smult_curve25519_ref.c

   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 }