { |
|
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339 /* XXX: Better algorithm for known-base-point scalar multiplication */ |
|
|
340 ge25519 t; |
|
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341 fixed (Byte* ge25519_base_xp = ge25519_base_x) fe25519.fe25519_unpack(&t.x, ge25519_base_xp); |
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342 fixed (Byte* ge25519_base_yp = ge25519_base_y) fe25519.fe25519_unpack(&t.y, ge25519_base_yp); |
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343 fixed (Byte* ge25519_base_zp = ge25519_base_z) fe25519.fe25519_unpack(&t.z, ge25519_base_zp); |
|
|
344 fixed (Byte* ge25519_base_tp = ge25519_base_t) fe25519.fe25519_unpack(&t.t, ge25519_base_tp); |
|
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345 ge25519_scalarmult(r, &t, s); |
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346 } |
|
|
347 } |
|
|
348 unsafe struct fe25519 { |
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349 public fixed UInt32 v[32]; // crypto_uint32 v[32]; |
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350 |
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351 const int WINDOWSIZE = 4; //#define WINDOWSIZE 4 /* Should be 1,2, or 4 */ |
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352 const int WINDOWMASK = ((1 << WINDOWSIZE) - 1); //#define WINDOWMASK ((1<<WINDOWSIZE)-1) |
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353 |
|
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354 static unsafe void reduce_add_sub(fe25519* r) { |
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355 for (int rep = 0; rep < 4; rep++) { |
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356 UInt32 t = r->v[31] >> 7; |
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357 r->v[31] &= 127; |
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|
358 t *= 19; |
|
|
359 r->v[0] += t; |
|
|
360 for (int i = 0; i < 31; i++) { |
|
|
361 t = r->v[i] >> 8; |
|
|
362 r->v[i + 1] += t; |
|
|
363 r->v[i] &= 255; |
|
|
364 } |
|
|
365 } |
|
|
366 } |
|
|
367 |
|
|
368 unsafe static void reduce_mul(fe25519* r) { |
|
|
369 for (int rep = 0; rep < 2; rep++) { |
|
|
370 UInt32 t = r->v[31] >> 7; |
|
|
371 r->v[31] &= 127; |
|
|
372 t *= 19; |
|
|
373 r->v[0] += t; |
|
|
374 for (int i = 0; i < 31; i++) { |
|
|
375 t = r->v[i] >> 8; |
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|
376 r->v[i + 1] += t; |
|
|
377 r->v[i] &= 255; |
|
|
378 } |
|
|
379 } |
|
|
380 } |
|
|
381 |
|
|
382 /* reduction modulo 2^255-19 */ |
|
|
383 unsafe static void freeze(fe25519* r) { |
|
|
384 UInt32 m = (r->v[31] == 127) ? 1u : 0; |
|
|
385 for (int i = 30; i > 1; i--) |
|
|
386 m *= (r->v[i] == 255) ? 1u : 0; |
|
|
387 m *= (r->v[0] >= 237) ? 1u : 0; |
|
|
388 |
|
|
389 r->v[31] -= m * 127; |
|
|
390 for (int i = 30; i > 0; i--) |
|
|
391 r->v[i] -= m * 255; |
|
|
392 r->v[0] -= m * 237; |
|
|
393 } |
|
|
394 |
|
|
395 /*freeze input before calling isone*/ |
|
|
396 unsafe static Boolean isone(fe25519* x) { |
|
|
397 bool r = x->v[0] == 1; |
|
|
398 for (int i = 1; i < 32; i++) r &= (x->v[i] == 0); |
|
|
399 return r; |
|
|
400 } |
|
|
401 |
|
|
402 /*freeze input before calling iszero*/ |
|
|
403 unsafe static Boolean iszero(fe25519* x) { |
|
|
404 bool r = (x->v[0] == 0); |
|
|
405 for (int i = 1; i < 32; i++) r &= (x->v[i] == 0); |
|
|
406 return r; |
|
|
407 } |
|
|
408 |
|
|
409 |
|
|
410 unsafe static Boolean issquare(fe25519* x) { |
|
|
411 Byte[] e = new Byte[32] { 0xf6, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f }; /* (p-1)/2 */ |
|
|
412 fe25519 t; |
|
|
413 |
|
|
414 fixed (Byte* ep = e) fe25519_pow(&t, x, ep); |
|
|
415 freeze(&t); |
|
|
416 return isone(&t) || iszero(&t); |
|
|
417 } |
|
|
418 |
|
|
419 public static unsafe void fe25519_unpack(fe25519* r, Byte* x) { //const unsigned char x[32] |
|
|
420 for (int i = 0; i < 32; i++) r->v[i] = x[i]; |
|
|
421 r->v[31] &= 127; |
|
|
422 } |
|
|
423 |
|
|
424 /* Assumes input x being reduced mod 2^255 */ |
|
|
425 public static unsafe void fe25519_pack(Byte* r, fe25519* x) { //unsigned char r[32] |
|
|
426 for (int i = 0; i < 32; i++) |
|
|
427 r[i] = (byte)x->v[i]; |
|
|
428 |
|
|
429 /* freeze byte array */ |
|
|
430 UInt32 m = (r[31] == 127) ? 1u : 0; /* XXX: some compilers might use branches; fix */ |
|
|
431 for (int i = 30; i > 1; i--) |
|
|
432 m *= (r[i] == 255) ? 1u : 0; |
|
|
433 m *= (r[0] >= 237) ? 1u : 0; |
|
|
434 r[31] -= (byte)(m * 127); |
|
|
435 for (int i = 30; i > 0; i--) |
|
|
436 r[i] -= (byte)(m * 255); |
|
|
437 r[0] -= (byte)(m * 237); |
|
|
438 } |
|
|
439 |
|
|
440 public static unsafe void fe25519_cmov(fe25519* r, fe25519* x, Byte b) { |
|
|
441 Byte nb = (Byte)(1 - b); |
|
|
442 for (int i = 0; i < 32; i++) r->v[i] = nb * r->v[i] + b * x->v[i]; |
|
|
443 } |
|
|
444 |
|
|
445 public static unsafe Byte fe25519_getparity(fe25519* x) { |
|
|
446 fe25519 t = new fe25519(); |
|
|
447 for (int i = 0; i < 32; i++) t.v[i] = x->v[i]; |
|
|
448 freeze(&t); |
|
|
449 return (Byte)(t.v[0] & 1); |
|
|
450 } |
|
|
451 |
|
|
452 public static unsafe void fe25519_setone(fe25519* r) { |
|
|
453 r->v[0] = 1; |
|
|
454 for (int i = 1; i < 32; i++) r->v[i] = 0; |
|
|
455 } |
|
|
456 |
|
|
457 static unsafe void fe25519_setzero(fe25519* r) { |
|
|
458 for (int i = 0; i < 32; i++) r->v[i] = 0; |
|
|
459 } |
|
|
460 |
|
|
461 public static unsafe void fe25519_neg(fe25519* r, fe25519* x) { |
|
|
462 fe25519 t = new fe25519(); |
|
|
463 for (int i = 0; i < 32; i++) t.v[i] = x->v[i]; |
|
|
464 fe25519_setzero(r); |
|
|
465 fe25519_sub(r, r, &t); |
|
|
466 } |
|
|
467 |
|
|
468 public static unsafe void fe25519_add(fe25519* r, fe25519* x, fe25519* y) { |
|
|
469 for (int i = 0; i < 32; i++) r->v[i] = x->v[i] + y->v[i]; |
|
|
470 reduce_add_sub(r); |
|
|
471 } |
|
|
472 |
|
|
473 public static unsafe void fe25519_sub(fe25519* r, fe25519* x, fe25519* y) { |
|
|
474 UInt32* t = stackalloc UInt32[32]; |
|
|
475 t[0] = x->v[0] + 0x1da; |
|
|
476 t[31] = x->v[31] + 0xfe; |
|
|
477 for (int i = 1; i < 31; i++) t[i] = x->v[i] + 0x1fe; |
|
|
478 for (int i = 0; i < 32; i++) r->v[i] = t[i] - y->v[i]; |
|
|
479 reduce_add_sub(r); |
|
|
480 } |
|
|
481 |
|
|
482 public static unsafe void fe25519_mul(fe25519* r, fe25519* x, fe25519* y) { |
|
|
483 UInt32* t = stackalloc UInt32[63]; |
|
|
484 for (int i = 0; i < 63; i++) t[i] = 0; |
|
|
485 for (int i = 0; i < 32; i++) |
|
|
486 for (int j = 0; j < 32; j++) |
|
|
487 t[i + j] += x->v[i] * y->v[j]; |
|
|
488 |
|
|
489 for (int i = 32; i < 63; i++) |
|
|
490 r->v[i - 32] = t[i - 32] + 38 * t[i]; |
|
|
491 r->v[31] = t[31]; /* result now in r[0]...r[31] */ |
|
|
492 |
|
|
493 reduce_mul(r); |
|
|
494 } |
|
|
495 |
|
|
496 public static unsafe void fe25519_square(fe25519* r, fe25519* x) { |
|
|
497 fe25519_mul(r, x, x); |
|
|
498 } |
|
|
499 |
|
|
500 /*XXX: Make constant time! */ |
|
|
501 public static unsafe void fe25519_pow(fe25519* r, fe25519* x, Byte* e) { |
|
|
502 /* |
|
|
503 fe25519 g; |
|
|
504 fe25519_setone(&g); |
|
|
505 int i; |
|
|
506 unsigned char j; |
|
|
507 for(i=32;i>0;i--) |
|
|
508 { |
|
|
509 for(j=128;j>0;j>>=1) |
|
|
510 { |
|
|
511 fe25519_square(&g,&g); |
|
|
512 if(e[i-1] & j) |
|
|
513 fe25519_mul(&g,&g,x); |
|
|
514 } |
|
|
515 } |
|
|
516 for(i=0;i<32;i++) r->v[i] = g.v[i]; |
|
|
517 */ |
|
|
518 fe25519 g; |
|
|
519 fe25519_setone(&g); |
|
|
520 fe25519[] pre = new fe25519[(1 << WINDOWSIZE)]; |
|
|
521 fe25519 t; |
|
|
522 Byte w; |
|
|
523 |
|
|
524 // Precomputation |
|
|
525 fixed (fe25519* prep = pre) fe25519_setone(prep); |
|
|
526 pre[1] = *x; |
|
|
527 for (int i = 2; i < (1 << WINDOWSIZE); i += 2) { |
|
|
528 fixed (fe25519* prep = pre) { |
|
|
529 fe25519_square(prep + i, prep + i / 2); |
|
|
530 fe25519_mul(prep + i + 1, prep + i, prep + 1); |
|
|
531 } |
|
|
532 } |
|
|
533 |
|
|
534 // Fixed-window scalar multiplication |
|
|
535 for (int i = 32; i > 0; i--) { |
|
|
536 for (int j = 8 - WINDOWSIZE; j >= 0; j -= WINDOWSIZE) { |
|
|
537 for (int k = 0; k < WINDOWSIZE; k++) |
|
|
538 fe25519_square(&g, &g); |
|
|
539 // Cache-timing resistant loading of precomputed value: |
|
|
540 w = (Byte)((e[i - 1] >> j) & WINDOWMASK); |
|
|
541 t = pre[0]; |
|
|
542 for (int k = 1; k < (1 << WINDOWSIZE); k++) fixed (fe25519* prekp = &pre[k]) fe25519_cmov(&t, prekp, (k == w) ? (Byte)1 : (Byte)0); |
|
|
543 fe25519_mul(&g, &g, &t); |
|
|
544 } |
|
|
545 } |
|
|
546 *r = g; |
|
|
547 } |
|
|
548 |
|
|
549 /* Return 0 on success, 1 otherwise */ |
|
|
550 public static unsafe Boolean fe25519_sqrt_vartime(fe25519* r, fe25519* x, Byte parity) { |
|
|
551 /* See HAC, Alg. 3.37 */ |
|
|
552 if (!issquare(x)) return true; |
|
|
553 Byte[] e = new Byte[32] { 0xfb, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f }; /* (p-1)/4 */ |
|
|
554 Byte[] e2 = new Byte[32] { 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f }; /* (p+3)/8 */ |
|
|
555 Byte[] e3 = new Byte[32] { 0xfd, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f }; /* (p-5)/8 */ |
|
|
556 fe25519 p = new fe25519(); // { { 0 } }; |
|
|
557 fe25519 d; |
|
|
558 fixed (Byte* ep = e) fe25519.fe25519_pow(&d, x, ep); |
|
|
559 freeze(&d); |
|
|
560 if (isone(&d)) |
|
|
561 fixed (Byte* e2p = e2) fe25519.fe25519_pow(r, x, e2p); |
|
|
562 else { |
|
|
563 for (int i = 0; i < 32; i++) |
|
|
564 d.v[i] = 4 * x->v[i]; |
|
|
565 fixed (Byte* e3p = e3) fe25519.fe25519_pow(&d, &d, e3p); |
|
|
566 for (int i = 0; i < 32; i++) |
|
|
567 r->v[i] = 2 * x->v[i]; |
|
|
568 fe25519_mul(r, r, &d); |
|
|
569 } |
|
|
570 freeze(r); |
|
|
571 if ((r->v[0] & 1) != (parity & 1)) { |
|
|
572 fe25519_sub(r, &p, r); |
|
|
573 } |
|
|
574 return false; |
|
|
575 } |
|
|
576 |
|
|
577 public static unsafe void fe25519_invert(fe25519* r, fe25519* x) { |
|
|
578 fe25519 z2; |
|
|
579 fe25519 z9; |
|
|
580 fe25519 z11; |
|
|
581 fe25519 z2_5_0; |
|
|
582 fe25519 z2_10_0; |
|
|
583 fe25519 z2_20_0; |
|
|
584 fe25519 z2_50_0; |
|
|
585 fe25519 z2_100_0; |
|
|
586 fe25519 t0; |
|
|
587 fe25519 t1; |
|
|
588 |
|
|
589 /* 2 */ |
|
|
590 fe25519_square(&z2, x); |
|
|
591 /* 4 */ |
|
|
592 fe25519_square(&t1, &z2); |
|
|
593 /* 8 */ |
|
|
594 fe25519_square(&t0, &t1); |
|
|
595 /* 9 */ |
|
|
596 fe25519_mul(&z9, &t0, x); |
|
|
597 /* 11 */ |
|
|
598 fe25519_mul(&z11, &z9, &z2); |
|
|
599 /* 22 */ |
|
|
600 fe25519_square(&t0, &z11); |
|
|
601 /* 2^5 - 2^0 = 31 */ |
|
|
602 fe25519_mul(&z2_5_0, &t0, &z9); |
|
|
603 |
|
|
604 /* 2^6 - 2^1 */ |
|
|
605 fe25519_square(&t0, &z2_5_0); |
|
|
606 /* 2^7 - 2^2 */ |
|
|
607 fe25519_square(&t1, &t0); |
|
|
608 /* 2^8 - 2^3 */ |
|
|
609 fe25519_square(&t0, &t1); |
|
|
610 /* 2^9 - 2^4 */ |
|
|
611 fe25519_square(&t1, &t0); |
|
|
612 /* 2^10 - 2^5 */ |
|
|
613 fe25519_square(&t0, &t1); |
|
|
614 /* 2^10 - 2^0 */ |
|
|
615 fe25519_mul(&z2_10_0, &t0, &z2_5_0); |
|
|
616 |
|
|
617 /* 2^11 - 2^1 */ |
|
|
618 fe25519_square(&t0, &z2_10_0); |
|
|
619 /* 2^12 - 2^2 */ |
|
|
620 fe25519_square(&t1, &t0); |
|
|
621 /* 2^20 - 2^10 */ |
|
|
622 for (int i = 2; i < 10; i += 2) { fe25519_square(&t0, &t1); fe25519_square(&t1, &t0); } |
|
|
623 /* 2^20 - 2^0 */ |
|
|
624 fe25519_mul(&z2_20_0, &t1, &z2_10_0); |
|
|
625 |
|
|
626 /* 2^21 - 2^1 */ |
|
|
627 fe25519_square(&t0, &z2_20_0); |
|
|
628 /* 2^22 - 2^2 */ |
|
|
629 fe25519_square(&t1, &t0); |
|
|
630 /* 2^40 - 2^20 */ |
|
|
631 for (int i = 2; i < 20; i += 2) { fe25519_square(&t0, &t1); fe25519_square(&t1, &t0); } |
|
|
632 /* 2^40 - 2^0 */ |
|
|
633 fe25519_mul(&t0, &t1, &z2_20_0); |
|
|
634 |
|
|
635 /* 2^41 - 2^1 */ |
|
|
636 fe25519_square(&t1, &t0); |
|
|
637 /* 2^42 - 2^2 */ |
|
|
638 fe25519_square(&t0, &t1); |
|
|
639 /* 2^50 - 2^10 */ |
|
|
640 for (int i = 2; i < 10; i += 2) { fe25519_square(&t1, &t0); fe25519_square(&t0, &t1); } |
|
|
641 /* 2^50 - 2^0 */ |
|
|
642 fe25519_mul(&z2_50_0, &t0, &z2_10_0); |
|
|
643 |
|
|
644 /* 2^51 - 2^1 */ |
|
|
645 fe25519_square(&t0, &z2_50_0); |
|
|
646 /* 2^52 - 2^2 */ |
|
|
647 fe25519_square(&t1, &t0); |
|
|
648 /* 2^100 - 2^50 */ |
|
|
649 for (int i = 2; i < 50; i += 2) { fe25519_square(&t0, &t1); fe25519_square(&t1, &t0); } |
|
|
650 /* 2^100 - 2^0 */ |
|
|
651 fe25519_mul(&z2_100_0, &t1, &z2_50_0); |
|
|
652 |
|
|
653 /* 2^101 - 2^1 */ |
|
|
654 fe25519_square(&t1, &z2_100_0); |
|
|
655 /* 2^102 - 2^2 */ |
|
|
656 fe25519_square(&t0, &t1); |
|
|
657 /* 2^200 - 2^100 */ |
|
|
658 for (int i = 2; i < 100; i += 2) { fe25519_square(&t1, &t0); fe25519_square(&t0, &t1); } |
|
|
659 /* 2^200 - 2^0 */ |
|
|
660 fe25519_mul(&t1, &t0, &z2_100_0); |
|
|
661 |
|
|
662 /* 2^201 - 2^1 */ |
|
|
663 fe25519_square(&t0, &t1); |
|
|
664 /* 2^202 - 2^2 */ |
|
|
665 fe25519_square(&t1, &t0); |
|
|
666 /* 2^250 - 2^50 */ |
|
|
667 for (int i = 2; i < 50; i += 2) { fe25519_square(&t0, &t1); fe25519_square(&t1, &t0); } |
|
|
668 /* 2^250 - 2^0 */ |
|
|
669 fe25519_mul(&t0, &t1, &z2_50_0); |
|
|
670 |
|
|
671 /* 2^251 - 2^1 */ |
|
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672 fe25519_square(&t1, &t0); |
|
|
673 /* 2^252 - 2^2 */ |
|
|
674 fe25519_square(&t0, &t1); |
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|
675 /* 2^253 - 2^3 */ |
|
|
676 fe25519_square(&t1, &t0); |
|
|
677 /* 2^254 - 2^4 */ |
|
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678 fe25519_square(&t0, &t1); |
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|
679 /* 2^255 - 2^5 */ |
|
|
680 fe25519_square(&t1, &t0); |
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|
681 /* 2^255 - 21 */ |
|
|
682 fe25519_mul(r, &t1, &z11); |
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|
683 } |
|
|
684 } |
|
|
685 |
|
|
686 public static unsafe void crypto_sign_keypair(out Byte[] pk, out Byte[] sk) { |
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|
687 sc25519 scsk; |
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|
688 ge25519 gepk; |
|
|
689 |
|
|
690 sk = new Byte[SECRETKEYBYTES]; |
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|
691 pk = new Byte[PUBLICKEYBYTES]; |
|
|
692 randombytes.generate(sk); |
|
|
693 fixed (Byte* skp = sk) crypto_hash.sha512.crypto_hash(skp, skp, 32); |
|
|
694 sk[0] &= 248; |
|
|
695 sk[31] &= 127; |
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|
696 sk[31] |= 64; |
|
|
697 |
|
|
698 fixed (Byte* skp = sk) sc25519.sc25519_from32bytes(&scsk, skp); |
|
|
699 |
|
|
700 ge25519.ge25519_scalarmult_base(&gepk, &scsk); |
|
|
701 fixed (Byte* pkp = pk) ge25519.ge25519_pack(pkp, &gepk); |
|
|
702 } |
|
|
703 |
|
|
704 public static unsafe Byte[] crypto_sign(Byte[] m, Byte[] sk) { |
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|
705 if (sk.Length != SECRETKEYBYTES) throw new ArgumentException("sk.Length != SECRETKEYBYTES"); |
|
|
706 Byte[] sm = new Byte[m.Length + 64]; |
|
|
707 UInt64 smlen; |
|
|
708 fixed (Byte* smp = sm, mp = m, skp = sk) crypto_sign(smp, out smlen, mp, (ulong)m.Length, skp); |
|
|
709 return sm; |
|
|
710 } |
|
|
711 public static unsafe void crypto_sign(Byte* sm, out UInt64 smlen, Byte* m, UInt64 mlen, Byte* sk) { |
|
|
712 sc25519 sck, scs, scsk; |
|
|
713 ge25519 ger; |
|
|
714 Byte* r = stackalloc Byte[32]; |
|
|
715 Byte* s = stackalloc Byte[32]; |
|
|
716 Byte* hmg = stackalloc Byte[crypto_hash.sha512.BYTES]; |
|
|
717 Byte* hmr = stackalloc Byte[crypto_hash.sha512.BYTES]; |
|
|
718 |
|
|
719 smlen = mlen + 64; |
|
|
720 for (UInt64 i = 0; i < mlen; i++) sm[32 + i] = m[i]; |
|
|
721 for (int i = 0; i < 32; i++) sm[i] = sk[32 + i]; |
|
|
722 crypto_hash.sha512.crypto_hash(hmg, sm, mlen + 32); /* Generate k as h(m,sk[32],...,sk[63]) */ |
|
|
723 |
|
|
724 sc25519.sc25519_from64bytes(&sck, hmg); |
|
|
725 ge25519.ge25519_scalarmult_base(&ger, &sck); |
|
|
726 ge25519.ge25519_pack(r, &ger); |
|
|
727 |
|
|
728 for (int i = 0; i < 32; i++) sm[i] = r[i]; |
|
|
729 |
|
|
730 crypto_hash.sha512.crypto_hash(hmr, sm, mlen + 32); /* Compute h(m,r) */ |
|
|
731 sc25519.sc25519_from64bytes(&scs, hmr); |
|
|
732 sc25519.sc25519_mul(&scs, &scs, &sck); |
|
|
733 |
|
|
734 sc25519.sc25519_from32bytes(&scsk, sk); |
|
|
735 sc25519.sc25519_add(&scs, &scs, &scsk); |
|
|
736 |
|
|
737 sc25519.sc25519_to32bytes(s, &scs); /* cat s */ |
|
|
738 for (UInt64 i = 0; i < 32; i++) |
|
|
739 sm[mlen + 32 + i] = s[i]; |
|
|
740 } |
|
|
741 |
|
|
742 public static unsafe Byte[] crypto_sign_open(Byte[] sm, Byte[] pk) { |
|
|
743 if (pk.Length != PUBLICKEYBYTES) throw new ArgumentException("pk.Length != PUBLICKEYBYTES"); |
|
|
744 Byte[] m = new Byte[sm.Length - 64]; |
|
|
745 UInt64 mlen; |
|
|
746 fixed (Byte* smp = sm, mp = m, pkp = pk) { |
|
|
747 if (crypto_sign_open(mp, out mlen, smp, (ulong)sm.Length, pkp) != 0) return null; |
|
|
748 } |
|
|
749 return m; |
|
|
750 } |
|
|
751 public static unsafe int crypto_sign_open(Byte* m, out UInt64 mlen, Byte* sm, UInt64 smlen, Byte* pk) { |
|
|
752 mlen = 0; |
|
|
753 if (smlen < 64) return -1; |
|
|
754 |
|
|
755 Byte* t1 = stackalloc Byte[32], t2 = stackalloc Byte[32]; |
|
|
756 ge25519 get1, get2, gepk; |
|
|
757 sc25519 schmr, scs; |
|
|
758 Byte* hmr = stackalloc Byte[crypto_hash.sha512.BYTES]; |
|
|
759 |
|
|
760 if (ge25519.ge25519_unpack_vartime(&get1, sm)) return -1; |
|
|
761 if (ge25519.ge25519_unpack_vartime(&gepk, pk)) return -1; |
|
|
762 |
|
|
763 crypto_hash.sha512.crypto_hash(hmr, sm, smlen - 32); |
|
|
764 |
|
|
765 sc25519.sc25519_from64bytes(&schmr, hmr); |
|
|
766 ge25519.ge25519_scalarmult(&get1, &get1, &schmr); |
|
|
767 ge25519.ge25519_add(&get1, &get1, &gepk); |
|
|
768 ge25519.ge25519_pack(t1, &get1); |
|
|
769 |
|
|
770 sc25519.sc25519_from32bytes(&scs, &sm[smlen - 32]); |
|
|
771 ge25519.ge25519_scalarmult_base(&get2, &scs); |
|
|
772 ge25519.ge25519_pack(t2, &get2); |
|
|
773 |
|
|
774 if (m != null) for (UInt64 i = 0; i < smlen - 64; i++) m[i] = sm[i + 32]; |
|
|
775 mlen = smlen - 64; |
|
|
776 |
|
|
777 return crypto_verify._32.crypto_verify(t1, t2); |
|
|
778 } |
|
|
779 } |
|
|
780 } |
