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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 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.Nat576;
public class SecT571Field
{
private static final long M59 = -1L >>> 5;
private static final long[] ROOT_Z = new long[]{ 0x2BE1195F08CAFB99L, 0x95F08CAF84657C23L, 0xCAF84657C232BE11L,
0x657C232BE1195F08L, 0xF84657C2308CAF84L, 0x7C232BE1195F08CAL, 0xBE1195F08CAF8465L, 0x5F08CAF84657C232L,
0x784657C232BE119L };
public static void add(long[] x, long[] y, long[] z)
{
for (int i = 0; i < 9; ++i)
{
z[i] = x[i] ^ y[i];
}
}
private static void add(long[] x, int xOff, long[] y, int yOff, long[] z, int zOff)
{
for (int i = 0; i < 9; ++i)
{
z[zOff + i] = x[xOff + i] ^ y[yOff + i];
}
}
public static void addBothTo(long[] x, long[] y, long[] z)
{
for (int i = 0; i < 9; ++i)
{
z[i] ^= x[i] ^ y[i];
}
}
private static void addBothTo(long[] x, int xOff, long[] y, int yOff, long[] z, int zOff)
{
for (int i = 0; i < 9; ++i)
{
z[zOff + i] ^= x[xOff + i] ^ y[yOff + i];
}
}
public static void addExt(long[] xx, long[] yy, long[] zz)
{
for (int i = 0; i < 18; ++i)
{
zz[i] = xx[i] ^ yy[i];
}
}
public static void addOne(long[] x, long[] z)
{
z[0] = x[0] ^ 1L;
for (int i = 1; i < 9; ++i)
{
z[i] = x[i];
}
}
private static void addTo(long[] x, long[] z)
{
for (int i = 0; i < 9; ++i)
{
z[i] ^= x[i];
}
}
public static long[] fromBigInteger(BigInteger x)
{
return Nat.fromBigInteger64(571, x);
}
public static void halfTrace(long[] x, long[] z)
{
long[] tt = Nat576.createExt64();
Nat576.copy64(x, z);
for (int i = 1; i < 571; 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 (Nat576.isZero64(x))
{
throw new IllegalStateException();
}
// Itoh-Tsujii inversion with bases { 2, 3, 5 }
long[] t0 = Nat576.create64();
long[] t1 = Nat576.create64();
long[] t2 = Nat576.create64();
square(x, t2);
// 5 | 570
square(t2, t0);
square(t0, t1);
multiply(t0, t1, t0);
squareN(t0, 2, t1);
multiply(t0, t1, t0);
multiply(t0, t2, t0);
// 3 | 114
squareN(t0, 5, t1);
multiply(t0, t1, t0);
squareN(t1, 5, t1);
multiply(t0, t1, t0);
// 2 | 38
squareN(t0, 15, t1);
multiply(t0, t1, t2);
// ! {2,3,5} | 19
squareN(t2, 30, t0);
squareN(t0, 30, t1);
multiply(t0, t1, t0);
// 3 | 9
squareN(t0, 60, t1);
multiply(t0, t1, t0);
squareN(t1, 60, t1);
multiply(t0, t1, t0);
// 3 | 3
squareN(t0, 180, t1);
multiply(t0, t1, t0);
squareN(t1, 180, t1);
multiply(t0, t1, t0);
multiply(t0, t2, z);
}
public static void multiply(long[] x, long[] y, long[] z)
{
long[] tt = Nat576.createExt64();
implMultiply(x, y, tt);
reduce(tt, z);
}
public static void multiplyAddToExt(long[] x, long[] y, long[] zz)
{
long[] tt = Nat576.createExt64();
implMultiply(x, y, tt);
addExt(zz, tt, zz);
}
public static void multiplyPrecomp(long[] x, long[] precomp, long[] z)
{
long[] tt = Nat576.createExt64();
implMultiplyPrecomp(x, precomp, tt);
reduce(tt, z);
}
public static void multiplyPrecompAddToExt(long[] x, long[] precomp, long[] zz)
{
long[] tt = Nat576.createExt64();
implMultiplyPrecomp(x, precomp, tt);
addExt(zz, tt, zz);
}
public static long[] precompMultiplicand(long[] x)
{
/*
* Precompute table of all 4-bit products of x (first section)
*/
int len = 9 << 4;
long[] t = new long[len << 1];
System.arraycopy(x, 0, t, 9, 9);
// reduce5(T0, 9);
int tOff = 0;
for (int i = 7; i > 0; --i)
{
tOff += 18;
Nat.shiftUpBit64(9, t, tOff >>> 1, 0L, t, tOff);
reduce5(t, tOff);
add(t, 9, t, tOff, t, tOff + 9);
}
/*
* Second section with all 4-bit products of x shifted 4 bits
*/
Nat.shiftUpBits64(len, t, 0, 4, 0L, t, len);
return t;
}
public static void reduce(long[] xx, long[] z)
{
long xx09 = xx[9];
long u = xx[17], v = xx09;
xx09 = v ^ (u >>> 59) ^ (u >>> 57) ^ (u >>> 54) ^ (u >>> 49);
v = xx[8] ^ (u << 5) ^ (u << 7) ^ (u << 10) ^ (u << 15);
for (int i = 16; i >= 10; --i)
{
u = xx[i];
z[i - 8] = v ^ (u >>> 59) ^ (u >>> 57) ^ (u >>> 54) ^ (u >>> 49);
v = xx[i - 9] ^ (u << 5) ^ (u << 7) ^ (u << 10) ^ (u << 15);
}
u = xx09;
z[1] = v ^ (u >>> 59) ^ (u >>> 57) ^ (u >>> 54) ^ (u >>> 49);
v = xx[0] ^ (u << 5) ^ (u << 7) ^ (u << 10) ^ (u << 15);
long x08 = z[8];
long t = x08 >>> 59;
z[0] = v ^ t ^ (t << 2) ^ (t << 5) ^ (t << 10);
z[8] = x08 & M59;
}
public static void reduce5(long[] z, int zOff)
{
long z8 = z[zOff + 8], t = z8 >>> 59;
z[zOff ] ^= t ^ (t << 2) ^ (t << 5) ^ (t << 10);
z[zOff + 8] = z8 & M59;
}
public static void sqrt(long[] x, long[] z)
{
long[] evn = Nat576.create64(), odd = Nat576.create64();
int pos = 0;
for (int i = 0; i < 4; ++i)
{
long u0 = Interleave.unshuffle(x[pos++]);
long u1 = Interleave.unshuffle(x[pos++]);
evn[i] = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
odd[i] = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);
}
{
long u0 = Interleave.unshuffle(x[pos]);
evn[4] = (u0 & 0x00000000FFFFFFFFL);
odd[4] = (u0 >>> 32);
}
multiply(odd, ROOT_Z, z);
add(z, evn, z);
}
public static void square(long[] x, long[] z)
{
long[] tt = Nat576.createExt64();
implSquare(x, tt);
reduce(tt, z);
}
public static void squareAddToExt(long[] x, long[] zz)
{
long[] tt = Nat576.createExt64();
implSquare(x, tt);
addExt(zz, tt, zz);
}
public static void squareN(long[] x, int n, long[] z)
{
// assert n > 0;
long[] tt = Nat576.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, 561, 569
return (int)(x[0] ^ (x[8] >>> 49) ^ (x[8] >>> 57)) & 1;
}
protected static void implMultiply(long[] x, long[] y, long[] zz)
{
// long[] precomp = precompMultiplicand(y);
//
// implMultiplyPrecomp(x, precomp, zz);
long[] u = new long[16];
for (int i = 0; i < 9; ++i)
{
implMulwAcc(u, x[i], y[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];
v0 ^= zz[14]; zz[7] = v0 ^ v1; v1 ^= zz[15];
v0 ^= zz[16]; zz[8] = v0 ^ v1; v1 ^= zz[17];
long w = v0 ^ v1;
zz[ 9] = zz[0] ^ w;
zz[10] = zz[1] ^ w;
zz[11] = zz[2] ^ w;
zz[12] = zz[3] ^ w;
zz[13] = zz[4] ^ w;
zz[14] = zz[5] ^ w;
zz[15] = zz[6] ^ w;
zz[16] = zz[7] ^ w;
zz[17] = zz[8] ^ w;
implMulwAcc(u, x[0] ^ x[1], y[0] ^ y[1], zz, 1);
implMulwAcc(u, x[0] ^ x[2], y[0] ^ y[2], zz, 2);
implMulwAcc(u, x[0] ^ x[3], y[0] ^ y[3], zz, 3);
implMulwAcc(u, x[1] ^ x[2], y[1] ^ y[2], zz, 3);
implMulwAcc(u, x[0] ^ x[4], y[0] ^ y[4], zz, 4);
implMulwAcc(u, x[1] ^ x[3], y[1] ^ y[3], zz, 4);
implMulwAcc(u, x[0] ^ x[5], y[0] ^ y[5], zz, 5);
implMulwAcc(u, x[1] ^ x[4], y[1] ^ y[4], zz, 5);
implMulwAcc(u, x[2] ^ x[3], y[2] ^ y[3], zz, 5);
implMulwAcc(u, x[0] ^ x[6], y[0] ^ y[6], zz, 6);
implMulwAcc(u, x[1] ^ x[5], y[1] ^ y[5], zz, 6);
implMulwAcc(u, x[2] ^ x[4], y[2] ^ y[4], zz, 6);
implMulwAcc(u, x[0] ^ x[7], y[0] ^ y[7], zz, 7);
implMulwAcc(u, x[1] ^ x[6], y[1] ^ y[6], zz, 7);
implMulwAcc(u, x[2] ^ x[5], y[2] ^ y[5], zz, 7);
implMulwAcc(u, x[3] ^ x[4], y[3] ^ y[4], zz, 7);
implMulwAcc(u, x[0] ^ x[8], y[0] ^ y[8], zz, 8);
implMulwAcc(u, x[1] ^ x[7], y[1] ^ y[7], zz, 8);
implMulwAcc(u, x[2] ^ x[6], y[2] ^ y[6], zz, 8);
implMulwAcc(u, x[3] ^ x[5], y[3] ^ y[5], zz, 8);
implMulwAcc(u, x[1] ^ x[8], y[1] ^ y[8], zz, 9);
implMulwAcc(u, x[2] ^ x[7], y[2] ^ y[7], zz, 9);
implMulwAcc(u, x[3] ^ x[6], y[3] ^ y[6], zz, 9);
implMulwAcc(u, x[4] ^ x[5], y[4] ^ y[5], zz, 9);
implMulwAcc(u, x[2] ^ x[8], y[2] ^ y[8], zz, 10);
implMulwAcc(u, x[3] ^ x[7], y[3] ^ y[7], zz, 10);
implMulwAcc(u, x[4] ^ x[6], y[4] ^ y[6], zz, 10);
implMulwAcc(u, x[3] ^ x[8], y[3] ^ y[8], zz, 11);
implMulwAcc(u, x[4] ^ x[7], y[4] ^ y[7], zz, 11);
implMulwAcc(u, x[5] ^ x[6], y[5] ^ y[6], zz, 11);
implMulwAcc(u, x[4] ^ x[8], y[4] ^ y[8], zz, 12);
implMulwAcc(u, x[5] ^ x[7], y[5] ^ y[7], zz, 12);
implMulwAcc(u, x[5] ^ x[8], y[5] ^ y[8], zz, 13);
implMulwAcc(u, x[6] ^ x[7], y[6] ^ y[7], zz, 13);
implMulwAcc(u, x[6] ^ x[8], y[6] ^ y[8], zz, 14);
implMulwAcc(u, x[7] ^ x[8], y[7] ^ y[8], zz, 15);
}
protected static void implMultiplyPrecomp(long[] x, long[] precomp, long[] zz)
{
int MASK = 0xF;
/*
* Lopez-Dahab algorithm
*/
for (int k = 56; k >= 0; k -= 8)
{
for (int j = 1; j < 9; j += 2)
{
int aVal = (int)(x[j] >>> k);
int u = aVal & MASK;
int v = (aVal >>> 4) & MASK;
addBothTo(precomp, 9 * u, precomp, 9 * (v + 16), zz, j - 1);
}
Nat.shiftUpBits64(16, zz, 0, 8, 0L);
}
for (int k = 56; k >= 0; k -= 8)
{
for (int j = 0; j < 9; j += 2)
{
int aVal = (int)(x[j] >>> k);
int u = aVal & MASK;
int v = (aVal >>> 4) & MASK;
addBothTo(precomp, 9 * u, precomp, 9 * (v + 16), zz, j);
}
if (k > 0)
{
Nat.shiftUpBits64(18, zz, 0, 8, 0L);
}
}
}
protected static void implMulwAcc(long[] u, long x, long y, long[] z, int zOff)
{
// u[0] = 0;
u[1] = y;
for (int i = 2; i < 16; i += 2)
{
u[i ] = u[i >>> 1] << 1;
u[i + 1] = u[i ] ^ y;
}
int j = (int)x;
long g, h = 0, l = u[j & 15]
^ u[(j >>> 4) & 15] << 4;
int k = 56;
do
{
j = (int)(x >>> k);
g = u[j & 15]
^ u[(j >>> 4) & 15] << 4;
l ^= (g << k);
h ^= (g >>> -k);
}
while ((k -= 8) > 0);
for (int p = 0; p < 7; ++p)
{
x = (x & 0xFEFEFEFEFEFEFEFEL) >>> 1;
h ^= x & ((y << p) >> 63);
}
// assert h >>> 63 == 0;
z[zOff ] ^= l;
z[zOff + 1] ^= h;
}
protected static void implSquare(long[] x, long[] zz)
{
Interleave.expand64To128(x, 0, 9, zz, 0);
}
}