org.bouncycastle.math.ec.rfc7748.X448Field 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 1.8 and up.
package org.bouncycastle.math.ec.rfc7748;
import org.bouncycastle.math.raw.Mod;
public abstract class X448Field
{
public static final int SIZE = 16;
private static final int M28 = 0x0FFFFFFF;
private static final long U32 = 0xFFFFFFFFL;
private static final int[] P32 = new int[]{ 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
protected X448Field() {}
public static void add(int[] x, int[] y, int[] z)
{
for (int i = 0; i < SIZE; ++i)
{
z[i] = x[i] + y[i];
}
}
public static void addOne(int[] z)
{
z[0] += 1;
}
public static void addOne(int[] z, int zOff)
{
z[zOff] += 1;
}
// public static void apm(int[] x, int[] y, int[] zp, int[] zm)
// {
// for (int i = 0; i < SIZE; ++i)
// {
// int xi = x[i], yi = y[i];
// zp[i] = xi + yi;
// zm[i] = xi - yi;
// }
// }
public static int areEqual(int[] x, int[] y)
{
int d = 0;
for (int i = 0; i < SIZE; ++i)
{
d |= x[i] ^ y[i];
}
d = (d >>> 1) | (d & 1);
return (d - 1) >> 31;
}
public static boolean areEqualVar(int[] x, int[] y)
{
return 0 != areEqual(x, y);
}
public static void carry(int[] z)
{
int z0 = z[0], z1 = z[1], z2 = z[2], z3 = z[3], z4 = z[4], z5 = z[5], z6 = z[6], z7 = z[7];
int z8 = z[8], z9 = z[9], z10 = z[10], z11 = z[11], z12 = z[12], z13 = z[13], z14 = z[14], z15 = z[15];
z1 += (z0 >>> 28); z0 &= M28;
z5 += (z4 >>> 28); z4 &= M28;
z9 += (z8 >>> 28); z8 &= M28;
z13 += (z12 >>> 28); z12 &= M28;
z2 += (z1 >>> 28); z1 &= M28;
z6 += (z5 >>> 28); z5 &= M28;
z10 += (z9 >>> 28); z9 &= M28;
z14 += (z13 >>> 28); z13 &= M28;
z3 += (z2 >>> 28); z2 &= M28;
z7 += (z6 >>> 28); z6 &= M28;
z11 += (z10 >>> 28); z10 &= M28;
z15 += (z14 >>> 28); z14 &= M28;
int t = z15 >>> 28; z15 &= M28;
z0 += t;
z8 += t;
z4 += (z3 >>> 28); z3 &= M28;
z8 += (z7 >>> 28); z7 &= M28;
z12 += (z11 >>> 28); z11 &= M28;
z1 += (z0 >>> 28); z0 &= M28;
z5 += (z4 >>> 28); z4 &= M28;
z9 += (z8 >>> 28); z8 &= M28;
z13 += (z12 >>> 28); z12 &= M28;
z[0] = z0; z[1] = z1; z[2] = z2; z[3] = z3; z[4] = z4; z[5] = z5; z[6] = z6; z[7] = z7;
z[8] = z8; z[9] = z9; z[10] = z10; z[11] = z11; z[12] = z12; z[13] = z13; z[14] = z14; z[15] = z15;
}
public static void cmov(int cond, int[] x, int xOff, int[] z, int zOff)
{
// assert 0 == cond || -1 == cond;
for (int i = 0; i < SIZE; ++i)
{
int z_i = z[zOff + i], diff = z_i ^ x[xOff + i];
z_i ^= (diff & cond);
z[zOff + i] = z_i;
}
}
public static void cnegate(int negate, int[] z)
{
// assert negate >>> 1 == 0;
int[] t = create();
sub(t, z, t);
cmov(-negate, t, 0, z, 0);
}
public static void copy(int[] x, int xOff, int[] z, int zOff)
{
for (int i = 0; i < SIZE; ++i)
{
z[zOff + i] = x[xOff + i];
}
}
public static int[] create()
{
return new int[SIZE];
}
public static int[] createTable(int n)
{
return new int[SIZE * n];
}
public static void cswap(int swap, int[] a, int[] b)
{
// assert swap >>> 1 == 0;
// assert a != b;
int mask = 0 - swap;
for (int i = 0; i < SIZE; ++i)
{
int ai = a[i], bi = b[i];
int dummy = mask & (ai ^ bi);
a[i] = ai ^ dummy;
b[i] = bi ^ dummy;
}
}
public static void decode(int[] x, int xOff, int[] z)
{
decode224(x, xOff, z, 0);
decode224(x, xOff + 7, z, 8);
}
public static void decode(byte[] x, int[] z)
{
decode56(x, 0, z, 0);
decode56(x, 7, z, 2);
decode56(x, 14, z, 4);
decode56(x, 21, z, 6);
decode56(x, 28, z, 8);
decode56(x, 35, z, 10);
decode56(x, 42, z, 12);
decode56(x, 49, z, 14);
}
public static void decode(byte[] x, int xOff, int[] z)
{
decode56(x, xOff, z, 0);
decode56(x, xOff + 7, z, 2);
decode56(x, xOff + 14, z, 4);
decode56(x, xOff + 21, z, 6);
decode56(x, xOff + 28, z, 8);
decode56(x, xOff + 35, z, 10);
decode56(x, xOff + 42, z, 12);
decode56(x, xOff + 49, z, 14);
}
public static void decode(byte[] x, int xOff, int[] z, int zOff)
{
decode56(x, xOff, z, zOff);
decode56(x, xOff + 7, z, zOff + 2);
decode56(x, xOff + 14, z, zOff + 4);
decode56(x, xOff + 21, z, zOff + 6);
decode56(x, xOff + 28, z, zOff + 8);
decode56(x, xOff + 35, z, zOff + 10);
decode56(x, xOff + 42, z, zOff + 12);
decode56(x, xOff + 49, z, zOff + 14);
}
private static void decode224(int[] x, int xOff, int[] z, int zOff)
{
int x0 = x[xOff + 0], x1 = x[xOff + 1], x2 = x[xOff + 2], x3 = x[xOff + 3];
int x4 = x[xOff + 4], x5 = x[xOff + 5], x6 = x[xOff + 6];
z[zOff + 0] = x0 & M28;
z[zOff + 1] = (x0 >>> 28 | x1 << 4) & M28;
z[zOff + 2] = (x1 >>> 24 | x2 << 8) & M28;
z[zOff + 3] = (x2 >>> 20 | x3 << 12) & M28;
z[zOff + 4] = (x3 >>> 16 | x4 << 16) & M28;
z[zOff + 5] = (x4 >>> 12 | x5 << 20) & M28;
z[zOff + 6] = (x5 >>> 8 | x6 << 24) & M28;
z[zOff + 7] = x6 >>> 4;
}
private static int decode24(byte[] bs, int off)
{
int n = bs[ off] & 0xFF;
n |= (bs[++off] & 0xFF) << 8;
n |= (bs[++off] & 0xFF) << 16;
return n;
}
private static int decode32(byte[] bs, int off)
{
int n = bs[ off] & 0xFF;
n |= (bs[++off] & 0xFF) << 8;
n |= (bs[++off] & 0xFF) << 16;
n |= bs[++off] << 24;
return n;
}
private static void decode56(byte[] bs, int off, int[] z, int zOff)
{
int lo = decode32(bs, off);
int hi = decode24(bs, off + 4);
z[zOff] = lo & M28;
z[zOff + 1] = (lo >>> 28) | (hi << 4);
}
public static void encode(int[] x, int[] z, int zOff)
{
encode224(x, 0, z, zOff);
encode224(x, 8, z, zOff + 7);
}
public static void encode(int[] x, byte[] z)
{
encode56(x, 0, z, 0);
encode56(x, 2, z, 7);
encode56(x, 4, z, 14);
encode56(x, 6, z, 21);
encode56(x, 8, z, 28);
encode56(x, 10, z, 35);
encode56(x, 12, z, 42);
encode56(x, 14, z, 49);
}
public static void encode(int[] x, byte[] z, int zOff)
{
encode56(x, 0, z, zOff);
encode56(x, 2, z, zOff + 7);
encode56(x, 4, z, zOff + 14);
encode56(x, 6, z, zOff + 21);
encode56(x, 8, z, zOff + 28);
encode56(x, 10, z, zOff + 35);
encode56(x, 12, z, zOff + 42);
encode56(x, 14, z, zOff + 49);
}
public static void encode(int[] x, int xOff, byte[] z, int zOff)
{
encode56(x, xOff, z, zOff);
encode56(x, xOff + 2, z, zOff + 7);
encode56(x, xOff + 4, z, zOff + 14);
encode56(x, xOff + 6, z, zOff + 21);
encode56(x, xOff + 8, z, zOff + 28);
encode56(x, xOff + 10, z, zOff + 35);
encode56(x, xOff + 12, z, zOff + 42);
encode56(x, xOff + 14, z, zOff + 49);
}
private static void encode224(int[] x, int xOff, int[] is, int off)
{
int x0 = x[xOff + 0], x1 = x[xOff + 1], x2 = x[xOff + 2], x3 = x[xOff + 3];
int x4 = x[xOff + 4], x5 = x[xOff + 5], x6 = x[xOff + 6], x7 = x[xOff + 7];
is[off + 0] = x0 | (x1 << 28);
is[off + 1] = (x1 >>> 4) | (x2 << 24);
is[off + 2] = (x2 >>> 8) | (x3 << 20);
is[off + 3] = (x3 >>> 12) | (x4 << 16);
is[off + 4] = (x4 >>> 16) | (x5 << 12);
is[off + 5] = (x5 >>> 20) | (x6 << 8);
is[off + 6] = (x6 >>> 24) | (x7 << 4);
}
private static void encode24(int n, byte[] bs, int off)
{
bs[ off] = (byte)(n );
bs[++off] = (byte)(n >>> 8);
bs[++off] = (byte)(n >>> 16);
}
private static void encode32(int n, byte[] bs, int off)
{
bs[ off] = (byte)(n );
bs[++off] = (byte)(n >>> 8);
bs[++off] = (byte)(n >>> 16);
bs[++off] = (byte)(n >>> 24);
}
private static void encode56(int[] x, int xOff, byte[] bs, int off)
{
int lo = x[xOff], hi = x[xOff + 1];
encode32(lo | (hi << 28), bs, off);
encode24(hi >>> 4, bs, off + 4);
}
public static void inv(int[] x, int[] z)
{
// int[] t = create();
// powPm3d4(x, t);
// sqr(t, 2, t);
// mul(t, x, z);
int[] t = create();
int[] u = new int[14];
copy(x, 0, t, 0);
normalize(t);
encode(t, u, 0);
Mod.modOddInverse(P32, u, u);
decode(u, 0, z);
}
public static void invVar(int[] x, int[] z)
{
int[] t = create();
int[] u = new int[14];
copy(x, 0, t, 0);
normalize(t);
encode(t, u, 0);
Mod.modOddInverseVar(P32, u, u);
decode(u, 0, z);
}
public static int isOne(int[] x)
{
int d = x[0] ^ 1;
for (int i = 1; i < SIZE; ++i)
{
d |= x[i];
}
d = (d >>> 1) | (d & 1);
return (d - 1) >> 31;
}
public static boolean isOneVar(int[] x)
{
return 0 != isOne(x);
}
public static int isZero(int[] x)
{
int d = 0;
for (int i = 0; i < SIZE; ++i)
{
d |= x[i];
}
d = (d >>> 1) | (d & 1);
return (d - 1) >> 31;
}
public static boolean isZeroVar(int[] x)
{
return 0 != isZero(x);
}
public static void mul(int[] x, int y, int[] z)
{
int x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6], x7 = x[7];
int x8 = x[8], x9 = x[9], x10 = x[10], x11 = x[11], x12 = x[12], x13 = x[13], x14 = x[14], x15 = x[15];
int z1, z5, z9, z13;
long c, d, e, f;
c = (long)x1 * y;
z1 = (int)c & M28; c >>>= 28;
d = (long)x5 * y;
z5 = (int)d & M28; d >>>= 28;
e = (long)x9 * y;
z9 = (int)e & M28; e >>>= 28;
f = (long)x13 * y;
z13 = (int)f & M28; f >>>= 28;
c += (long)x2 * y;
z[2] = (int)c & M28; c >>>= 28;
d += (long)x6 * y;
z[6] = (int)d & M28; d >>>= 28;
e += (long)x10 * y;
z[10] = (int)e & M28; e >>>= 28;
f += (long)x14 * y;
z[14] = (int)f & M28; f >>>= 28;
c += (long)x3 * y;
z[3] = (int)c & M28; c >>>= 28;
d += (long)x7 * y;
z[7] = (int)d & M28; d >>>= 28;
e += (long)x11 * y;
z[11] = (int)e & M28; e >>>= 28;
f += (long)x15 * y;
z[15] = (int)f & M28; f >>>= 28;
d += f;
c += (long)x4 * y;
z[4] = (int)c & M28; c >>>= 28;
d += (long)x8 * y;
z[8] = (int)d & M28; d >>>= 28;
e += (long)x12 * y;
z[12] = (int)e & M28; e >>>= 28;
f += (long)x0 * y;
z[0] = (int)f & M28; f >>>= 28;
z[1] = z1 + (int)f;
z[5] = z5 + (int)c;
z[9] = z9 + (int)d;
z[13] = z13 + (int)e;
}
public static void mul(int[] x, int[] y, int[] z)
{
int x0 = x[0];
int x1 = x[1];
int x2 = x[2];
int x3 = x[3];
int x4 = x[4];
int x5 = x[5];
int x6 = x[6];
int x7 = x[7];
int u0 = x[8];
int u1 = x[9];
int u2 = x[10];
int u3 = x[11];
int u4 = x[12];
int u5 = x[13];
int u6 = x[14];
int u7 = x[15];
int y0 = y[0];
int y1 = y[1];
int y2 = y[2];
int y3 = y[3];
int y4 = y[4];
int y5 = y[5];
int y6 = y[6];
int y7 = y[7];
int v0 = y[8];
int v1 = y[9];
int v2 = y[10];
int v3 = y[11];
int v4 = y[12];
int v5 = y[13];
int v6 = y[14];
int v7 = y[15];
int s0 = x0 + u0;
int s1 = x1 + u1;
int s2 = x2 + u2;
int s3 = x3 + u3;
int s4 = x4 + u4;
int s5 = x5 + u5;
int s6 = x6 + u6;
int s7 = x7 + u7;
int t0 = y0 + v0;
int t1 = y1 + v1;
int t2 = y2 + v2;
int t3 = y3 + v3;
int t4 = y4 + v4;
int t5 = y5 + v5;
int t6 = y6 + v6;
int t7 = y7 + v7;
int z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14, z15;
long c, d;
long f0 = (long)x0 * y0;
long f8 = (long)x7 * y1
+ (long)x6 * y2
+ (long)x5 * y3
+ (long)x4 * y4
+ (long)x3 * y5
+ (long)x2 * y6
+ (long)x1 * y7;
long g0 = (long)u0 * v0;
long g8 = (long)u7 * v1
+ (long)u6 * v2
+ (long)u5 * v3
+ (long)u4 * v4
+ (long)u3 * v5
+ (long)u2 * v6
+ (long)u1 * v7;
long h0 = (long)s0 * t0;
long h8 = (long)s7 * t1
+ (long)s6 * t2
+ (long)s5 * t3
+ (long)s4 * t4
+ (long)s3 * t5
+ (long)s2 * t6
+ (long)s1 * t7;
c = f0 + g0 + h8 - f8;
z0 = (int)c & M28; c >>>= 28;
d = g8 + h0 - f0 + h8;
z8 = (int)d & M28; d >>>= 28;
long f1 = (long)x1 * y0
+ (long)x0 * y1;
long f9 = (long)x7 * y2
+ (long)x6 * y3
+ (long)x5 * y4
+ (long)x4 * y5
+ (long)x3 * y6
+ (long)x2 * y7;
long g1 = (long)u1 * v0
+ (long)u0 * v1;
long g9 = (long)u7 * v2
+ (long)u6 * v3
+ (long)u5 * v4
+ (long)u4 * v5
+ (long)u3 * v6
+ (long)u2 * v7;
long h1 = (long)s1 * t0
+ (long)s0 * t1;
long h9 = (long)s7 * t2
+ (long)s6 * t3
+ (long)s5 * t4
+ (long)s4 * t5
+ (long)s3 * t6
+ (long)s2 * t7;
c += f1 + g1 + h9 - f9;
z1 = (int)c & M28; c >>>= 28;
d += g9 + h1 - f1 + h9;
z9 = (int)d & M28; d >>>= 28;
long f2 = (long)x2 * y0
+ (long)x1 * y1
+ (long)x0 * y2;
long f10 = (long)x7 * y3
+ (long)x6 * y4
+ (long)x5 * y5
+ (long)x4 * y6
+ (long)x3 * y7;
long g2 = (long)u2 * v0
+ (long)u1 * v1
+ (long)u0 * v2;
long g10 = (long)u7 * v3
+ (long)u6 * v4
+ (long)u5 * v5
+ (long)u4 * v6
+ (long)u3 * v7;
long h2 = (long)s2 * t0
+ (long)s1 * t1
+ (long)s0 * t2;
long h10 = (long)s7 * t3
+ (long)s6 * t4
+ (long)s5 * t5
+ (long)s4 * t6
+ (long)s3 * t7;
c += f2 + g2 + h10 - f10;
z2 = (int)c & M28; c >>>= 28;
d += g10 + h2 - f2 + h10;
z10 = (int)d & M28; d >>>= 28;
long f3 = (long)x3 * y0
+ (long)x2 * y1
+ (long)x1 * y2
+ (long)x0 * y3;
long f11 = (long)x7 * y4
+ (long)x6 * y5
+ (long)x5 * y6
+ (long)x4 * y7;
long g3 = (long)u3 * v0
+ (long)u2 * v1
+ (long)u1 * v2
+ (long)u0 * v3;
long g11 = (long)u7 * v4
+ (long)u6 * v5
+ (long)u5 * v6
+ (long)u4 * v7;
long h3 = (long)s3 * t0
+ (long)s2 * t1
+ (long)s1 * t2
+ (long)s0 * t3;
long h11 = (long)s7 * t4
+ (long)s6 * t5
+ (long)s5 * t6
+ (long)s4 * t7;
c += f3 + g3 + h11 - f11;
z3 = (int)c & M28; c >>>= 28;
d += g11 + h3 - f3 + h11;
z11 = (int)d & M28; d >>>= 28;
long f4 = (long)x4 * y0
+ (long)x3 * y1
+ (long)x2 * y2
+ (long)x1 * y3
+ (long)x0 * y4;
long f12 = (long)x7 * y5
+ (long)x6 * y6
+ (long)x5 * y7;
long g4 = (long)u4 * v0
+ (long)u3 * v1
+ (long)u2 * v2
+ (long)u1 * v3
+ (long)u0 * v4;
long g12 = (long)u7 * v5
+ (long)u6 * v6
+ (long)u5 * v7;
long h4 = (long)s4 * t0
+ (long)s3 * t1
+ (long)s2 * t2
+ (long)s1 * t3
+ (long)s0 * t4;
long h12 = (long)s7 * t5
+ (long)s6 * t6
+ (long)s5 * t7;
c += f4 + g4 + h12 - f12;
z4 = (int)c & M28; c >>>= 28;
d += g12 + h4 - f4 + h12;
z12 = (int)d & M28; d >>>= 28;
long f5 = (long)x5 * y0
+ (long)x4 * y1
+ (long)x3 * y2
+ (long)x2 * y3
+ (long)x1 * y4
+ (long)x0 * y5;
long f13 = (long)x7 * y6
+ (long)x6 * y7;
long g5 = (long)u5 * v0
+ (long)u4 * v1
+ (long)u3 * v2
+ (long)u2 * v3
+ (long)u1 * v4
+ (long)u0 * v5;
long g13 = (long)u7 * v6
+ (long)u6 * v7;
long h5 = (long)s5 * t0
+ (long)s4 * t1
+ (long)s3 * t2
+ (long)s2 * t3
+ (long)s1 * t4
+ (long)s0 * t5;
long h13 = (long)s7 * t6
+ (long)s6 * t7;
c += f5 + g5 + h13 - f13;
z5 = (int)c & M28; c >>>= 28;
d += g13 + h5 - f5 + h13;
z13 = (int)d & M28; d >>>= 28;
long f6 = (long)x6 * y0
+ (long)x5 * y1
+ (long)x4 * y2
+ (long)x3 * y3
+ (long)x2 * y4
+ (long)x1 * y5
+ (long)x0 * y6;
long f14 = (long)x7 * y7;
long g6 = (long)u6 * v0
+ (long)u5 * v1
+ (long)u4 * v2
+ (long)u3 * v3
+ (long)u2 * v4
+ (long)u1 * v5
+ (long)u0 * v6;
long g14 = (long)u7 * v7;
long h6 = (long)s6 * t0
+ (long)s5 * t1
+ (long)s4 * t2
+ (long)s3 * t3
+ (long)s2 * t4
+ (long)s1 * t5
+ (long)s0 * t6;
long h14 = (long)s7 * t7;
c += f6 + g6 + h14 - f14;
z6 = (int)c & M28; c >>>= 28;
d += g14 + h6 - f6 + h14;
z14 = (int)d & M28; d >>>= 28;
long f7 = (long)x7 * y0
+ (long)x6 * y1
+ (long)x5 * y2
+ (long)x4 * y3
+ (long)x3 * y4
+ (long)x2 * y5
+ (long)x1 * y6
+ (long)x0 * y7;
long g7 = (long)u7 * v0
+ (long)u6 * v1
+ (long)u5 * v2
+ (long)u4 * v3
+ (long)u3 * v4
+ (long)u2 * v5
+ (long)u1 * v6
+ (long)u0 * v7;
long h7 = (long)s7 * t0
+ (long)s6 * t1
+ (long)s5 * t2
+ (long)s4 * t3
+ (long)s3 * t4
+ (long)s2 * t5
+ (long)s1 * t6
+ (long)s0 * t7;
c += f7 + g7;
z7 = (int)c & M28; c >>>= 28;
d += h7 - f7;
z15 = (int)d & M28; d >>>= 28;
c += d;
c += z8;
z8 = (int)c & M28; c >>>= 28;
d += z0;
z0 = (int)d & M28; d >>>= 28;
z9 += (int)c;
z1 += (int)d;
z[0] = z0;
z[1] = z1;
z[2] = z2;
z[3] = z3;
z[4] = z4;
z[5] = z5;
z[6] = z6;
z[7] = z7;
z[8] = z8;
z[9] = z9;
z[10] = z10;
z[11] = z11;
z[12] = z12;
z[13] = z13;
z[14] = z14;
z[15] = z15;
}
public static void negate(int[] x, int[] z)
{
int[] zero = create();
sub(zero, x, z);
}
public static void normalize(int[] z)
{
// int x = ((z[15] >>> (28 - 1)) & 1);
reduce(z, 1);
reduce(z, -1);
// assert z[15] >>> 28 == 0;
}
public static void one(int[] z)
{
z[0] = 1;
for (int i = 1; i < SIZE; ++i)
{
z[i] = 0;
}
}
private static void powPm3d4(int[] x, int[] z)
{
// z = x^((p-3)/4) = x^(2^446 - 2^222 - 1)
// (223 1s) (1 0s) (222 1s)
// Addition chain: 1 2 3 6 9 18 19 37 74 111 [222] [223]
int[] x2 = create(); sqr(x, x2); mul(x, x2, x2);
int[] x3 = create(); sqr(x2, x3); mul(x, x3, x3);
int[] x6 = create(); sqr(x3, 3, x6); mul(x3, x6, x6);
int[] x9 = create(); sqr(x6, 3, x9); mul(x3, x9, x9);
int[] x18 = create(); sqr(x9, 9, x18); mul(x9, x18, x18);
int[] x19 = create(); sqr(x18, x19); mul(x, x19, x19);
int[] x37 = create(); sqr(x19, 18, x37); mul(x18, x37, x37);
int[] x74 = create(); sqr(x37, 37, x74); mul(x37, x74, x74);
int[] x111 = create(); sqr(x74, 37, x111); mul(x37, x111, x111);
int[] x222 = create(); sqr(x111, 111, x222); mul(x111, x222, x222);
int[] x223 = create(); sqr(x222, x223); mul(x, x223, x223);
int[] t = create();
sqr(x223, 223, t);
mul(t, x222, z);
}
private static void reduce(int[] z, int x)
{
int t = z[15], z15 = t & M28;
t = (t >>> 28) + x;
long cc = t;
for (int i = 0; i < 8; ++i)
{
cc += z[i] & U32; z[i] = (int)cc & M28; cc >>= 28;
}
cc += t;
for (int i = 8; i < 15; ++i)
{
cc += z[i] & U32; z[i] = (int)cc & M28; cc >>= 28;
}
z[15] = z15 + (int)cc;
}
public static void sqr(int[] x, int[] z)
{
int x0 = x[0];
int x1 = x[1];
int x2 = x[2];
int x3 = x[3];
int x4 = x[4];
int x5 = x[5];
int x6 = x[6];
int x7 = x[7];
int u0 = x[8];
int u1 = x[9];
int u2 = x[10];
int u3 = x[11];
int u4 = x[12];
int u5 = x[13];
int u6 = x[14];
int u7 = x[15];
int x0_2 = x0 * 2;
int x1_2 = x1 * 2;
int x2_2 = x2 * 2;
int x3_2 = x3 * 2;
int x4_2 = x4 * 2;
int x5_2 = x5 * 2;
int x6_2 = x6 * 2;
int u0_2 = u0 * 2;
int u1_2 = u1 * 2;
int u2_2 = u2 * 2;
int u3_2 = u3 * 2;
int u4_2 = u4 * 2;
int u5_2 = u5 * 2;
int u6_2 = u6 * 2;
int s0 = x0 + u0;
int s1 = x1 + u1;
int s2 = x2 + u2;
int s3 = x3 + u3;
int s4 = x4 + u4;
int s5 = x5 + u5;
int s6 = x6 + u6;
int s7 = x7 + u7;
/*
* NOTE: Currently s1_2 and/or s5_2 might reach 0x80000000 (because our carry chains land at
* x[1], x[5], x[9], x[13]). So extra care is needed to ensure they are treated as unsigned
* multiplicands below. To avoid depending on the precise carry chains, we assume this
* affects all the s?_2 variables.
*/
int s0_2 = s0 * 2;
int s1_2 = s1 * 2;
int s2_2 = s2 * 2;
int s3_2 = s3 * 2;
int s4_2 = s4 * 2;
int s5_2 = s5 * 2;
int s6_2 = s6 * 2;
int z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12, z13, z14, z15;
long c, d;
long f0 = (long)x0 * x0;
long f8 = (long)x7 * x1_2
+ (long)x6 * x2_2
+ (long)x5 * x3_2
+ (long)x4 * x4;
long g0 = (long)u0 * u0;
long g8 = (long)u7 * u1_2
+ (long)u6 * u2_2
+ (long)u5 * u3_2
+ (long)u4 * u4;
long h0 = (long)s0 * s0;
long h8 = (long)s7 * (s1_2 & U32)
+ (long)s6 * (s2_2 & U32)
+ (long)s5 * (s3_2 & U32)
+ (long)s4 * s4;
c = f0 + g0 + h8 - f8;
z0 = (int)c & M28; c >>>= 28;
d = g8 + h0 - f0 + h8;
z8 = (int)d & M28; d >>>= 28;
long f1 = (long)x1 * x0_2;
long f9 = (long)x7 * x2_2
+ (long)x6 * x3_2
+ (long)x5 * x4_2;
long g1 = (long)u1 * u0_2;
long g9 = (long)u7 * u2_2
+ (long)u6 * u3_2
+ (long)u5 * u4_2;
long h1 = (long)s1 * (s0_2 & U32);
long h9 = (long)s7 * (s2_2 & U32)
+ (long)s6 * (s3_2 & U32)
+ (long)s5 * (s4_2 & U32);
c += f1 + g1 + h9 - f9;
z1 = (int)c & M28; c >>>= 28;
d += g9 + h1 - f1 + h9;
z9 = (int)d & M28; d >>>= 28;
long f2 = (long)x2 * x0_2
+ (long)x1 * x1;
long f10 = (long)x7 * x3_2
+ (long)x6 * x4_2
+ (long)x5 * x5;
long g2 = (long)u2 * u0_2
+ (long)u1 * u1;
long g10 = (long)u7 * u3_2
+ (long)u6 * u4_2
+ (long)u5 * u5;
long h2 = (long)s2 * (s0_2 & U32)
+ (long)s1 * s1;
long h10 = (long)s7 * (s3_2 & U32)
+ (long)s6 * (s4_2 & U32)
+ (long)s5 * s5;
c += f2 + g2 + h10 - f10;
z2 = (int)c & M28; c >>>= 28;
d += g10 + h2 - f2 + h10;
z10 = (int)d & M28; d >>>= 28;
long f3 = (long)x3 * x0_2
+ (long)x2 * x1_2;
long f11 = (long)x7 * x4_2
+ (long)x6 * x5_2;
long g3 = (long)u3 * u0_2
+ (long)u2 * u1_2;
long g11 = (long)u7 * u4_2
+ (long)u6 * u5_2;
long h3 = (long)s3 * (s0_2 & U32)
+ (long)s2 * (s1_2 & U32);
long h11 = (long)s7 * (s4_2 & U32)
+ (long)s6 * (s5_2 & U32);
c += f3 + g3 + h11 - f11;
z3 = (int)c & M28; c >>>= 28;
d += g11 + h3 - f3 + h11;
z11 = (int)d & M28; d >>>= 28;
long f4 = (long)x4 * x0_2
+ (long)x3 * x1_2
+ (long)x2 * x2;
long f12 = (long)x7 * x5_2
+ (long)x6 * x6;
long g4 = (long)u4 * u0_2
+ (long)u3 * u1_2
+ (long)u2 * u2;
long g12 = (long)u7 * u5_2
+ (long)u6 * u6;
long h4 = (long)s4 * (s0_2 & U32)
+ (long)s3 * (s1_2 & U32)
+ (long)s2 * s2;
long h12 = (long)s7 * (s5_2 & U32)
+ (long)s6 * s6;
c += f4 + g4 + h12 - f12;
z4 = (int)c & M28; c >>>= 28;
d += g12 + h4 - f4 + h12;
z12 = (int)d & M28; d >>>= 28;
long f5 = (long)x5 * x0_2
+ (long)x4 * x1_2
+ (long)x3 * x2_2;
long f13 = (long)x7 * x6_2;
long g5 = (long)u5 * u0_2
+ (long)u4 * u1_2
+ (long)u3 * u2_2;
long g13 = (long)u7 * u6_2;
long h5 = (long)s5 * (s0_2 & U32)
+ (long)s4 * (s1_2 & U32)
+ (long)s3 * (s2_2 & U32);
long h13 = (long)s7 * (s6_2 & U32);
c += f5 + g5 + h13 - f13;
z5 = (int)c & M28; c >>>= 28;
d += g13 + h5 - f5 + h13;
z13 = (int)d & M28; d >>>= 28;
long f6 = (long)x6 * x0_2
+ (long)x5 * x1_2
+ (long)x4 * x2_2
+ (long)x3 * x3;
long f14 = (long)x7 * x7;
long g6 = (long)u6 * u0_2
+ (long)u5 * u1_2
+ (long)u4 * u2_2
+ (long)u3 * u3;
long g14 = (long)u7 * u7;
long h6 = (long)s6 * (s0_2 & U32)
+ (long)s5 * (s1_2 & U32)
+ (long)s4 * (s2_2 & U32)
+ (long)s3 * s3;
long h14 = (long)s7 * s7;
c += f6 + g6 + h14 - f14;
z6 = (int)c & M28; c >>>= 28;
d += g14 + h6 - f6 + h14;
z14 = (int)d & M28; d >>>= 28;
long f7 = (long)x7 * x0_2
+ (long)x6 * x1_2
+ (long)x5 * x2_2
+ (long)x4 * x3_2;
long g7 = (long)u7 * u0_2
+ (long)u6 * u1_2
+ (long)u5 * u2_2
+ (long)u4 * u3_2;
long h7 = (long)s7 * (s0_2 & U32)
+ (long)s6 * (s1_2 & U32)
+ (long)s5 * (s2_2 & U32)
+ (long)s4 * (s3_2 & U32);
c += f7 + g7;
z7 = (int)c & M28; c >>>= 28;
d += h7 - f7;
z15 = (int)d & M28; d >>>= 28;
c += d;
c += z8;
z8 = (int)c & M28; c >>>= 28;
d += z0;
z0 = (int)d & M28; d >>>= 28;
z9 += (int)c;
z1 += (int)d;
z[0] = z0;
z[1] = z1;
z[2] = z2;
z[3] = z3;
z[4] = z4;
z[5] = z5;
z[6] = z6;
z[7] = z7;
z[8] = z8;
z[9] = z9;
z[10] = z10;
z[11] = z11;
z[12] = z12;
z[13] = z13;
z[14] = z14;
z[15] = z15;
}
public static void sqr(int[] x, int n, int[] z)
{
// assert n > 0;
sqr(x, z);
while (--n > 0)
{
sqr(z, z);
}
}
public static boolean sqrtRatioVar(int[] u, int[] v, int[] z)
{
int[] u3v = create();
int[] u5v3 = create();
sqr(u, u3v);
mul(u3v, v, u3v);
sqr(u3v, u5v3);
mul(u3v, u, u3v);
mul(u5v3, u, u5v3);
mul(u5v3, v, u5v3);
int[] x = create();
powPm3d4(u5v3, x);
mul(x, u3v, x);
int[] t = create();
sqr(x, t);
mul(t, v, t);
sub(u, t, t);
normalize(t);
if (isZeroVar(t))
{
copy(x, 0, z, 0);
return true;
}
return false;
}
public static void sub(int[] x, int[] y, int[] z)
{
int x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6], x7 = x[7];
int x8 = x[8], x9 = x[9], x10 = x[10], x11 = x[11], x12 = x[12], x13 = x[13], x14 = x[14], x15 = x[15];
int y0 = y[0], y1 = y[1], y2 = y[2], y3 = y[3], y4 = y[4], y5 = y[5], y6 = y[6], y7 = y[7];
int y8 = y[8], y9 = y[9], y10 = y[10], y11 = y[11], y12 = y[12], y13 = y[13], y14 = y[14], y15 = y[15];
int z0 = x0 + 0x1FFFFFFE - y0;
int z1 = x1 + 0x1FFFFFFE - y1;
int z2 = x2 + 0x1FFFFFFE - y2;
int z3 = x3 + 0x1FFFFFFE - y3;
int z4 = x4 + 0x1FFFFFFE - y4;
int z5 = x5 + 0x1FFFFFFE - y5;
int z6 = x6 + 0x1FFFFFFE - y6;
int z7 = x7 + 0x1FFFFFFE - y7;
int z8 = x8 + 0x1FFFFFFC - y8;
int z9 = x9 + 0x1FFFFFFE - y9;
int z10 = x10 + 0x1FFFFFFE - y10;
int z11 = x11 + 0x1FFFFFFE - y11;
int z12 = x12 + 0x1FFFFFFE - y12;
int z13 = x13 + 0x1FFFFFFE - y13;
int z14 = x14 + 0x1FFFFFFE - y14;
int z15 = x15 + 0x1FFFFFFE - y15;
z2 += z1 >>> 28; z1 &= M28;
z6 += z5 >>> 28; z5 &= M28;
z10 += z9 >>> 28; z9 &= M28;
z14 += z13 >>> 28; z13 &= M28;
z3 += z2 >>> 28; z2 &= M28;
z7 += z6 >>> 28; z6 &= M28;
z11 += z10 >>> 28; z10 &= M28;
z15 += z14 >>> 28; z14 &= M28;
int t = z15 >>> 28; z15 &= M28;
z0 += t;
z8 += t;
z4 += z3 >>> 28; z3 &= M28;
z8 += z7 >>> 28; z7 &= M28;
z12 += z11 >>> 28; z11 &= M28;
z1 += z0 >>> 28; z0 &= M28;
z5 += z4 >>> 28; z4 &= M28;
z9 += z8 >>> 28; z8 &= M28;
z13 += z12 >>> 28; z12 &= M28;
z[0] = z0;
z[1] = z1;
z[2] = z2;
z[3] = z3;
z[4] = z4;
z[5] = z5;
z[6] = z6;
z[7] = z7;
z[8] = z8;
z[9] = z9;
z[10] = z10;
z[11] = z11;
z[12] = z12;
z[13] = z13;
z[14] = z14;
z[15] = z15;
}
public static void subOne(int[] z)
{
int[] one = create();
one[0] = 1;
sub(z, one, z);
}
public static void zero(int[] z)
{
for (int i = 0; i < SIZE; ++i)
{
z[i] = 0;
}
}
}
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