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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8.
package org.bouncycastle.math.ec.custom.sec;
import java.math.BigInteger;
import org.bouncycastle.math.raw.Interleave;
import org.bouncycastle.math.raw.Nat;
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];
}
private static void addTo(long[] x, long[] z)
{
z[0] ^= x[0];
z[1] ^= x[1];
z[2] ^= x[2];
}
public static long[] fromBigInteger(BigInteger x)
{
return Nat.fromBigInteger64(163, x);
}
public static void halfTrace(long[] x, long[] z)
{
long[] tt = Nat192.createExt64();
Nat192.copy64(x, z);
for (int i = 1; i < 163; i += 2)
{
implSquare(z, tt);
reduce(tt, z);
implSquare(z, tt);
reduce(tt, z);
addTo(x, 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 = new long[8];
implMultiply(x, y, tt);
reduce(tt, z);
}
public static void multiplyAddToExt(long[] x, long[] y, long[] zz)
{
long[] tt = new long[8];
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[] u = zz;
long[] H = new long[10];
implMulw(u, f0, g0, H, 0); // H(0) 55/54 bits
implMulw(u, f2, g2, H, 2); // H(INF) 55/50 bits
long t0 = f0 ^ f1 ^ f2;
long t1 = g0 ^ g1 ^ g2;
implMulw(u, t0, t1, H, 4); // H(1) 55/54 bits
long t2 = (f1 << 1) ^ (f2 << 2);
long t3 = (g1 << 1) ^ (g2 << 2);
implMulw(u, f0 ^ t2, g0 ^ t3, H, 6); // H(t) 55/56 bits
implMulw(u, 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[] u, long x, long y, long[] z, int zOff)
{
// assert x >>> 56 == 0;
// assert y >>> 56 == 0;
// 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, 3, zz, 0);
}
}