org.bouncycastle.math.ec.custom.sec.SecT239Field Maven / Gradle / Ivy
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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.Nat256;
public class SecT239Field
{
private static final long M47 = -1L >>> 17;
private static final long M60 = -1L >>> 4;
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];
z[3] = x[3] ^ y[3];
}
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];
zz[6] = xx[6] ^ yy[6];
zz[7] = xx[7] ^ yy[7];
}
public static void addOne(long[] x, long[] z)
{
z[0] = x[0] ^ 1L;
z[1] = x[1];
z[2] = x[2];
z[3] = x[3];
}
private static void addTo(long[] x, long[] z)
{
z[0] ^= x[0];
z[1] ^= x[1];
z[2] ^= x[2];
z[3] ^= x[3];
}
public static long[] fromBigInteger(BigInteger x)
{
return Nat.fromBigInteger64(239, x);
}
public static void halfTrace(long[] x, long[] z)
{
long[] tt = Nat256.createExt64();
Nat256.copy64(x, z);
for (int i = 1; i < 239; 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 (Nat256.isZero64(x))
{
throw new IllegalStateException();
}
// Itoh-Tsujii inversion
long[] t0 = Nat256.create64();
long[] t1 = Nat256.create64();
square(x, t0);
multiply(t0, x, t0);
square(t0, t0);
multiply(t0, x, t0);
squareN(t0, 3, t1);
multiply(t1, t0, t1);
square(t1, t1);
multiply(t1, x, t1);
squareN(t1, 7, t0);
multiply(t0, t1, t0);
squareN(t0, 14, t1);
multiply(t1, t0, t1);
square(t1, t1);
multiply(t1, x, t1);
squareN(t1, 29, t0);
multiply(t0, t1, t0);
square(t0, t0);
multiply(t0, x, t0);
squareN(t0, 59, t1);
multiply(t1, t0, t1);
square(t1, t1);
multiply(t1, x, t1);
squareN(t1, 119, t0);
multiply(t0, t1, t0);
square(t0, z);
}
public static void multiply(long[] x, long[] y, long[] z)
{
long[] tt = Nat256.createExt64();
implMultiply(x, y, tt);
reduce(tt, z);
}
public static void multiplyAddToExt(long[] x, long[] y, long[] zz)
{
long[] tt = Nat256.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];
long x4 = xx[4], x5 = xx[5], x6 = xx[6], x7 = xx[7];
x3 ^= (x7 << 17);
x4 ^= (x7 >>> 47);
x5 ^= (x7 << 47);
x6 ^= (x7 >>> 17);
x2 ^= (x6 << 17);
x3 ^= (x6 >>> 47);
x4 ^= (x6 << 47);
x5 ^= (x6 >>> 17);
x1 ^= (x5 << 17);
x2 ^= (x5 >>> 47);
x3 ^= (x5 << 47);
x4 ^= (x5 >>> 17);
x0 ^= (x4 << 17);
x1 ^= (x4 >>> 47);
x2 ^= (x4 << 47);
x3 ^= (x4 >>> 17);
long t = x3 >>> 47;
z[0] = x0 ^ t;
z[1] = x1;
z[2] = x2 ^ (t << 30);
z[3] = x3 & M47;
}
public static void reduce17(long[] z, int zOff)
{
long z3 = z[zOff + 3], t = z3 >>> 47;
z[zOff ] ^= t;
z[zOff + 2] ^= (t << 30);
z[zOff + 3] = z3 & M47;
}
public static void sqrt(long[] x, long[] z)
{
long u0, u1;
u0 = Interleave.unshuffle(x[0]); u1 = Interleave.unshuffle(x[1]);
long e0 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
long c0 = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);
u0 = Interleave.unshuffle(x[2]); u1 = Interleave.unshuffle(x[3]);
long e1 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
long c1 = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);
long c2, c3;
c3 = (c1 >>> 49);
c2 = (c0 >>> 49) | (c1 << 15);
c1 ^= (c0 << 15);
long[] tt = Nat256.createExt64();
int[] shifts = { 39, 120 };
for (int i = 0; i < shifts.length; ++i)
{
int w = shifts[i] >>> 6, s = shifts[i] & 63;
// assert s != 0;
tt[w ] ^= (c0 << s);
tt[w + 1] ^= (c1 << s) | (c0 >>> -s);
tt[w + 2] ^= (c2 << s) | (c1 >>> -s);
tt[w + 3] ^= (c3 << s) | (c2 >>> -s);
tt[w + 4] ^= (c3 >>> -s);
}
reduce(tt, z);
z[0] ^= e0;
z[1] ^= e1;
}
public static void square(long[] x, long[] z)
{
long[] tt = Nat256.createExt64();
implSquare(x, tt);
reduce(tt, z);
}
public static void squareAddToExt(long[] x, long[] zz)
{
long[] tt = Nat256.createExt64();
implSquare(x, tt);
addExt(zz, tt, zz);
}
public static void squareN(long[] x, int n, long[] z)
{
// assert n > 0;
long[] tt = Nat256.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, 81, 162
return (int)(x[0] ^ (x[1] >>> 17) ^ (x[2] >>> 34)) & 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], z6 = zz[6], z7 = zz[7];
zz[0] = z0 ^ (z1 << 60);
zz[1] = (z1 >>> 4) ^ (z2 << 56);
zz[2] = (z2 >>> 8) ^ (z3 << 52);
zz[3] = (z3 >>> 12) ^ (z4 << 48);
zz[4] = (z4 >>> 16) ^ (z5 << 44);
zz[5] = (z5 >>> 20) ^ (z6 << 40);
zz[6] = (z6 >>> 24) ^ (z7 << 36);
zz[7] = (z7 >>> 28);
}
protected static void implExpand(long[] x, long[] z)
{
long x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3];
z[0] = x0 & M60;
z[1] = ((x0 >>> 60) ^ (x1 << 4)) & M60;
z[2] = ((x1 >>> 56) ^ (x2 << 8)) & M60;
z[3] = ((x2 >>> 52) ^ (x3 << 12));
}
protected static void implMultiply(long[] x, long[] y, long[] zz)
{
/*
* "Two-level seven-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
*/
long[] f = new long[4], g = new long[4];
implExpand(x, f);
implExpand(y, g);
long[] u = new long[8];
implMulwAcc(u, f[0], g[0], zz, 0);
implMulwAcc(u, f[1], g[1], zz, 1);
implMulwAcc(u, f[2], g[2], zz, 2);
implMulwAcc(u, f[3], g[3], zz, 3);
// U *= (1 - t^n)
for (int i = 5; i > 0; --i)
{
zz[i] ^= zz[i - 1];
}
implMulwAcc(u, f[0] ^ f[1], g[0] ^ g[1], zz, 1);
implMulwAcc(u, f[2] ^ f[3], g[2] ^ g[3], zz, 3);
// V *= (1 - t^2n)
for (int i = 7; i > 1; --i)
{
zz[i] ^= zz[i - 2];
}
// Double-length recursion
{
long c0 = f[0] ^ f[2], c1 = f[1] ^ f[3];
long d0 = g[0] ^ g[2], d1 = g[1] ^ g[3];
implMulwAcc(u, c0 ^ c1, d0 ^ d1, zz, 3);
long[] t = new long[3];
implMulwAcc(u, c0, d0, t, 0);
implMulwAcc(u, c1, d1, t, 1);
long t0 = t[0], t1 = t[1], t2 = t[2];
zz[2] ^= t0;
zz[3] ^= t0 ^ t1;
zz[4] ^= t2 ^ t1;
zz[5] ^= t2;
}
implCompactExt(zz);
}
protected static void implMulwAcc(long[] u, long x, long y, long[] z, int zOff)
{
// assert x >>> 60 == 0;
// assert y >>> 60 == 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 & 7]
^ (u[(j >>> 3) & 7] << 3);
int k = 54;
do
{
j = (int)(x >>> k);
g = u[j & 7]
^ u[(j >>> 3) & 7] << 3;
l ^= (g << k);
h ^= (g >>> -k);
}
while ((k -= 6) > 0);
h ^= ((x & 0x0820820820820820L) & ((y << 4) >> 63)) >>> 5;
// assert h >>> 55 == 0;
z[zOff ] ^= l & M60;
z[zOff + 1] ^= (l >>> 60) ^ (h << 4);
}
protected static void implSquare(long[] x, long[] zz)
{
Interleave.expand64To128(x, 0, 4, zz, 0);
}
}