| package org.bouncycastle.math.ec.custom.sec; |
| |
| import java.math.BigInteger; |
| |
| import org.bouncycastle.math.raw.Interleave; |
| import org.bouncycastle.math.raw.Nat192; |
| |
| public class SecT163Field |
| { |
| private static final long M35 = -1L >>> 29; |
| private static final long M55 = -1L >>> 9; |
| |
| private static final long[] ROOT_Z = new long[]{ 0xB6DB6DB6DB6DB6B0L, 0x492492492492DB6DL, 0x492492492L }; |
| |
| public static void add(long[] x, long[] y, long[] z) |
| { |
| z[0] = x[0] ^ y[0]; |
| z[1] = x[1] ^ y[1]; |
| z[2] = x[2] ^ y[2]; |
| } |
| |
| public static void addExt(long[] xx, long[] yy, long[] zz) |
| { |
| zz[0] = xx[0] ^ yy[0]; |
| zz[1] = xx[1] ^ yy[1]; |
| zz[2] = xx[2] ^ yy[2]; |
| zz[3] = xx[3] ^ yy[3]; |
| zz[4] = xx[4] ^ yy[4]; |
| zz[5] = xx[5] ^ yy[5]; |
| } |
| |
| public static void addOne(long[] x, long[] z) |
| { |
| z[0] = x[0] ^ 1L; |
| z[1] = x[1]; |
| z[2] = x[2]; |
| } |
| |
| public static long[] fromBigInteger(BigInteger x) |
| { |
| long[] z = Nat192.fromBigInteger64(x); |
| reduce29(z, 0); |
| return z; |
| } |
| |
| public static void invert(long[] x, long[] z) |
| { |
| if (Nat192.isZero64(x)) |
| { |
| throw new IllegalStateException(); |
| } |
| |
| // Itoh-Tsujii inversion with bases { 2, 3 } |
| |
| long[] t0 = Nat192.create64(); |
| long[] t1 = Nat192.create64(); |
| |
| square(x, t0); |
| |
| // 3 | 162 |
| squareN(t0, 1, t1); |
| multiply(t0, t1, t0); |
| squareN(t1, 1, t1); |
| multiply(t0, t1, t0); |
| |
| // 3 | 54 |
| squareN(t0, 3, t1); |
| multiply(t0, t1, t0); |
| squareN(t1, 3, t1); |
| multiply(t0, t1, t0); |
| |
| // 3 | 18 |
| squareN(t0, 9, t1); |
| multiply(t0, t1, t0); |
| squareN(t1, 9, t1); |
| multiply(t0, t1, t0); |
| |
| // 3 | 6 |
| squareN(t0, 27, t1); |
| multiply(t0, t1, t0); |
| squareN(t1, 27, t1); |
| multiply(t0, t1, t0); |
| |
| // 2 | 2 |
| squareN(t0, 81, t1); |
| multiply(t0, t1, z); |
| } |
| |
| public static void multiply(long[] x, long[] y, long[] z) |
| { |
| long[] tt = Nat192.createExt64(); |
| implMultiply(x, y, tt); |
| reduce(tt, z); |
| } |
| |
| public static void multiplyAddToExt(long[] x, long[] y, long[] zz) |
| { |
| long[] tt = Nat192.createExt64(); |
| implMultiply(x, y, tt); |
| addExt(zz, tt, zz); |
| } |
| |
| public static void reduce(long[] xx, long[] z) |
| { |
| long x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4], x5 = xx[5]; |
| |
| x2 ^= (x5 << 29) ^ (x5 << 32) ^ (x5 << 35) ^ (x5 << 36); |
| x3 ^= (x5 >>> 35) ^ (x5 >>> 32) ^ (x5 >>> 29) ^ (x5 >>> 28); |
| |
| x1 ^= (x4 << 29) ^ (x4 << 32) ^ (x4 << 35) ^ (x4 << 36); |
| x2 ^= (x4 >>> 35) ^ (x4 >>> 32) ^ (x4 >>> 29) ^ (x4 >>> 28); |
| |
| x0 ^= (x3 << 29) ^ (x3 << 32) ^ (x3 << 35) ^ (x3 << 36); |
| x1 ^= (x3 >>> 35) ^ (x3 >>> 32) ^ (x3 >>> 29) ^ (x3 >>> 28); |
| |
| long t = x2 >>> 35; |
| z[0] = x0 ^ t ^ (t << 3) ^ (t << 6) ^ (t << 7); |
| z[1] = x1; |
| z[2] = x2 & M35; |
| } |
| |
| public static void reduce29(long[] z, int zOff) |
| { |
| long z2 = z[zOff + 2], t = z2 >>> 35; |
| z[zOff ] ^= t ^ (t << 3) ^ (t << 6) ^ (t << 7); |
| z[zOff + 2] = z2 & M35; |
| } |
| |
| public static void sqrt(long[] x, long[] z) |
| { |
| long[] odd = Nat192.create64(); |
| |
| long u0, u1; |
| u0 = Interleave.unshuffle(x[0]); u1 = Interleave.unshuffle(x[1]); |
| long e0 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32); |
| odd[0] = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L); |
| |
| u0 = Interleave.unshuffle(x[2]); |
| long e1 = (u0 & 0x00000000FFFFFFFFL); |
| odd[1] = (u0 >>> 32); |
| |
| multiply(odd, ROOT_Z, z); |
| |
| z[0] ^= e0; |
| z[1] ^= e1; |
| } |
| |
| public static void square(long[] x, long[] z) |
| { |
| long[] tt = Nat192.createExt64(); |
| implSquare(x, tt); |
| reduce(tt, z); |
| } |
| |
| public static void squareAddToExt(long[] x, long[] zz) |
| { |
| long[] tt = Nat192.createExt64(); |
| implSquare(x, tt); |
| addExt(zz, tt, zz); |
| } |
| |
| public static void squareN(long[] x, int n, long[] z) |
| { |
| // assert n > 0; |
| |
| long[] tt = Nat192.createExt64(); |
| implSquare(x, tt); |
| reduce(tt, z); |
| |
| while (--n > 0) |
| { |
| implSquare(z, tt); |
| reduce(tt, z); |
| } |
| } |
| |
| public static int trace(long[] x) |
| { |
| // Non-zero-trace bits: 0, 157 |
| return (int)(x[0] ^ (x[2] >>> 29)) & 1; |
| } |
| |
| protected static void implCompactExt(long[] zz) |
| { |
| long z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4], z5 = zz[5]; |
| zz[0] = z0 ^ (z1 << 55); |
| zz[1] = (z1 >>> 9) ^ (z2 << 46); |
| zz[2] = (z2 >>> 18) ^ (z3 << 37); |
| zz[3] = (z3 >>> 27) ^ (z4 << 28); |
| zz[4] = (z4 >>> 36) ^ (z5 << 19); |
| zz[5] = (z5 >>> 45); |
| } |
| |
| protected static void implMultiply(long[] x, long[] y, long[] zz) |
| { |
| /* |
| * "Five-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein. |
| */ |
| |
| long f0 = x[0], f1 = x[1], f2 = x[2]; |
| f2 = ((f1 >>> 46) ^ (f2 << 18)); |
| f1 = ((f0 >>> 55) ^ (f1 << 9)) & M55; |
| f0 &= M55; |
| |
| long g0 = y[0], g1 = y[1], g2 = y[2]; |
| g2 = ((g1 >>> 46) ^ (g2 << 18)); |
| g1 = ((g0 >>> 55) ^ (g1 << 9)) & M55; |
| g0 &= M55; |
| |
| long[] H = new long[10]; |
| |
| implMulw(f0, g0, H, 0); // H(0) 55/54 bits |
| implMulw(f2, g2, H, 2); // H(INF) 55/50 bits |
| |
| long t0 = f0 ^ f1 ^ f2; |
| long t1 = g0 ^ g1 ^ g2; |
| |
| implMulw(t0, t1, H, 4); // H(1) 55/54 bits |
| |
| long t2 = (f1 << 1) ^ (f2 << 2); |
| long t3 = (g1 << 1) ^ (g2 << 2); |
| |
| implMulw(f0 ^ t2, g0 ^ t3, H, 6); // H(t) 55/56 bits |
| implMulw(t0 ^ t2, t1 ^ t3, H, 8); // H(t + 1) 55/56 bits |
| |
| long t4 = H[6] ^ H[8]; |
| long t5 = H[7] ^ H[9]; |
| |
| // assert t5 >>> 55 == 0; |
| |
| // Calculate V |
| long v0 = (t4 << 1) ^ H[6]; |
| long v1 = t4 ^ (t5 << 1) ^ H[7]; |
| long v2 = t5; |
| |
| // Calculate U |
| long u0 = H[0]; |
| long u1 = H[1] ^ H[0] ^ H[4]; |
| long u2 = H[1] ^ H[5]; |
| |
| // Calculate W |
| long w0 = u0 ^ v0 ^ (H[2] << 4) ^ (H[2] << 1); |
| long w1 = u1 ^ v1 ^ (H[3] << 4) ^ (H[3] << 1); |
| long w2 = u2 ^ v2; |
| |
| // Propagate carries |
| w1 ^= (w0 >>> 55); w0 &= M55; |
| w2 ^= (w1 >>> 55); w1 &= M55; |
| |
| // assert (w0 & 1L) == 0; |
| |
| // Divide W by t |
| |
| w0 = (w0 >>> 1) ^ ((w1 & 1L) << 54); |
| w1 = (w1 >>> 1) ^ ((w2 & 1L) << 54); |
| w2 = (w2 >>> 1); |
| |
| // Divide W by (t + 1) |
| |
| w0 ^= (w0 << 1); |
| w0 ^= (w0 << 2); |
| w0 ^= (w0 << 4); |
| w0 ^= (w0 << 8); |
| w0 ^= (w0 << 16); |
| w0 ^= (w0 << 32); |
| |
| w0 &= M55; w1 ^= (w0 >>> 54); |
| |
| w1 ^= (w1 << 1); |
| w1 ^= (w1 << 2); |
| w1 ^= (w1 << 4); |
| w1 ^= (w1 << 8); |
| w1 ^= (w1 << 16); |
| w1 ^= (w1 << 32); |
| |
| w1 &= M55; w2 ^= (w1 >>> 54); |
| |
| w2 ^= (w2 << 1); |
| w2 ^= (w2 << 2); |
| w2 ^= (w2 << 4); |
| w2 ^= (w2 << 8); |
| w2 ^= (w2 << 16); |
| w2 ^= (w2 << 32); |
| |
| // assert w2 >>> 52 == 0; |
| |
| zz[0] = u0; |
| zz[1] = u1 ^ w0 ^ H[2]; |
| zz[2] = u2 ^ w1 ^ w0 ^ H[3]; |
| zz[3] = w2 ^ w1; |
| zz[4] = w2 ^ H[2]; |
| zz[5] = H[3]; |
| |
| implCompactExt(zz); |
| } |
| |
| protected static void implMulw(long x, long y, long[] z, int zOff) |
| { |
| // assert x >>> 56 == 0; |
| // assert y >>> 56 == 0; |
| |
| long[] u = new long[8]; |
| // u[0] = 0; |
| u[1] = y; |
| u[2] = u[1] << 1; |
| u[3] = u[2] ^ y; |
| u[4] = u[2] << 1; |
| u[5] = u[4] ^ y; |
| u[6] = u[3] << 1; |
| u[7] = u[6] ^ y; |
| |
| int j = (int)x; |
| long g, h = 0, l = u[j & 3]; |
| int k = 47; |
| do |
| { |
| j = (int)(x >>> k); |
| g = u[j & 7] |
| ^ u[(j >>> 3) & 7] << 3 |
| ^ u[(j >>> 6) & 7] << 6; |
| l ^= (g << k); |
| h ^= (g >>> -k); |
| } |
| while ((k -= 9) > 0); |
| |
| // assert h >>> 47 == 0; |
| |
| z[zOff ] = l & M55; |
| z[zOff + 1] = (l >>> 55) ^ (h << 9); |
| } |
| |
| protected static void implSquare(long[] x, long[] zz) |
| { |
| Interleave.expand64To128(x[0], zz, 0); |
| Interleave.expand64To128(x[1], zz, 2); |
| |
| long x2 = x[2]; |
| zz[4] = Interleave.expand32to64((int)x2); |
| zz[5] = Interleave.expand8to16((int)(x2 >>> 32)) & 0xFFFFFFFFL; |
| } |
| } |