1/* $OpenBSD: smult_curve25519_ref.c,v 1.2 2013/11/02 22:02:14 markus Exp $ */ 2/* 3version 20081011 4Matthew Dempsky 5Public domain. 6Derived from public domain code by D. J. Bernstein. 7*/ 8 9#include "includes.h" 10__RCSID("$NetBSD: smult_curve25519_ref.c,v 1.5 2017/04/18 18:41:46 christos Exp $"); 11 12int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *); 13 14static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) 15{ 16 unsigned int j; 17 unsigned int u; 18 u = 0; 19 for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; } 20 u += a[31] + b[31]; out[31] = u; 21} 22 23static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) 24{ 25 unsigned int j; 26 unsigned int u; 27 u = 218; 28 for (j = 0;j < 31;++j) { 29 u += a[j] + 65280 - b[j]; 30 out[j] = u & 255; 31 u >>= 8; 32 } 33 u += a[31] - b[31]; 34 out[31] = u; 35} 36 37static void squeeze(unsigned int a[32]) 38{ 39 unsigned int j; 40 unsigned int u; 41 u = 0; 42 for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; } 43 u += a[31]; a[31] = u & 127; 44 u = 19 * (u >> 7); 45 for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; } 46 u += a[31]; a[31] = u; 47} 48 49static const unsigned int minusp[32] = { 50 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 51} ; 52 53static void freeze(unsigned int a[32]) 54{ 55 unsigned int aorig[32]; 56 unsigned int j; 57 unsigned int negative; 58 59 for (j = 0;j < 32;++j) aorig[j] = a[j]; 60 add(a,a,minusp); 61 negative = -((a[31] >> 7) & 1); 62 for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]); 63} 64 65static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32]) 66{ 67 unsigned int i; 68 unsigned int j; 69 unsigned int u; 70 71 for (i = 0;i < 32;++i) { 72 u = 0; 73 for (j = 0;j <= i;++j) u += a[j] * b[i - j]; 74 for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j]; 75 out[i] = u; 76 } 77 squeeze(out); 78} 79 80static void mult121665(unsigned int out[32],const unsigned int a[32]) 81{ 82 unsigned int j; 83 unsigned int u; 84 85 u = 0; 86 for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; } 87 u += 121665 * a[31]; out[31] = u & 127; 88 u = 19 * (u >> 7); 89 for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; } 90 u += out[j]; out[j] = u; 91} 92 93static void square(unsigned int out[32],const unsigned int a[32]) 94{ 95 unsigned int i; 96 unsigned int j; 97 unsigned int u; 98 99 for (i = 0;i < 32;++i) { 100 u = 0; 101 for (j = 0;j < i - j;++j) u += a[j] * a[i - j]; 102 for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j]; 103 u *= 2; 104 if ((i & 1) == 0) { 105 u += a[i / 2] * a[i / 2]; 106 u += 38 * a[i / 2 + 16] * a[i / 2 + 16]; 107 } 108 out[i] = u; 109 } 110 squeeze(out); 111} 112 113static void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b) 114{ 115 unsigned int j; 116 unsigned int t; 117 unsigned int bminus1; 118 119 bminus1 = b - 1; 120 for (j = 0;j < 64;++j) { 121 t = bminus1 & (r[j] ^ s[j]); 122 p[j] = s[j] ^ t; 123 q[j] = r[j] ^ t; 124 } 125} 126 127static void mainloop(unsigned int work[64],const unsigned char e[32]) 128{ 129 unsigned int xzm1[64]; 130 unsigned int xzm[64]; 131 unsigned int xzmb[64]; 132 unsigned int xzm1b[64]; 133 unsigned int xznb[64]; 134 unsigned int xzn1b[64]; 135 unsigned int a0[64]; 136 unsigned int a1[64]; 137 unsigned int b0[64]; 138 unsigned int b1[64]; 139 unsigned int c1[64]; 140 unsigned int r[32]; 141 unsigned int s[32]; 142 unsigned int t[32]; 143 unsigned int u[32]; 144 unsigned int j; 145 unsigned int b; 146 int pos; 147 148 for (j = 0;j < 32;++j) xzm1[j] = work[j]; 149 xzm1[32] = 1; 150 for (j = 33;j < 64;++j) xzm1[j] = 0; 151 152 xzm[0] = 1; 153 for (j = 1;j < 64;++j) xzm[j] = 0; 154 155 for (pos = 254;pos >= 0;--pos) { 156 b = e[pos / 8] >> (pos & 7); 157 b &= 1; 158 select(xzmb,xzm1b,xzm,xzm1,b); 159 add(a0,xzmb,xzmb + 32); 160 sub(a0 + 32,xzmb,xzmb + 32); 161 add(a1,xzm1b,xzm1b + 32); 162 sub(a1 + 32,xzm1b,xzm1b + 32); 163 square(b0,a0); 164 square(b0 + 32,a0 + 32); 165 mult(b1,a1,a0 + 32); 166 mult(b1 + 32,a1 + 32,a0); 167 add(c1,b1,b1 + 32); 168 sub(c1 + 32,b1,b1 + 32); 169 square(r,c1 + 32); 170 sub(s,b0,b0 + 32); 171 mult121665(t,s); 172 add(u,t,b0); 173 mult(xznb,b0,b0 + 32); 174 mult(xznb + 32,s,u); 175 square(xzn1b,c1); 176 mult(xzn1b + 32,r,work); 177 select(xzm,xzm1,xznb,xzn1b,b); 178 } 179 180 for (j = 0;j < 64;++j) work[j] = xzm[j]; 181} 182 183static void recip(unsigned int out[32],const unsigned int z[32]) 184{ 185 unsigned int z2[32]; 186 unsigned int z9[32]; 187 unsigned int z11[32]; 188 unsigned int z2_5_0[32]; 189 unsigned int z2_10_0[32]; 190 unsigned int z2_20_0[32]; 191 unsigned int z2_50_0[32]; 192 unsigned int z2_100_0[32]; 193 unsigned int t0[32]; 194 unsigned int t1[32]; 195 int i; 196 197 /* 2 */ square(z2,z); 198 /* 4 */ square(t1,z2); 199 /* 8 */ square(t0,t1); 200 /* 9 */ mult(z9,t0,z); 201 /* 11 */ mult(z11,z9,z2); 202 /* 22 */ square(t0,z11); 203 /* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9); 204 205 /* 2^6 - 2^1 */ square(t0,z2_5_0); 206 /* 2^7 - 2^2 */ square(t1,t0); 207 /* 2^8 - 2^3 */ square(t0,t1); 208 /* 2^9 - 2^4 */ square(t1,t0); 209 /* 2^10 - 2^5 */ square(t0,t1); 210 /* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0); 211 212 /* 2^11 - 2^1 */ square(t0,z2_10_0); 213 /* 2^12 - 2^2 */ square(t1,t0); 214 /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); } 215 /* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0); 216 217 /* 2^21 - 2^1 */ square(t0,z2_20_0); 218 /* 2^22 - 2^2 */ square(t1,t0); 219 /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); } 220 /* 2^40 - 2^0 */ mult(t0,t1,z2_20_0); 221 222 /* 2^41 - 2^1 */ square(t1,t0); 223 /* 2^42 - 2^2 */ square(t0,t1); 224 /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); } 225 /* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0); 226 227 /* 2^51 - 2^1 */ square(t0,z2_50_0); 228 /* 2^52 - 2^2 */ square(t1,t0); 229 /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); } 230 /* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0); 231 232 /* 2^101 - 2^1 */ square(t1,z2_100_0); 233 /* 2^102 - 2^2 */ square(t0,t1); 234 /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); } 235 /* 2^200 - 2^0 */ mult(t1,t0,z2_100_0); 236 237 /* 2^201 - 2^1 */ square(t0,t1); 238 /* 2^202 - 2^2 */ square(t1,t0); 239 /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); } 240 /* 2^250 - 2^0 */ mult(t0,t1,z2_50_0); 241 242 /* 2^251 - 2^1 */ square(t1,t0); 243 /* 2^252 - 2^2 */ square(t0,t1); 244 /* 2^253 - 2^3 */ square(t1,t0); 245 /* 2^254 - 2^4 */ square(t0,t1); 246 /* 2^255 - 2^5 */ square(t1,t0); 247 /* 2^255 - 21 */ mult(out,t1,z11); 248} 249 250int crypto_scalarmult_curve25519(unsigned char *q, 251 const unsigned char *n, 252 const unsigned char *p) 253{ 254 unsigned int work[96]; 255 unsigned char e[32]; 256 unsigned int i; 257 for (i = 0;i < 32;++i) e[i] = n[i]; 258 e[0] &= 248; 259 e[31] &= 127; 260 e[31] |= 64; 261 for (i = 0;i < 32;++i) work[i] = p[i]; 262 mainloop(work,e); 263 recip(work + 32,work + 32); 264 mult(work + 64,work,work + 32); 265 freeze(work + 64); 266 for (i = 0;i < 32;++i) q[i] = work[64 + i]; 267 return 0; 268} 269