smult_curve25519_ref.c 6.71 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265
/* $OpenBSD: smult_curve25519_ref.c,v 1.2 2013/11/02 22:02:14 markus Exp $ */
/*
version 20081011
Matthew Dempsky
Public domain.
Derived from public domain code by D. J. Bernstein.
*/

int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *);

static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
{
  unsigned int j;
  unsigned int u;
  u = 0;
  for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; }
  u += a[31] + b[31]; out[31] = u;
}

static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
{
  unsigned int j;
  unsigned int u;
  u = 218;
  for (j = 0;j < 31;++j) {
    u += a[j] + 65280 - b[j];
    out[j] = u & 255;
    u >>= 8;
  }
  u += a[31] - b[31];
  out[31] = u;
}

static void squeeze(unsigned int a[32])
{
  unsigned int j;
  unsigned int u;
  u = 0;
  for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
  u += a[31]; a[31] = u & 127;
  u = 19 * (u >> 7);
  for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
  u += a[31]; a[31] = u;
}

static const unsigned int minusp[32] = {
 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
} ;

static void freeze(unsigned int a[32])
{
  unsigned int aorig[32];
  unsigned int j;
  unsigned int negative;

  for (j = 0;j < 32;++j) aorig[j] = a[j];
  add(a,a,minusp);
  negative = -((a[31] >> 7) & 1);
  for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]);
}

static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
{
  unsigned int i;
  unsigned int j;
  unsigned int u;

  for (i = 0;i < 32;++i) {
    u = 0;
    for (j = 0;j <= i;++j) u += a[j] * b[i - j];
    for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j];
    out[i] = u;
  }
  squeeze(out);
}

static void mult121665(unsigned int out[32],const unsigned int a[32])
{
  unsigned int j;
  unsigned int u;

  u = 0;
  for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; }
  u += 121665 * a[31]; out[31] = u & 127;
  u = 19 * (u >> 7);
  for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; }
  u += out[j]; out[j] = u;
}

static void square(unsigned int out[32],const unsigned int a[32])
{
  unsigned int i;
  unsigned int j;
  unsigned int u;

  for (i = 0;i < 32;++i) {
    u = 0;
    for (j = 0;j < i - j;++j) u += a[j] * a[i - j];
    for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j];
    u *= 2;
    if ((i & 1) == 0) {
      u += a[i / 2] * a[i / 2];
      u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
    }
    out[i] = u;
  }
  squeeze(out);
}

static void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b)
{
  unsigned int j;
  unsigned int t;
  unsigned int bminus1;

  bminus1 = b - 1;
  for (j = 0;j < 64;++j) {
    t = bminus1 & (r[j] ^ s[j]);
    p[j] = s[j] ^ t;
    q[j] = r[j] ^ t;
  }
}

static void mainloop(unsigned int work[64],const unsigned char e[32])
{
  unsigned int xzm1[64];
  unsigned int xzm[64];
  unsigned int xzmb[64];
  unsigned int xzm1b[64];
  unsigned int xznb[64];
  unsigned int xzn1b[64];
  unsigned int a0[64];
  unsigned int a1[64];
  unsigned int b0[64];
  unsigned int b1[64];
  unsigned int c1[64];
  unsigned int r[32];
  unsigned int s[32];
  unsigned int t[32];
  unsigned int u[32];
  unsigned int j;
  unsigned int b;
  int pos;

  for (j = 0;j < 32;++j) xzm1[j] = work[j];
  xzm1[32] = 1;
  for (j = 33;j < 64;++j) xzm1[j] = 0;

  xzm[0] = 1;
  for (j = 1;j < 64;++j) xzm[j] = 0;

  for (pos = 254;pos >= 0;--pos) {
    b = e[pos / 8] >> (pos & 7);
    b &= 1;
    select(xzmb,xzm1b,xzm,xzm1,b);
    add(a0,xzmb,xzmb + 32);
    sub(a0 + 32,xzmb,xzmb + 32);
    add(a1,xzm1b,xzm1b + 32);
    sub(a1 + 32,xzm1b,xzm1b + 32);
    square(b0,a0);
    square(b0 + 32,a0 + 32);
    mult(b1,a1,a0 + 32);
    mult(b1 + 32,a1 + 32,a0);
    add(c1,b1,b1 + 32);
    sub(c1 + 32,b1,b1 + 32);
    square(r,c1 + 32);
    sub(s,b0,b0 + 32);
    mult121665(t,s);
    add(u,t,b0);
    mult(xznb,b0,b0 + 32);
    mult(xznb + 32,s,u);
    square(xzn1b,c1);
    mult(xzn1b + 32,r,work);
    select(xzm,xzm1,xznb,xzn1b,b);
  }

  for (j = 0;j < 64;++j) work[j] = xzm[j];
}

static void recip(unsigned int out[32],const unsigned int z[32])
{
  unsigned int z2[32];
  unsigned int z9[32];
  unsigned int z11[32];
  unsigned int z2_5_0[32];
  unsigned int z2_10_0[32];
  unsigned int z2_20_0[32];
  unsigned int z2_50_0[32];
  unsigned int z2_100_0[32];
  unsigned int t0[32];
  unsigned int t1[32];
  int i;

  /* 2 */ square(z2,z);
  /* 4 */ square(t1,z2);
  /* 8 */ square(t0,t1);
  /* 9 */ mult(z9,t0,z);
  /* 11 */ mult(z11,z9,z2);
  /* 22 */ square(t0,z11);
  /* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9);

  /* 2^6 - 2^1 */ square(t0,z2_5_0);
  /* 2^7 - 2^2 */ square(t1,t0);
  /* 2^8 - 2^3 */ square(t0,t1);
  /* 2^9 - 2^4 */ square(t1,t0);
  /* 2^10 - 2^5 */ square(t0,t1);
  /* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0);

  /* 2^11 - 2^1 */ square(t0,z2_10_0);
  /* 2^12 - 2^2 */ square(t1,t0);
  /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); }
  /* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0);

  /* 2^21 - 2^1 */ square(t0,z2_20_0);
  /* 2^22 - 2^2 */ square(t1,t0);
  /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); }
  /* 2^40 - 2^0 */ mult(t0,t1,z2_20_0);

  /* 2^41 - 2^1 */ square(t1,t0);
  /* 2^42 - 2^2 */ square(t0,t1);
  /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); }
  /* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0);

  /* 2^51 - 2^1 */ square(t0,z2_50_0);
  /* 2^52 - 2^2 */ square(t1,t0);
  /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
  /* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0);

  /* 2^101 - 2^1 */ square(t1,z2_100_0);
  /* 2^102 - 2^2 */ square(t0,t1);
  /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); }
  /* 2^200 - 2^0 */ mult(t1,t0,z2_100_0);

  /* 2^201 - 2^1 */ square(t0,t1);
  /* 2^202 - 2^2 */ square(t1,t0);
  /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
  /* 2^250 - 2^0 */ mult(t0,t1,z2_50_0);

  /* 2^251 - 2^1 */ square(t1,t0);
  /* 2^252 - 2^2 */ square(t0,t1);
  /* 2^253 - 2^3 */ square(t1,t0);
  /* 2^254 - 2^4 */ square(t0,t1);
  /* 2^255 - 2^5 */ square(t1,t0);
  /* 2^255 - 21 */ mult(out,t1,z11);
}

int crypto_scalarmult_curve25519(unsigned char *q,
  const unsigned char *n,
  const unsigned char *p)
{
  unsigned int work[96];
  unsigned char e[32];
  unsigned int i;
  for (i = 0;i < 32;++i) e[i] = n[i];
  e[0] &= 248;
  e[31] &= 127;
  e[31] |= 64;
  for (i = 0;i < 32;++i) work[i] = p[i];
  mainloop(work,e);
  recip(work + 32,work + 32);
  mult(work + 64,work,work + 32);
  freeze(work + 64);
  for (i = 0;i < 32;++i) q[i] = work[64 + i];
  return 0;
}