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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 1.8 and up.
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.Nat448;
public class SecT409Field
{
private static final long M25 = -1L >>> 39;
private static final long M59 = -1L >>> 5;
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];
z[4] = x[4] ^ y[4];
z[5] = x[5] ^ y[5];
z[6] = x[6] ^ y[6];
}
public static void addExt(long[] xx, long[] yy, long[] zz)
{
for (int i = 0; i < 13; ++i)
{
zz[i] = xx[i] ^ yy[i];
}
}
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];
z[4] = x[4];
z[5] = x[5];
z[6] = x[6];
}
private static void addTo(long[] x, long[] z)
{
z[0] ^= x[0];
z[1] ^= x[1];
z[2] ^= x[2];
z[3] ^= x[3];
z[4] ^= x[4];
z[5] ^= x[5];
z[6] ^= x[6];
}
public static long[] fromBigInteger(BigInteger x)
{
return Nat.fromBigInteger64(409, x);
}
public static void halfTrace(long[] x, long[] z)
{
long[] tt = Nat.create64(13);
Nat448.copy64(x, z);
for (int i = 1; i < 409; 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 (Nat448.isZero64(x))
{
throw new IllegalStateException();
}
// Itoh-Tsujii inversion with bases { 2, 3 }
long[] t0 = Nat448.create64();
long[] t1 = Nat448.create64();
long[] t2 = Nat448.create64();
square(x, t0);
// 3 | 408
squareN(t0, 1, t1);
multiply(t0, t1, t0);
squareN(t1, 1, t1);
multiply(t0, t1, t0);
// 2 | 136
squareN(t0, 3, t1);
multiply(t0, t1, t0);
// 2 | 68
squareN(t0, 6, t1);
multiply(t0, t1, t0);
// 2 | 34
squareN(t0, 12, t1);
multiply(t0, t1, t2);
// ! {2,3} | 17
squareN(t2, 24, t0);
squareN(t0, 24, t1);
multiply(t0, t1, t0);
// 2 | 8
squareN(t0, 48, t1);
multiply(t0, t1, t0);
// 2 | 4
squareN(t0, 96, t1);
multiply(t0, t1, t0);
// 2 | 2
squareN(t0, 192, t1);
multiply(t0, t1, t0);
multiply(t0, t2, z);
}
public static void multiply(long[] x, long[] y, long[] z)
{
long[] tt = Nat448.createExt64();
implMultiply(x, y, tt);
reduce(tt, z);
}
public static void multiplyAddToExt(long[] x, long[] y, long[] zz)
{
long[] tt = Nat448.createExt64();
implMultiply(x, y, tt);
addExt(zz, tt, zz);
}
public static void reduce(long[] xx, long[] z)
{
long x00 = xx[0], x01 = xx[1], x02 = xx[2], x03 = xx[3];
long x04 = xx[4], x05 = xx[5], x06 = xx[6], x07 = xx[7];
long u = xx[12];
x05 ^= (u << 39);
x06 ^= (u >>> 25) ^ (u << 62);
x07 ^= (u >>> 2);
u = xx[11];
x04 ^= (u << 39);
x05 ^= (u >>> 25) ^ (u << 62);
x06 ^= (u >>> 2);
u = xx[10];
x03 ^= (u << 39);
x04 ^= (u >>> 25) ^ (u << 62);
x05 ^= (u >>> 2);
u = xx[9];
x02 ^= (u << 39);
x03 ^= (u >>> 25) ^ (u << 62);
x04 ^= (u >>> 2);
u = xx[8];
x01 ^= (u << 39);
x02 ^= (u >>> 25) ^ (u << 62);
x03 ^= (u >>> 2);
u = x07;
x00 ^= (u << 39);
x01 ^= (u >>> 25) ^ (u << 62);
x02 ^= (u >>> 2);
long t = x06 >>> 25;
z[0] = x00 ^ t;
z[1] = x01 ^ (t << 23);
z[2] = x02;
z[3] = x03;
z[4] = x04;
z[5] = x05;
z[6] = x06 & M25;
}
public static void reduce39(long[] z, int zOff)
{
long z6 = z[zOff + 6], t = z6 >>> 25;
z[zOff ] ^= t;
z[zOff + 1] ^= (t << 23);
z[zOff + 6] = z6 & M25;
}
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);
u0 = Interleave.unshuffle(x[4]); u1 = Interleave.unshuffle(x[5]);
long e2 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
long c2 = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);
u0 = Interleave.unshuffle(x[6]);
long e3 = (u0 & 0x00000000FFFFFFFFL);
long c3 = (u0 >>> 32);
z[0] = e0 ^ (c0 << 44);
z[1] = e1 ^ (c1 << 44) ^ (c0 >>> 20);
z[2] = e2 ^ (c2 << 44) ^ (c1 >>> 20);
z[3] = e3 ^ (c3 << 44) ^ (c2 >>> 20) ^ (c0 << 13);
z[4] = (c3 >>> 20) ^ (c1 << 13) ^ (c0 >>> 51);
z[5] = (c2 << 13) ^ (c1 >>> 51);
z[6] = (c3 << 13) ^ (c2 >>> 51);
// assert (c3 >>> 51) == 0;
}
public static void square(long[] x, long[] z)
{
long[] tt = Nat.create64(13);
implSquare(x, tt);
reduce(tt, z);
}
public static void squareAddToExt(long[] x, long[] zz)
{
long[] tt = Nat.create64(13);
implSquare(x, tt);
addExt(zz, tt, zz);
}
public static void squareN(long[] x, int n, long[] z)
{
// assert n > 0;
long[] tt = Nat.create64(13);
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 implCompactExt(long[] zz)
{
long z00 = zz[ 0], z01 = zz[ 1], z02 = zz[ 2], z03 = zz[ 3], z04 = zz[ 4], z05 = zz[ 5], z06 = zz[ 6];
long z07 = zz[ 7], z08 = zz[ 8], z09 = zz[ 9], z10 = zz[10], z11 = zz[11], z12 = zz[12], z13 = zz[13];
zz[ 0] = z00 ^ (z01 << 59);
zz[ 1] = (z01 >>> 5) ^ (z02 << 54);
zz[ 2] = (z02 >>> 10) ^ (z03 << 49);
zz[ 3] = (z03 >>> 15) ^ (z04 << 44);
zz[ 4] = (z04 >>> 20) ^ (z05 << 39);
zz[ 5] = (z05 >>> 25) ^ (z06 << 34);
zz[ 6] = (z06 >>> 30) ^ (z07 << 29);
zz[ 7] = (z07 >>> 35) ^ (z08 << 24);
zz[ 8] = (z08 >>> 40) ^ (z09 << 19);
zz[ 9] = (z09 >>> 45) ^ (z10 << 14);
zz[10] = (z10 >>> 50) ^ (z11 << 9);
zz[11] = (z11 >>> 55) ^ (z12 << 4)
^ (z13 << 63);
zz[12] = (z13 >>> 1);
// zz[13] = 0;
}
protected static void implExpand(long[] x, long[] z)
{
long x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6];
z[0] = x0 & M59;
z[1] = ((x0 >>> 59) ^ (x1 << 5)) & M59;
z[2] = ((x1 >>> 54) ^ (x2 << 10)) & M59;
z[3] = ((x2 >>> 49) ^ (x3 << 15)) & M59;
z[4] = ((x3 >>> 44) ^ (x4 << 20)) & M59;
z[5] = ((x4 >>> 39) ^ (x5 << 25)) & M59;
z[6] = ((x5 >>> 34) ^ (x6 << 30));
}
protected static void implMultiply(long[] x, long[] y, long[] zz)
{
long[] a = new long[7], b = new long[7];
implExpand(x, a);
implExpand(y, b);
long[] u = new long[8];
for (int i = 0; i < 7; ++i)
{
implMulwAcc(u, a[i], b[i], zz, i << 1);
}
long v0 = zz[0], v1 = zz[1];
v0 ^= zz[ 2]; zz[1] = v0 ^ v1; v1 ^= zz[ 3];
v0 ^= zz[ 4]; zz[2] = v0 ^ v1; v1 ^= zz[ 5];
v0 ^= zz[ 6]; zz[3] = v0 ^ v1; v1 ^= zz[ 7];
v0 ^= zz[ 8]; zz[4] = v0 ^ v1; v1 ^= zz[ 9];
v0 ^= zz[10]; zz[5] = v0 ^ v1; v1 ^= zz[11];
v0 ^= zz[12]; zz[6] = v0 ^ v1; v1 ^= zz[13];
long w = v0 ^ v1;
zz[ 7] = zz[0] ^ w;
zz[ 8] = zz[1] ^ w;
zz[ 9] = zz[2] ^ w;
zz[10] = zz[3] ^ w;
zz[11] = zz[4] ^ w;
zz[12] = zz[5] ^ w;
zz[13] = zz[6] ^ w;
implMulwAcc(u, a[0] ^ a[1], b[0] ^ b[1], zz, 1);
implMulwAcc(u, a[0] ^ a[2], b[0] ^ b[2], zz, 2);
implMulwAcc(u, a[0] ^ a[3], b[0] ^ b[3], zz, 3);
implMulwAcc(u, a[1] ^ a[2], b[1] ^ b[2], zz, 3);
implMulwAcc(u, a[0] ^ a[4], b[0] ^ b[4], zz, 4);
implMulwAcc(u, a[1] ^ a[3], b[1] ^ b[3], zz, 4);
implMulwAcc(u, a[0] ^ a[5], b[0] ^ b[5], zz, 5);
implMulwAcc(u, a[1] ^ a[4], b[1] ^ b[4], zz, 5);
implMulwAcc(u, a[2] ^ a[3], b[2] ^ b[3], zz, 5);
implMulwAcc(u, a[0] ^ a[6], b[0] ^ b[6], zz, 6);
implMulwAcc(u, a[1] ^ a[5], b[1] ^ b[5], zz, 6);
implMulwAcc(u, a[2] ^ a[4], b[2] ^ b[4], zz, 6);
implMulwAcc(u, a[1] ^ a[6], b[1] ^ b[6], zz, 7);
implMulwAcc(u, a[2] ^ a[5], b[2] ^ b[5], zz, 7);
implMulwAcc(u, a[3] ^ a[4], b[3] ^ b[4], zz, 7);
implMulwAcc(u, a[2] ^ a[6], b[2] ^ b[6], zz, 8);
implMulwAcc(u, a[3] ^ a[5], b[3] ^ b[5], zz, 8);
implMulwAcc(u, a[3] ^ a[6], b[3] ^ b[6], zz, 9);
implMulwAcc(u, a[4] ^ a[5], b[4] ^ b[5], zz, 9);
implMulwAcc(u, a[4] ^ a[6], b[4] ^ b[6], zz, 10);
implMulwAcc(u, a[5] ^ a[6], b[5] ^ b[6], zz, 11);
implCompactExt(zz);
}
protected static void implMulwAcc(long[] u, long x, long y, long[] z, int zOff)
{
// assert x >>> 59 == 0;
// assert y >>> 59 == 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);
// assert h >>> 53 == 0;
z[zOff ] ^= l & M59;
z[zOff + 1] ^= (l >>> 59) ^ (h << 5);
}
protected static void implSquare(long[] x, long[] zz)
{
Interleave.expand64To128(x, 0, 6, zz, 0);
zz[12] = Interleave.expand32to64((int)x[6]);
}
}
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