org.bouncycastle.math.ec.custom.sec.SecT283Field Maven / Gradle / Ivy
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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.Nat320;
public class SecT283Field
{
private static final long M27 = -1L >>> 37;
private static final long M57 = -1L >>> 7;
private static final long[] ROOT_Z = new long[]{ 0x0C30C30C30C30808L, 0x30C30C30C30C30C3L, 0x820820820820830CL, 0x0820820820820820L, 0x2082082L };
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];
}
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];
zz[8] = xx[8] ^ yy[8];
}
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];
}
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];
}
public static long[] fromBigInteger(BigInteger x)
{
return Nat.fromBigInteger64(283, x);
}
public static void halfTrace(long[] x, long[] z)
{
long[] tt = Nat.create64(9);
Nat320.copy64(x, z);
for (int i = 1; i < 283; 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 (Nat320.isZero64(x))
{
throw new IllegalStateException();
}
// Itoh-Tsujii inversion
long[] t0 = Nat320.create64();
long[] t1 = Nat320.create64();
square(x, t0);
multiply(t0, x, t0);
squareN(t0, 2, t1);
multiply(t1, t0, t1);
squareN(t1, 4, t0);
multiply(t0, t1, t0);
squareN(t0, 8, t1);
multiply(t1, t0, t1);
square(t1, t1);
multiply(t1, x, t1);
squareN(t1, 17, t0);
multiply(t0, t1, t0);
square(t0, t0);
multiply(t0, x, t0);
squareN(t0, 35, t1);
multiply(t1, t0, t1);
squareN(t1, 70, t0);
multiply(t0, t1, t0);
square(t0, t0);
multiply(t0, x, t0);
squareN(t0, 141, t1);
multiply(t1, t0, t1);
square(t1, z);
}
public static void multiply(long[] x, long[] y, long[] z)
{
long[] tt = Nat320.createExt64();
implMultiply(x, y, tt);
reduce(tt, z);
}
public static void multiplyAddToExt(long[] x, long[] y, long[] zz)
{
long[] tt = Nat320.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], x4 = xx[4];
long x5 = xx[5], x6 = xx[6], x7 = xx[7], x8 = xx[8];
x3 ^= (x8 << 37) ^ (x8 << 42) ^ (x8 << 44) ^ (x8 << 49);
x4 ^= (x8 >>> 27) ^ (x8 >>> 22) ^ (x8 >>> 20) ^ (x8 >>> 15);
x2 ^= (x7 << 37) ^ (x7 << 42) ^ (x7 << 44) ^ (x7 << 49);
x3 ^= (x7 >>> 27) ^ (x7 >>> 22) ^ (x7 >>> 20) ^ (x7 >>> 15);
x1 ^= (x6 << 37) ^ (x6 << 42) ^ (x6 << 44) ^ (x6 << 49);
x2 ^= (x6 >>> 27) ^ (x6 >>> 22) ^ (x6 >>> 20) ^ (x6 >>> 15);
x0 ^= (x5 << 37) ^ (x5 << 42) ^ (x5 << 44) ^ (x5 << 49);
x1 ^= (x5 >>> 27) ^ (x5 >>> 22) ^ (x5 >>> 20) ^ (x5 >>> 15);
long t = x4 >>> 27;
z[0] = x0 ^ t ^ (t << 5) ^ (t << 7) ^ (t << 12);
z[1] = x1;
z[2] = x2;
z[3] = x3;
z[4] = x4 & M27;
}
public static void reduce37(long[] z, int zOff)
{
long z4 = z[zOff + 4], t = z4 >>> 27;
z[zOff ] ^= t ^ (t << 5) ^ (t << 7) ^ (t << 12);
z[zOff + 4] = z4 & M27;
}
public static void sqrt(long[] x, long[] z)
{
long[] odd = Nat320.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]); u1 = Interleave.unshuffle(x[3]);
long e1 = (u0 & 0x00000000FFFFFFFFL) | (u1 << 32);
odd[1] = (u0 >>> 32) | (u1 & 0xFFFFFFFF00000000L);
u0 = Interleave.unshuffle(x[4]);
long e2 = (u0 & 0x00000000FFFFFFFFL);
odd[2] = (u0 >>> 32);
multiply(odd, ROOT_Z, z);
z[0] ^= e0;
z[1] ^= e1;
z[2] ^= e2;
}
public static void square(long[] x, long[] z)
{
long[] tt = Nat.create64(9);
implSquare(x, tt);
reduce(tt, z);
}
public static void squareAddToExt(long[] x, long[] zz)
{
long[] tt = Nat.create64(9);
implSquare(x, tt);
addExt(zz, tt, zz);
}
public static void squareN(long[] x, int n, long[] z)
{
// assert n > 0;
long[] tt = Nat.create64(9);
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, 271
return (int)(x[0] ^ (x[4] >>> 15)) & 1;
}
protected static void implCompactExt(long[] zz)
{
long z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4];
long z5 = zz[5], z6 = zz[6], z7 = zz[7], z8 = zz[8], z9 = zz[9];
zz[0] = z0 ^ (z1 << 57);
zz[1] = (z1 >>> 7) ^ (z2 << 50);
zz[2] = (z2 >>> 14) ^ (z3 << 43);
zz[3] = (z3 >>> 21) ^ (z4 << 36);
zz[4] = (z4 >>> 28) ^ (z5 << 29);
zz[5] = (z5 >>> 35) ^ (z6 << 22);
zz[6] = (z6 >>> 42) ^ (z7 << 15);
zz[7] = (z7 >>> 49) ^ (z8 << 8);
zz[8] = (z8 >>> 56) ^ (z9 << 1);
zz[9] = (z9 >>> 63); // Zero!
}
protected static void implExpand(long[] x, long[] z)
{
long x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4];
z[0] = x0 & M57;
z[1] = ((x0 >>> 57) ^ (x1 << 7)) & M57;
z[2] = ((x1 >>> 50) ^ (x2 << 14)) & M57;
z[3] = ((x2 >>> 43) ^ (x3 << 21)) & M57;
z[4] = ((x3 >>> 36) ^ (x4 << 28));
}
// protected static void addMs(long[] zz, int zOff, long[] p, int... ms)
// {
// long t0 = 0, t1 = 0;
// for (int m : ms)
// {
// int i = (m - 1) << 1;
// t0 ^= p[i ];
// t1 ^= p[i + 1];
// }
// zz[zOff ] ^= t0;
// zz[zOff + 1] ^= t1;
// }
protected static void implMultiply(long[] x, long[] y, long[] zz)
{
/*
* Formula (17) from "Some New Results on Binary Polynomial Multiplication",
* Murat Cenk and M. Anwar Hasan.
*
* The formula as given contained an error in the term t25, as noted below
*/
long[] a = new long[5], b = new long[5];
implExpand(x, a);
implExpand(y, b);
long[] p = new long[26];
implMulw(a[0], b[0], p, 0); // m1
implMulw(a[1], b[1], p, 2); // m2
implMulw(a[2], b[2], p, 4); // m3
implMulw(a[3], b[3], p, 6); // m4
implMulw(a[4], b[4], p, 8); // m5
long u0 = a[0] ^ a[1], v0 = b[0] ^ b[1];
long u1 = a[0] ^ a[2], v1 = b[0] ^ b[2];
long u2 = a[2] ^ a[4], v2 = b[2] ^ b[4];
long u3 = a[3] ^ a[4], v3 = b[3] ^ b[4];
implMulw(u1 ^ a[3], v1 ^ b[3], p, 18); // m10
implMulw(u2 ^ a[1], v2 ^ b[1], p, 20); // m11
long A4 = u0 ^ u3 , B4 = v0 ^ v3;
long A5 = A4 ^ a[2], B5 = B4 ^ b[2];
implMulw(A4, B4, p, 22); // m12
implMulw(A5, B5, p, 24); // m13
implMulw(u0, v0, p, 10); // m6
implMulw(u1, v1, p, 12); // m7
implMulw(u2, v2, p, 14); // m8
implMulw(u3, v3, p, 16); // m9
// Original method, corresponding to formula (16)
// addMs(zz, 0, p, 1);
// addMs(zz, 1, p, 1, 2, 6);
// addMs(zz, 2, p, 1, 2, 3, 7);
// addMs(zz, 3, p, 1, 3, 4, 5, 8, 10, 12, 13);
// addMs(zz, 4, p, 1, 2, 4, 5, 6, 9, 10, 11, 13);
// addMs(zz, 5, p, 1, 2, 3, 5, 7, 11, 12, 13);
// addMs(zz, 6, p, 3, 4, 5, 8);
// addMs(zz, 7, p, 4, 5, 9);
// addMs(zz, 8, p, 5);
// Improved method factors out common single-word terms
// NOTE: p1,...,p26 in the paper maps to p[0],...,p[25] here
zz[0] = p[ 0];
zz[9] = p[ 9];
long t1 = p[ 0] ^ p[ 1];
long t2 = t1 ^ p[ 2];
long t3 = t2 ^ p[10];
zz[1] = t3;
long t4 = p[ 3] ^ p[ 4];
long t5 = p[11] ^ p[12];
long t6 = t4 ^ t5;
long t7 = t2 ^ t6;
zz[2] = t7;
long t8 = t1 ^ t4;
long t9 = p[ 5] ^ p[ 6];
long t10 = t8 ^ t9;
long t11 = t10 ^ p[ 8];
long t12 = p[13] ^ p[14];
long t13 = t11 ^ t12;
long t14 = p[18] ^ p[22];
long t15 = t14 ^ p[24];
long t16 = t13 ^ t15;
zz[3] = t16;
long t17 = p[ 7] ^ p[ 8];
long t18 = t17 ^ p[ 9];
long t19 = t18 ^ p[17];
zz[8] = t19;
long t20 = t18 ^ t9;
long t21 = p[15] ^ p[16];
long t22 = t20 ^ t21;
zz[7] = t22;
long t23 = t22 ^ t3;
long t24 = p[19] ^ p[20];
// long t25 = p[23] ^ p[24];
long t25 = p[25] ^ p[24]; // Fixes an error in the paper: p[23] -> p{25]
long t26 = p[18] ^ p[23];
long t27 = t24 ^ t25;
long t28 = t27 ^ t26;
long t29 = t28 ^ t23;
zz[4] = t29;
long t30 = t7 ^ t19;
long t31 = t27 ^ t30;
long t32 = p[21] ^ p[22];
long t33 = t31 ^ t32;
zz[5] = t33;
long t34 = t11 ^ p[0];
long t35 = t34 ^ p[9];
long t36 = t35 ^ t12;
long t37 = t36 ^ p[21];
long t38 = t37 ^ p[23];
long t39 = t38 ^ p[25];
zz[6] = t39;
implCompactExt(zz);
}
protected static void implMulw(long x, long y, long[] z, int zOff)
{
// assert x >>> 57 == 0;
// assert y >>> 57 == 0;
long[] u = new long[8];
// 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], zz, 0);
Interleave.expand64To128(x[1], zz, 2);
Interleave.expand64To128(x[2], zz, 4);
Interleave.expand64To128(x[3], zz, 6);
zz[8] = Interleave.expand32to64((int)x[4]);
}
}