1 /* $OpenBSD: smult_curve25519_ref.c,v 1.2 2013/11/02 22:02:14 markus Exp $ */ 2 /* 3 version 20081011 4 Matthew Dempsky 5 Public domain. 6 Derived from public domain code by D. J. Bernstein. 7 */ 8 9 int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *); 10 11 static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) 12 { 13 unsigned int j; 14 unsigned int u; 15 u = 0; 16 for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; } 17 u += a[31] + b[31]; out[31] = u; 18 } 19 20 static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) 21 { 22 unsigned int j; 23 unsigned int u; 24 u = 218; 25 for (j = 0;j < 31;++j) { 26 u += a[j] + 65280 - b[j]; 27 out[j] = u & 255; 28 u >>= 8; 29 } 30 u += a[31] - b[31]; 31 out[31] = u; 32 } 33 34 static void squeeze(unsigned int a[32]) 35 { 36 unsigned int j; 37 unsigned int u; 38 u = 0; 39 for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; } 40 u += a[31]; a[31] = u & 127; 41 u = 19 * (u >> 7); 42 for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; } 43 u += a[31]; a[31] = u; 44 } 45 46 static const unsigned int minusp[32] = { 47 19, 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, 128 48 } ; 49 50 static void freeze(unsigned int a[32]) 51 { 52 unsigned int aorig[32]; 53 unsigned int j; 54 unsigned int negative; 55 56 for (j = 0;j < 32;++j) aorig[j] = a[j]; 57 add(a,a,minusp); 58 negative = -((a[31] >> 7) & 1); 59 for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]); 60 } 61 62 static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) 63 { 64 unsigned int i; 65 unsigned int j; 66 unsigned int u; 67 68 for (i = 0;i < 32;++i) { 69 u = 0; 70 for (j = 0;j <= i;++j) u += a[j] * b[i - j]; 71 for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j]; 72 out[i] = u; 73 } 74 squeeze(out); 75 } 76 77 static void mult121665(unsigned int out[32],const unsigned int a[32]) 78 { 79 unsigned int j; 80 unsigned int u; 81 82 u = 0; 83 for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; } 84 u += 121665 * a[31]; out[31] = u & 127; 85 u = 19 * (u >> 7); 86 for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; } 87 u += out[j]; out[j] = u; 88 } 89 90 static void square(unsigned int out[32],const unsigned int a[32]) 91 { 92 unsigned int i; 93 unsigned int j; 94 unsigned int u; 95 96 for (i = 0;i < 32;++i) { 97 u = 0; 98 for (j = 0;j < i - j;++j) u += a[j] * a[i - j]; 99 for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j]; 100 u *= 2; 101 if ((i & 1) == 0) { 102 u += a[i / 2] * a[i / 2]; 103 u += 38 * a[i / 2 + 16] * a[i / 2 + 16]; 104 } 105 out[i] = u; 106 } 107 squeeze(out); 108 } 109 110 static void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b) 111 { 112 unsigned int j; 113 unsigned int t; 114 unsigned int bminus1; 115 116 bminus1 = b - 1; 117 for (j = 0;j < 64;++j) { 118 t = bminus1 & (r[j] ^ s[j]); 119 p[j] = s[j] ^ t; 120 q[j] = r[j] ^ t; 121 } 122 } 123 124 static void mainloop(unsigned int work[64],const unsigned char e[32]) 125 { 126 unsigned int xzm1[64]; 127 unsigned int xzm[64]; 128 unsigned int xzmb[64]; 129 unsigned int xzm1b[64]; 130 unsigned int xznb[64]; 131 unsigned int xzn1b[64]; 132 unsigned int a0[64]; 133 unsigned int a1[64]; 134 unsigned int b0[64]; 135 unsigned int b1[64]; 136 unsigned int c1[64]; 137 unsigned int r[32]; 138 unsigned int s[32]; 139 unsigned int t[32]; 140 unsigned int u[32]; 141 unsigned int j; 142 unsigned int b; 143 int pos; 144 145 for (j = 0;j < 32;++j) xzm1[j] = work[j]; 146 xzm1[32] = 1; 147 for (j = 33;j < 64;++j) xzm1[j] = 0; 148 149 xzm[0] = 1; 150 for (j = 1;j < 64;++j) xzm[j] = 0; 151 152 for (pos = 254;pos >= 0;--pos) { 153 b = e[pos / 8] >> (pos & 7); 154 b &= 1; 155 select(xzmb,xzm1b,xzm,xzm1,b); 156 add(a0,xzmb,xzmb + 32); 157 sub(a0 + 32,xzmb,xzmb + 32); 158 add(a1,xzm1b,xzm1b + 32); 159 sub(a1 + 32,xzm1b,xzm1b + 32); 160 square(b0,a0); 161 square(b0 + 32,a0 + 32); 162 mult(b1,a1,a0 + 32); 163 mult(b1 + 32,a1 + 32,a0); 164 add(c1,b1,b1 + 32); 165 sub(c1 + 32,b1,b1 + 32); 166 square(r,c1 + 32); 167 sub(s,b0,b0 + 32); 168 mult121665(t,s); 169 add(u,t,b0); 170 mult(xznb,b0,b0 + 32); 171 mult(xznb + 32,s,u); 172 square(xzn1b,c1); 173 mult(xzn1b + 32,r,work); 174 select(xzm,xzm1,xznb,xzn1b,b); 175 } 176 177 for (j = 0;j < 64;++j) work[j] = xzm[j]; 178 } 179 180 static void recip(unsigned int out[32],const unsigned int z[32]) 181 { 182 unsigned int z2[32]; 183 unsigned int z9[32]; 184 unsigned int z11[32]; 185 unsigned int z2_5_0[32]; 186 unsigned int z2_10_0[32]; 187 unsigned int z2_20_0[32]; 188 unsigned int z2_50_0[32]; 189 unsigned int z2_100_0[32]; 190 unsigned int t0[32]; 191 unsigned int t1[32]; 192 int i; 193 194 /* 2 */ square(z2,z); 195 /* 4 */ square(t1,z2); 196 /* 8 */ square(t0,t1); 197 /* 9 */ mult(z9,t0,z); 198 /* 11 */ mult(z11,z9,z2); 199 /* 22 */ square(t0,z11); 200 /* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9); 201 202 /* 2^6 - 2^1 */ square(t0,z2_5_0); 203 /* 2^7 - 2^2 */ square(t1,t0); 204 /* 2^8 - 2^3 */ square(t0,t1); 205 /* 2^9 - 2^4 */ square(t1,t0); 206 /* 2^10 - 2^5 */ square(t0,t1); 207 /* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0); 208 209 /* 2^11 - 2^1 */ square(t0,z2_10_0); 210 /* 2^12 - 2^2 */ square(t1,t0); 211 /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); } 212 /* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0); 213 214 /* 2^21 - 2^1 */ square(t0,z2_20_0); 215 /* 2^22 - 2^2 */ square(t1,t0); 216 /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); } 217 /* 2^40 - 2^0 */ mult(t0,t1,z2_20_0); 218 219 /* 2^41 - 2^1 */ square(t1,t0); 220 /* 2^42 - 2^2 */ square(t0,t1); 221 /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); } 222 /* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0); 223 224 /* 2^51 - 2^1 */ square(t0,z2_50_0); 225 /* 2^52 - 2^2 */ square(t1,t0); 226 /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); } 227 /* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0); 228 229 /* 2^101 - 2^1 */ square(t1,z2_100_0); 230 /* 2^102 - 2^2 */ square(t0,t1); 231 /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); } 232 /* 2^200 - 2^0 */ mult(t1,t0,z2_100_0); 233 234 /* 2^201 - 2^1 */ square(t0,t1); 235 /* 2^202 - 2^2 */ square(t1,t0); 236 /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); } 237 /* 2^250 - 2^0 */ mult(t0,t1,z2_50_0); 238 239 /* 2^251 - 2^1 */ square(t1,t0); 240 /* 2^252 - 2^2 */ square(t0,t1); 241 /* 2^253 - 2^3 */ square(t1,t0); 242 /* 2^254 - 2^4 */ square(t0,t1); 243 /* 2^255 - 2^5 */ square(t1,t0); 244 /* 2^255 - 21 */ mult(out,t1,z11); 245 } 246 247 int crypto_scalarmult_curve25519(unsigned char *q, 248 const unsigned char *n, 249 const unsigned char *p) 250 { 251 unsigned int work[96]; 252 unsigned char e[32]; 253 unsigned int i; 254 for (i = 0;i < 32;++i) e[i] = n[i]; 255 e[0] &= 248; 256 e[31] &= 127; 257 e[31] |= 64; 258 for (i = 0;i < 32;++i) work[i] = p[i]; 259 mainloop(work,e); 260 recip(work + 32,work + 32); 261 mult(work + 64,work,work + 32); 262 freeze(work + 64); 263 for (i = 0;i < 32;++i) q[i] = work[64 + i]; 264 return 0; 265 } 266
