1 /* $OpenBSD: sc25519.c,v 1.3 2013/12/09 11:03:45 markus Exp $ */ 2 3 /* 4 * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange, 5 * Peter Schwabe, Bo-Yin Yang. 6 * Copied from supercop-20130419/crypto_sign/ed25519/ref/sc25519.c 7 */ 8 9 #include "includes.h" 10 11 #include "sc25519.h" 12 13 /*Arithmetic modulo the group order m = 2^252 + 27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 */ 14 15 static const crypto_uint32 m[32] = {0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, 0xDE, 0xF9, 0xDE, 0x14, 16 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10}; 17 18 static const crypto_uint32 mu[33] = {0x1B, 0x13, 0x2C, 0x0A, 0xA3, 0xE5, 0x9C, 0xED, 0xA7, 0x29, 0x63, 0x08, 0x5D, 0x21, 0x06, 0x21, 19 0xEB, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0F}; 20 21 static crypto_uint32 lt(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ 22 { 23 unsigned int x = a; 24 x -= (unsigned int) b; /* 0..65535: no; 4294901761..4294967295: yes */ 25 x >>= 31; /* 0: no; 1: yes */ 26 return x; 27 } 28 29 /* Reduce coefficients of r before calling reduce_add_sub */ 30 static void reduce_add_sub(sc25519 *r) 31 { 32 crypto_uint32 pb = 0; 33 crypto_uint32 b; 34 crypto_uint32 mask; 35 int i; 36 unsigned char t[32]; 37 38 for(i=0;i<32;i++) 39 { 40 pb += m[i]; 41 b = lt(r->v[i],pb); 42 t[i] = r->v[i]-pb+(b<<8); 43 pb = b; 44 } 45 mask = b - 1; 46 for(i=0;i<32;i++) 47 r->v[i] ^= mask & (r->v[i] ^ t[i]); 48 } 49 50 /* Reduce coefficients of x before calling barrett_reduce */ 51 static void barrett_reduce(sc25519 *r, const crypto_uint32 x[64]) 52 { 53 /* See HAC, Alg. 14.42 */ 54 int i,j; 55 crypto_uint32 q2[66]; 56 crypto_uint32 *q3 = q2 + 33; 57 crypto_uint32 r1[33]; 58 crypto_uint32 r2[33]; 59 crypto_uint32 carry; 60 crypto_uint32 pb = 0; 61 crypto_uint32 b; 62 63 for (i = 0;i < 66;++i) q2[i] = 0; 64 for (i = 0;i < 33;++i) r2[i] = 0; 65 66 for(i=0;i<33;i++) 67 for(j=0;j<33;j++) 68 if(i+j >= 31) q2[i+j] += mu[i]*x[j+31]; 69 carry = q2[31] >> 8; 70 q2[32] += carry; 71 carry = q2[32] >> 8; 72 q2[33] += carry; 73 74 for(i=0;i<33;i++)r1[i] = x[i]; 75 for(i=0;i<32;i++) 76 for(j=0;j<33;j++) 77 if(i+j < 33) r2[i+j] += m[i]*q3[j]; 78 79 for(i=0;i<32;i++) 80 { 81 carry = r2[i] >> 8; 82 r2[i+1] += carry; 83 r2[i] &= 0xff; 84 } 85 86 for(i=0;i<32;i++) 87 { 88 pb += r2[i]; 89 b = lt(r1[i],pb); 90 r->v[i] = r1[i]-pb+(b<<8); 91 pb = b; 92 } 93 94 /* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3 95 * If so: Handle it here! 96 */ 97 98 reduce_add_sub(r); 99 reduce_add_sub(r); 100 } 101 102 void sc25519_from32bytes(sc25519 *r, const unsigned char x[32]) 103 { 104 int i; 105 crypto_uint32 t[64]; 106 for(i=0;i<32;i++) t[i] = x[i]; 107 for(i=32;i<64;++i) t[i] = 0; 108 barrett_reduce(r, t); 109 } 110 111 void shortsc25519_from16bytes(shortsc25519 *r, const unsigned char x[16]) 112 { 113 int i; 114 for(i=0;i<16;i++) r->v[i] = x[i]; 115 } 116 117 void sc25519_from64bytes(sc25519 *r, const unsigned char x[64]) 118 { 119 int i; 120 crypto_uint32 t[64]; 121 for(i=0;i<64;i++) t[i] = x[i]; 122 barrett_reduce(r, t); 123 } 124 125 void sc25519_from_shortsc(sc25519 *r, const shortsc25519 *x) 126 { 127 int i; 128 for(i=0;i<16;i++) 129 r->v[i] = x->v[i]; 130 for(i=0;i<16;i++) 131 r->v[16+i] = 0; 132 } 133 134 void sc25519_to32bytes(unsigned char r[32], const sc25519 *x) 135 { 136 int i; 137 for(i=0;i<32;i++) r[i] = x->v[i]; 138 } 139 140 int sc25519_iszero_vartime(const sc25519 *x) 141 { 142 int i; 143 for(i=0;i<32;i++) 144 if(x->v[i] != 0) return 0; 145 return 1; 146 } 147 148 int sc25519_isshort_vartime(const sc25519 *x) 149 { 150 int i; 151 for(i=31;i>15;i--) 152 if(x->v[i] != 0) return 0; 153 return 1; 154 } 155 156 int sc25519_lt_vartime(const sc25519 *x, const sc25519 *y) 157 { 158 int i; 159 for(i=31;i>=0;i--) 160 { 161 if(x->v[i] < y->v[i]) return 1; 162 if(x->v[i] > y->v[i]) return 0; 163 } 164 return 0; 165 } 166 167 void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y) 168 { 169 int i, carry; 170 for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i]; 171 for(i=0;i<31;i++) 172 { 173 carry = r->v[i] >> 8; 174 r->v[i+1] += carry; 175 r->v[i] &= 0xff; 176 } 177 reduce_add_sub(r); 178 } 179 180 void sc25519_sub_nored(sc25519 *r, const sc25519 *x, const sc25519 *y) 181 { 182 crypto_uint32 b = 0; 183 crypto_uint32 t; 184 int i; 185 for(i=0;i<32;i++) 186 { 187 t = x->v[i] - y->v[i] - b; 188 r->v[i] = t & 255; 189 b = (t >> 8) & 1; 190 } 191 } 192 193 void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y) 194 { 195 int i,j,carry; 196 crypto_uint32 t[64]; 197 for(i=0;i<64;i++)t[i] = 0; 198 199 for(i=0;i<32;i++) 200 for(j=0;j<32;j++) 201 t[i+j] += x->v[i] * y->v[j]; 202 203 /* Reduce coefficients */ 204 for(i=0;i<63;i++) 205 { 206 carry = t[i] >> 8; 207 t[i+1] += carry; 208 t[i] &= 0xff; 209 } 210 211 barrett_reduce(r, t); 212 } 213 214 void sc25519_mul_shortsc(sc25519 *r, const sc25519 *x, const shortsc25519 *y) 215 { 216 sc25519 t; 217 sc25519_from_shortsc(&t, y); 218 sc25519_mul(r, x, &t); 219 } 220 221 void sc25519_window3(signed char r[85], const sc25519 *s) 222 { 223 char carry; 224 int i; 225 for(i=0;i<10;i++) 226 { 227 r[8*i+0] = s->v[3*i+0] & 7; 228 r[8*i+1] = (s->v[3*i+0] >> 3) & 7; 229 r[8*i+2] = (s->v[3*i+0] >> 6) & 7; 230 r[8*i+2] ^= (s->v[3*i+1] << 2) & 7; 231 r[8*i+3] = (s->v[3*i+1] >> 1) & 7; 232 r[8*i+4] = (s->v[3*i+1] >> 4) & 7; 233 r[8*i+5] = (s->v[3*i+1] >> 7) & 7; 234 r[8*i+5] ^= (s->v[3*i+2] << 1) & 7; 235 r[8*i+6] = (s->v[3*i+2] >> 2) & 7; 236 r[8*i+7] = (s->v[3*i+2] >> 5) & 7; 237 } 238 r[8*i+0] = s->v[3*i+0] & 7; 239 r[8*i+1] = (s->v[3*i+0] >> 3) & 7; 240 r[8*i+2] = (s->v[3*i+0] >> 6) & 7; 241 r[8*i+2] ^= (s->v[3*i+1] << 2) & 7; 242 r[8*i+3] = (s->v[3*i+1] >> 1) & 7; 243 r[8*i+4] = (s->v[3*i+1] >> 4) & 7; 244 245 /* Making it signed */ 246 carry = 0; 247 for(i=0;i<84;i++) 248 { 249 r[i] += carry; 250 r[i+1] += r[i] >> 3; 251 r[i] &= 7; 252 carry = r[i] >> 2; 253 r[i] -= carry<<3; 254 } 255 r[84] += carry; 256 } 257 258 void sc25519_window5(signed char r[51], const sc25519 *s) 259 { 260 char carry; 261 int i; 262 for(i=0;i<6;i++) 263 { 264 r[8*i+0] = s->v[5*i+0] & 31; 265 r[8*i+1] = (s->v[5*i+0] >> 5) & 31; 266 r[8*i+1] ^= (s->v[5*i+1] << 3) & 31; 267 r[8*i+2] = (s->v[5*i+1] >> 2) & 31; 268 r[8*i+3] = (s->v[5*i+1] >> 7) & 31; 269 r[8*i+3] ^= (s->v[5*i+2] << 1) & 31; 270 r[8*i+4] = (s->v[5*i+2] >> 4) & 31; 271 r[8*i+4] ^= (s->v[5*i+3] << 4) & 31; 272 r[8*i+5] = (s->v[5*i+3] >> 1) & 31; 273 r[8*i+6] = (s->v[5*i+3] >> 6) & 31; 274 r[8*i+6] ^= (s->v[5*i+4] << 2) & 31; 275 r[8*i+7] = (s->v[5*i+4] >> 3) & 31; 276 } 277 r[8*i+0] = s->v[5*i+0] & 31; 278 r[8*i+1] = (s->v[5*i+0] >> 5) & 31; 279 r[8*i+1] ^= (s->v[5*i+1] << 3) & 31; 280 r[8*i+2] = (s->v[5*i+1] >> 2) & 31; 281 282 /* Making it signed */ 283 carry = 0; 284 for(i=0;i<50;i++) 285 { 286 r[i] += carry; 287 r[i+1] += r[i] >> 5; 288 r[i] &= 31; 289 carry = r[i] >> 4; 290 r[i] -= carry<<5; 291 } 292 r[50] += carry; 293 } 294 295 void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2) 296 { 297 int i; 298 for(i=0;i<31;i++) 299 { 300 r[4*i] = ( s1->v[i] & 3) ^ (( s2->v[i] & 3) << 2); 301 r[4*i+1] = ((s1->v[i] >> 2) & 3) ^ (((s2->v[i] >> 2) & 3) << 2); 302 r[4*i+2] = ((s1->v[i] >> 4) & 3) ^ (((s2->v[i] >> 4) & 3) << 2); 303 r[4*i+3] = ((s1->v[i] >> 6) & 3) ^ (((s2->v[i] >> 6) & 3) << 2); 304 } 305 r[124] = ( s1->v[31] & 3) ^ (( s2->v[31] & 3) << 2); 306 r[125] = ((s1->v[31] >> 2) & 3) ^ (((s2->v[31] >> 2) & 3) << 2); 307 r[126] = ((s1->v[31] >> 4) & 3) ^ (((s2->v[31] >> 4) & 3) << 2); 308 } 309
