Annotation of src/usr.bin/ssh/smult_curve25519_ref.c, Revision 1.1
1.1 ! markus 1: /*
! 2: version 20081011
! 3: Matthew Dempsky
! 4: Public domain.
! 5: Derived from public domain code by D. J. Bernstein.
! 6: */
! 7:
! 8: int crypto_scalarmult_curve25519(unsigned char *, const unsigned char *, const unsigned char *);
! 9:
! 10: static void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
! 11: {
! 12: unsigned int j;
! 13: unsigned int u;
! 14: u = 0;
! 15: for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; }
! 16: u += a[31] + b[31]; out[31] = u;
! 17: }
! 18:
! 19: static void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
! 20: {
! 21: unsigned int j;
! 22: unsigned int u;
! 23: u = 218;
! 24: for (j = 0;j < 31;++j) {
! 25: u += a[j] + 65280 - b[j];
! 26: out[j] = u & 255;
! 27: u >>= 8;
! 28: }
! 29: u += a[31] - b[31];
! 30: out[31] = u;
! 31: }
! 32:
! 33: static void squeeze(unsigned int a[32])
! 34: {
! 35: unsigned int j;
! 36: unsigned int u;
! 37: u = 0;
! 38: for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
! 39: u += a[31]; a[31] = u & 127;
! 40: u = 19 * (u >> 7);
! 41: for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
! 42: u += a[31]; a[31] = u;
! 43: }
! 44:
! 45: static const unsigned int minusp[32] = {
! 46: 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
! 47: } ;
! 48:
! 49: static void freeze(unsigned int a[32])
! 50: {
! 51: unsigned int aorig[32];
! 52: unsigned int j;
! 53: unsigned int negative;
! 54:
! 55: for (j = 0;j < 32;++j) aorig[j] = a[j];
! 56: add(a,a,minusp);
! 57: negative = -((a[31] >> 7) & 1);
! 58: for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]);
! 59: }
! 60:
! 61: static void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
! 62: {
! 63: unsigned int i;
! 64: unsigned int j;
! 65: unsigned int u;
! 66:
! 67: for (i = 0;i < 32;++i) {
! 68: u = 0;
! 69: for (j = 0;j <= i;++j) u += a[j] * b[i - j];
! 70: for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j];
! 71: out[i] = u;
! 72: }
! 73: squeeze(out);
! 74: }
! 75:
! 76: static void mult121665(unsigned int out[32],const unsigned int a[32])
! 77: {
! 78: unsigned int j;
! 79: unsigned int u;
! 80:
! 81: u = 0;
! 82: for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; }
! 83: u += 121665 * a[31]; out[31] = u & 127;
! 84: u = 19 * (u >> 7);
! 85: for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; }
! 86: u += out[j]; out[j] = u;
! 87: }
! 88:
! 89: static void square(unsigned int out[32],const unsigned int a[32])
! 90: {
! 91: unsigned int i;
! 92: unsigned int j;
! 93: unsigned int u;
! 94:
! 95: for (i = 0;i < 32;++i) {
! 96: u = 0;
! 97: for (j = 0;j < i - j;++j) u += a[j] * a[i - j];
! 98: for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j];
! 99: u *= 2;
! 100: if ((i & 1) == 0) {
! 101: u += a[i / 2] * a[i / 2];
! 102: u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
! 103: }
! 104: out[i] = u;
! 105: }
! 106: squeeze(out);
! 107: }
! 108:
! 109: static void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b)
! 110: {
! 111: unsigned int j;
! 112: unsigned int t;
! 113: unsigned int bminus1;
! 114:
! 115: bminus1 = b - 1;
! 116: for (j = 0;j < 64;++j) {
! 117: t = bminus1 & (r[j] ^ s[j]);
! 118: p[j] = s[j] ^ t;
! 119: q[j] = r[j] ^ t;
! 120: }
! 121: }
! 122:
! 123: static void mainloop(unsigned int work[64],const unsigned char e[32])
! 124: {
! 125: unsigned int xzm1[64];
! 126: unsigned int xzm[64];
! 127: unsigned int xzmb[64];
! 128: unsigned int xzm1b[64];
! 129: unsigned int xznb[64];
! 130: unsigned int xzn1b[64];
! 131: unsigned int a0[64];
! 132: unsigned int a1[64];
! 133: unsigned int b0[64];
! 134: unsigned int b1[64];
! 135: unsigned int c1[64];
! 136: unsigned int r[32];
! 137: unsigned int s[32];
! 138: unsigned int t[32];
! 139: unsigned int u[32];
! 140: unsigned int j;
! 141: unsigned int b;
! 142: int pos;
! 143:
! 144: for (j = 0;j < 32;++j) xzm1[j] = work[j];
! 145: xzm1[32] = 1;
! 146: for (j = 33;j < 64;++j) xzm1[j] = 0;
! 147:
! 148: xzm[0] = 1;
! 149: for (j = 1;j < 64;++j) xzm[j] = 0;
! 150:
! 151: for (pos = 254;pos >= 0;--pos) {
! 152: b = e[pos / 8] >> (pos & 7);
! 153: b &= 1;
! 154: select(xzmb,xzm1b,xzm,xzm1,b);
! 155: add(a0,xzmb,xzmb + 32);
! 156: sub(a0 + 32,xzmb,xzmb + 32);
! 157: add(a1,xzm1b,xzm1b + 32);
! 158: sub(a1 + 32,xzm1b,xzm1b + 32);
! 159: square(b0,a0);
! 160: square(b0 + 32,a0 + 32);
! 161: mult(b1,a1,a0 + 32);
! 162: mult(b1 + 32,a1 + 32,a0);
! 163: add(c1,b1,b1 + 32);
! 164: sub(c1 + 32,b1,b1 + 32);
! 165: square(r,c1 + 32);
! 166: sub(s,b0,b0 + 32);
! 167: mult121665(t,s);
! 168: add(u,t,b0);
! 169: mult(xznb,b0,b0 + 32);
! 170: mult(xznb + 32,s,u);
! 171: square(xzn1b,c1);
! 172: mult(xzn1b + 32,r,work);
! 173: select(xzm,xzm1,xznb,xzn1b,b);
! 174: }
! 175:
! 176: for (j = 0;j < 64;++j) work[j] = xzm[j];
! 177: }
! 178:
! 179: static void recip(unsigned int out[32],const unsigned int z[32])
! 180: {
! 181: unsigned int z2[32];
! 182: unsigned int z9[32];
! 183: unsigned int z11[32];
! 184: unsigned int z2_5_0[32];
! 185: unsigned int z2_10_0[32];
! 186: unsigned int z2_20_0[32];
! 187: unsigned int z2_50_0[32];
! 188: unsigned int z2_100_0[32];
! 189: unsigned int t0[32];
! 190: unsigned int t1[32];
! 191: int i;
! 192:
! 193: /* 2 */ square(z2,z);
! 194: /* 4 */ square(t1,z2);
! 195: /* 8 */ square(t0,t1);
! 196: /* 9 */ mult(z9,t0,z);
! 197: /* 11 */ mult(z11,z9,z2);
! 198: /* 22 */ square(t0,z11);
! 199: /* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9);
! 200:
! 201: /* 2^6 - 2^1 */ square(t0,z2_5_0);
! 202: /* 2^7 - 2^2 */ square(t1,t0);
! 203: /* 2^8 - 2^3 */ square(t0,t1);
! 204: /* 2^9 - 2^4 */ square(t1,t0);
! 205: /* 2^10 - 2^5 */ square(t0,t1);
! 206: /* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0);
! 207:
! 208: /* 2^11 - 2^1 */ square(t0,z2_10_0);
! 209: /* 2^12 - 2^2 */ square(t1,t0);
! 210: /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); }
! 211: /* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0);
! 212:
! 213: /* 2^21 - 2^1 */ square(t0,z2_20_0);
! 214: /* 2^22 - 2^2 */ square(t1,t0);
! 215: /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); }
! 216: /* 2^40 - 2^0 */ mult(t0,t1,z2_20_0);
! 217:
! 218: /* 2^41 - 2^1 */ square(t1,t0);
! 219: /* 2^42 - 2^2 */ square(t0,t1);
! 220: /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); }
! 221: /* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0);
! 222:
! 223: /* 2^51 - 2^1 */ square(t0,z2_50_0);
! 224: /* 2^52 - 2^2 */ square(t1,t0);
! 225: /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
! 226: /* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0);
! 227:
! 228: /* 2^101 - 2^1 */ square(t1,z2_100_0);
! 229: /* 2^102 - 2^2 */ square(t0,t1);
! 230: /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); }
! 231: /* 2^200 - 2^0 */ mult(t1,t0,z2_100_0);
! 232:
! 233: /* 2^201 - 2^1 */ square(t0,t1);
! 234: /* 2^202 - 2^2 */ square(t1,t0);
! 235: /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
! 236: /* 2^250 - 2^0 */ mult(t0,t1,z2_50_0);
! 237:
! 238: /* 2^251 - 2^1 */ square(t1,t0);
! 239: /* 2^252 - 2^2 */ square(t0,t1);
! 240: /* 2^253 - 2^3 */ square(t1,t0);
! 241: /* 2^254 - 2^4 */ square(t0,t1);
! 242: /* 2^255 - 2^5 */ square(t1,t0);
! 243: /* 2^255 - 21 */ mult(out,t1,z11);
! 244: }
! 245:
! 246: int crypto_scalarmult_curve25519(unsigned char *q,
! 247: const unsigned char *n,
! 248: const unsigned char *p)
! 249: {
! 250: unsigned int work[96];
! 251: unsigned char e[32];
! 252: unsigned int i;
! 253: for (i = 0;i < 32;++i) e[i] = n[i];
! 254: e[0] &= 248;
! 255: e[31] &= 127;
! 256: e[31] |= 64;
! 257: for (i = 0;i < 32;++i) work[i] = p[i];
! 258: mainloop(work,e);
! 259: recip(work + 32,work + 32);
! 260: mult(work + 64,work,work + 32);
! 261: freeze(work + 64);
! 262: for (i = 0;i < 32;++i) q[i] = work[64 + i];
! 263: return 0;
! 264: }