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