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org.bouncycastle.math.ec.custom.sec.SecT113Field Maven / Gradle / Ivy
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.Nat128;
public class SecT113Field
{
private static final long M49 = -1L >>> 15;
private static final long M57 = -1L >>> 7;
public static void add(long[] x, long[] y, long[] z)
{
z[0] = x[0] ^ y[0];
z[1] = x[1] ^ y[1];
}
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];
}
public static void addOne(long[] x, long[] z)
{
z[0] = x[0] ^ 1L;
z[1] = x[1];
}
private static void addTo(long[] x, long[] z)
{
z[0] ^= x[0];
z[1] ^= x[1];
}
public static long[] fromBigInteger(BigInteger x)
{
return Nat.fromBigInteger64(113, x);
}
public static void halfTrace(long[] x, long[] z)
{
long[] tt = Nat128.createExt64();
Nat128.copy64(x, z);
for (int i = 1; i < 113; 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 (Nat128.isZero64(x))
{
throw new IllegalStateException();
}
// Itoh-Tsujii inversion
long[] t0 = Nat128.create64();
long[] t1 = Nat128.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);
squareN(t1, 28, t0);
multiply(t0, t1, t0);
squareN(t0, 56, t1);
multiply(t1, t0, t1);
square(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];
x1 ^= (x3 << 15) ^ (x3 << 24);
x2 ^= (x3 >>> 49) ^ (x3 >>> 40);
x0 ^= (x2 << 15) ^ (x2 << 24);
x1 ^= (x2 >>> 49) ^ (x2 >>> 40);
long t = x1 >>> 49;
z[0] = x0 ^ t ^ (t << 9);
z[1] = x1 & M49;
}
public static void reduce15(long[] z, int zOff)
{
long z1 = z[zOff + 1], t = z1 >>> 49;
z[zOff ] ^= t ^ (t << 9);
z[zOff + 1] = z1 & M49;
}
public static void sqrt(long[] x, long[] z)
{
long u0 = Interleave.unshuffle(x[0]), u1 = Interleave.unshuffle(x[1]);
long e0 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
long c0 = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);
z[0] = e0 ^ (c0 << 57) ^ (c0 << 5);
z[1] = (c0 >>> 7) ^ (c0 >>> 59);
}
public static void square(long[] x, long[] z)
{
long[] tt = Nat128.createExt64();
implSquare(x, tt);
reduce(tt, z);
}
public static void squareAddToExt(long[] x, long[] zz)
{
long[] tt = Nat128.createExt64();
implSquare(x, tt);
addExt(zz, tt, zz);
}
public static void squareN(long[] x, int n, long[] z)
{
// assert n > 0;
long[] tt = Nat128.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
return (int)(x[0]) & 1;
}
protected static void implMultiply(long[] x, long[] y, long[] zz)
{
/*
* "Three-way recursion" as described in "Batch binary Edwards", Daniel J. Bernstein.
*/
long f0 = x[0], f1 = x[1];
f1 = ((f0 >>> 57) ^ (f1 << 7)) & M57;
f0 &= M57;
long g0 = y[0], g1 = y[1];
g1 = ((g0 >>> 57) ^ (g1 << 7)) & M57;
g0 &= M57;
long[] u = zz;
long[] H = new long[6];
implMulw(u, f0, g0, H, 0); // H(0) 57/56 bits
implMulw(u, f1, g1, H, 2); // H(INF) 57/54 bits
implMulw(u, f0 ^ f1, g0 ^ g1, H, 4); // H(1) 57/56 bits
long r = H[1] ^ H[2];
long z0 = H[0],
z3 = H[3],
z1 = H[4] ^ z0 ^ r,
z2 = H[5] ^ z3 ^ r;
zz[0] = z0 ^ (z1 << 57);
zz[1] = (z1 >>> 7) ^ (z2 << 50);
zz[2] = (z2 >>> 14) ^ (z3 << 43);
zz[3] = (z3 >>> 21);
}
protected static void implMulw(long[] u, long x, long y, long[] z, int zOff)
{
// assert x >>> 57 == 0;
// assert y >>> 57 == 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];
int k = 48;
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);
h ^= ((x & 0x0100804020100800L) & ((y << 7) >> 63)) >>> 8;
// assert h >>> 49 == 0;
z[zOff ] = l & M57;
z[zOff + 1] = (l >>> 57) ^ (h << 7);
}
protected static void implSquare(long[] x, long[] zz)
{
Interleave.expand64To128(x, 0, 2, zz, 0);
}
}
