org.bouncycastle.math.ec.rfc7748.X25519Field Maven / Gradle / Ivy
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package org.bouncycastle.math.ec.rfc7748;
public abstract class X25519Field
{
public static final int SIZE = 10;
private static final int M24 = 0x00FFFFFF;
private static final int M25 = 0x01FFFFFF;
private static final int M26 = 0x03FFFFFF;
private static final int[] ROOT_NEG_ONE = new int[]{ 0x020EA0B0, 0x0386C9D2, 0x00478C4E, 0x0035697F, 0x005E8630,
0x01FBD7A7, 0x0340264F, 0x01F0B2B4, 0x00027E0E, 0x00570649 };
protected X25519Field() {}
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 void carry(int[] z)
{
int z0 = z[0], z1 = z[1], z2 = z[2], z3 = z[3], z4 = z[4];
int z5 = z[5], z6 = z[6], z7 = z[7], z8 = z[8], z9 = z[9];
z2 += (z1 >> 26); z1 &= M26;
z4 += (z3 >> 26); z3 &= M26;
z7 += (z6 >> 26); z6 &= M26;
z9 += (z8 >> 26); z8 &= M26;
z3 += (z2 >> 25); z2 &= M25;
z5 += (z4 >> 25); z4 &= M25;
z8 += (z7 >> 25); z7 &= M25;
// z0 += (z9 >> 24) * 19; z9 &= M24;
z0 += (z9 >> 25) * 38; z9 &= M25;
z1 += (z0 >> 26); z0 &= M26;
z6 += (z5 >> 26); z5 &= M26;
z2 += (z1 >> 26); z1 &= M26;
z4 += (z3 >> 26); z3 &= M26;
z7 += (z6 >> 26); z6 &= M26;
z9 += (z8 >> 26); z8 &= M26;
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;
}
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 mask = 0 - negate;
for (int i = 0; i < SIZE; ++i)
{
z[i] = (z[i] ^ mask) - mask;
}
}
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(byte[] x, int xOff, int[] z)
{
decode128(x, xOff, z, 0);
decode128(x, xOff + 16, z, 5);
z[9] &= M24;
}
private static void decode128(byte[] bs, int off, int[] z, int zOff)
{
int t0 = decode32(bs, off + 0);
int t1 = decode32(bs, off + 4);
int t2 = decode32(bs, off + 8);
int t3 = decode32(bs, off + 12);
z[zOff + 0] = t0 & M26;
z[zOff + 1] = ((t1 << 6) | (t0 >>> 26)) & M26;
z[zOff + 2] = ((t2 << 12) | (t1 >>> 20)) & M25;
z[zOff + 3] = ((t3 << 19) | (t2 >>> 13)) & M26;
z[zOff + 4] = t3 >>> 7;
}
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;
}
public static void encode(int[] x, byte[] z, int zOff)
{
encode128(x, 0, z, zOff);
encode128(x, 5, z, zOff + 16);
}
private static void encode128(int[] x, int xOff, byte[] bs, int off)
{
int x0 = x[xOff + 0], x1 = x[xOff + 1], x2 = x[xOff + 2], x3 = x[xOff + 3], x4 = x[xOff + 4];
int t0 = x0 | (x1 << 26); encode32(t0, bs, off + 0);
int t1 = (x1 >>> 6) | (x2 << 20); encode32(t1, bs, off + 4);
int t2 = (x2 >>> 12) | (x3 << 13); encode32(t2, bs, off + 8);
int t3 = (x3 >>> 19) | (x4 << 7); encode32(t3, bs, off + 12);
}
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);
}
public static void inv(int[] x, int[] z)
{
// z = x^(p-2) = x^7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEB
// (250 1s) (1 0s) (1 1s) (1 0s) (2 1s)
// Addition chain: [1] [2] 3 5 10 15 25 50 75 125 [250]
int[] x2 = create();
int[] t = create();
powPm5d8(x, x2, t);
sqr(t, 3, t);
mul(t, x2, z);
}
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];
int x5 = x[5], x6 = x[6], x7 = x[7], x8 = x[8], x9 = x[9];
long c0, c1, c2, c3;
c0 = (long)x2 * y; x2 = (int)c0 & M25; c0 >>= 25;
c1 = (long)x4 * y; x4 = (int)c1 & M25; c1 >>= 25;
c2 = (long)x7 * y; x7 = (int)c2 & M25; c2 >>= 25;
// c3 = (long)x9 * y; x9 = (int)c3 & M24; c3 >>= 24;
// c3 *= 19;
c3 = (long)x9 * y; x9 = (int)c3 & M25; c3 >>= 25;
c3 *= 38;
c3 += (long)x0 * y; z[0] = (int)c3 & M26; c3 >>= 26;
c1 += (long)x5 * y; z[5] = (int)c1 & M26; c1 >>= 26;
c3 += (long)x1 * y; z[1] = (int)c3 & M26; c3 >>= 26;
c0 += (long)x3 * y; z[3] = (int)c0 & M26; c0 >>= 26;
c1 += (long)x6 * y; z[6] = (int)c1 & M26; c1 >>= 26;
c2 += (long)x8 * y; z[8] = (int)c2 & M26; c2 >>= 26;
z[2] = x2 + (int)c3;
z[4] = x4 + (int)c0;
z[7] = x7 + (int)c1;
z[9] = x9 + (int)c2;
}
public static void mul(int[] x, int[] y, int[] z)
{
int x0 = x[0], y0 = y[0];
int x1 = x[1], y1 = y[1];
int x2 = x[2], y2 = y[2];
int x3 = x[3], y3 = y[3];
int x4 = x[4], y4 = y[4];
int u0 = x[5], v0 = y[5];
int u1 = x[6], v1 = y[6];
int u2 = x[7], v2 = y[7];
int u3 = x[8], v3 = y[8];
int u4 = x[9], v4 = y[9];
long a0 = (long)x0 * y0;
long a1 = (long)x0 * y1
+ (long)x1 * y0;
long a2 = (long)x0 * y2
+ (long)x1 * y1
+ (long)x2 * y0;
long a3 = (long)x1 * y2
+ (long)x2 * y1;
a3 <<= 1;
a3 += (long)x0 * y3
+ (long)x3 * y0;
long a4 = (long)x2 * y2;
a4 <<= 1;
a4 += (long)x0 * y4
+ (long)x1 * y3
+ (long)x3 * y1
+ (long)x4 * y0;
long a5 = (long)x1 * y4
+ (long)x2 * y3
+ (long)x3 * y2
+ (long)x4 * y1;
a5 <<= 1;
long a6 = (long)x2 * y4
+ (long)x4 * y2;
a6 <<= 1;
a6 += (long)x3 * y3;
long a7 = (long)x3 * y4
+ (long)x4 * y3;
long a8 = (long)x4 * y4;
a8 <<= 1;
long b0 = (long)u0 * v0;
long b1 = (long)u0 * v1
+ (long)u1 * v0;
long b2 = (long)u0 * v2
+ (long)u1 * v1
+ (long)u2 * v0;
long b3 = (long)u1 * v2
+ (long)u2 * v1;
b3 <<= 1;
b3 += (long)u0 * v3
+ (long)u3 * v0;
long b4 = (long)u2 * v2;
b4 <<= 1;
b4 += (long)u0 * v4
+ (long)u1 * v3
+ (long)u3 * v1
+ (long)u4 * v0;
long b5 = (long)u1 * v4
+ (long)u2 * v3
+ (long)u3 * v2
+ (long)u4 * v1;
// b5 <<= 1;
long b6 = (long)u2 * v4
+ (long)u4 * v2;
b6 <<= 1;
b6 += (long)u3 * v3;
long b7 = (long)u3 * v4
+ (long)u4 * v3;
long b8 = (long)u4 * v4;
// b8 <<= 1;
a0 -= b5 * 76;
a1 -= b6 * 38;
a2 -= b7 * 38;
a3 -= b8 * 76;
a5 -= b0;
a6 -= b1;
a7 -= b2;
a8 -= b3;
// long a9 = -b4;
x0 += u0; y0 += v0;
x1 += u1; y1 += v1;
x2 += u2; y2 += v2;
x3 += u3; y3 += v3;
x4 += u4; y4 += v4;
long c0 = (long)x0 * y0;
long c1 = (long)x0 * y1
+ (long)x1 * y0;
long c2 = (long)x0 * y2
+ (long)x1 * y1
+ (long)x2 * y0;
long c3 = (long)x1 * y2
+ (long)x2 * y1;
c3 <<= 1;
c3 += (long)x0 * y3
+ (long)x3 * y0;
long c4 = (long)x2 * y2;
c4 <<= 1;
c4 += (long)x0 * y4
+ (long)x1 * y3
+ (long)x3 * y1
+ (long)x4 * y0;
long c5 = (long)x1 * y4
+ (long)x2 * y3
+ (long)x3 * y2
+ (long)x4 * y1;
c5 <<= 1;
long c6 = (long)x2 * y4
+ (long)x4 * y2;
c6 <<= 1;
c6 += (long)x3 * y3;
long c7 = (long)x3 * y4
+ (long)x4 * y3;
long c8 = (long)x4 * y4;
c8 <<= 1;
int z8, z9;
long t;
t = a8 + (c3 - a3);
z8 = (int)t & M26; t >>= 26;
// t += a9 + (c4 - a4);
t += (c4 - a4) - b4;
// z9 = (int)t & M24; t >>= 24;
// t = a0 + (t + ((c5 - a5) << 1)) * 19;
z9 = (int)t & M25; t >>= 25;
t = a0 + (t + c5 - a5) * 38;
z[0] = (int)t & M26; t >>= 26;
t += a1 + (c6 - a6) * 38;
z[1] = (int)t & M26; t >>= 26;
t += a2 + (c7 - a7) * 38;
z[2] = (int)t & M25; t >>= 25;
t += a3 + (c8 - a8) * 38;
z[3] = (int)t & M26; t >>= 26;
// t += a4 - a9 * 38;
t += a4 + b4 * 38;
z[4] = (int)t & M25; t >>= 25;
t += a5 + (c0 - a0);
z[5] = (int)t & M26; t >>= 26;
t += a6 + (c1 - a1);
z[6] = (int)t & M26; t >>= 26;
t += a7 + (c2 - a2);
z[7] = (int)t & M25; t >>= 25;
t += z8;
z[8] = (int)t & M26; t >>= 26;
z[9] = z9 + (int)t;
}
public static void negate(int[] x, int[] z)
{
for (int i = 0; i < SIZE; ++i)
{
z[i] = -x[i];
}
}
public static void normalize(int[] z)
{
int x = ((z[9] >>> 23) & 1);
reduce(z, x);
reduce(z, -x);
// assert z[9] >>> 24 == 0;
}
public static void one(int[] z)
{
z[0] = 1;
for (int i = 1; i < SIZE; ++i)
{
z[i] = 0;
}
}
private static void powPm5d8(int[] x, int[] rx2, int[] rz)
{
// z = x^((p-5)/8) = x^FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD
// (250 1s) (1 0s) (1 1s)
// Addition chain: [1] 2 3 5 10 15 25 50 75 125 [250]
int[] x2 = rx2; sqr(x, x2); mul(x, x2, x2);
int[] x3 = create(); sqr(x2, x3); mul(x, x3, x3);
int[] x5 = x3; sqr(x3, 2, x5); mul(x2, x5, x5);
int[] x10 = create(); sqr(x5, 5, x10); mul(x5, x10, x10);
int[] x15 = create(); sqr(x10, 5, x15); mul(x5, x15, x15);
int[] x25 = x5; sqr(x15, 10, x25); mul(x10, x25, x25);
int[] x50 = x10; sqr(x25, 25, x50); mul(x25, x50, x50);
int[] x75 = x15; sqr(x50, 25, x75); mul(x25, x75, x75);
int[] x125 = x25; sqr(x75, 50, x125); mul(x50, x125, x125);
int[] x250 = x50; sqr(x125, 125, x250); mul(x125, x250, x250);
int[] t = x125;
sqr(x250, 2, t);
mul(t, x, rz);
}
private static void reduce(int[] z, int x)
{
int t = z[9], z9 = t & M24;
t = (t >> 24) + x;
long cc = t * 19;
cc += z[0]; z[0] = (int)cc & M26; cc >>= 26;
cc += z[1]; z[1] = (int)cc & M26; cc >>= 26;
cc += z[2]; z[2] = (int)cc & M25; cc >>= 25;
cc += z[3]; z[3] = (int)cc & M26; cc >>= 26;
cc += z[4]; z[4] = (int)cc & M25; cc >>= 25;
cc += z[5]; z[5] = (int)cc & M26; cc >>= 26;
cc += z[6]; z[6] = (int)cc & M26; cc >>= 26;
cc += z[7]; z[7] = (int)cc & M25; cc >>= 25;
cc += z[8]; z[8] = (int)cc & M26; cc >>= 26;
z[9] = z9 + (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 u0 = x[5];
int u1 = x[6];
int u2 = x[7];
int u3 = x[8];
int u4 = x[9];
int x1_2 = x1 * 2;
int x2_2 = x2 * 2;
int x3_2 = x3 * 2;
int x4_2 = x4 * 2;
long a0 = (long)x0 * x0;
long a1 = (long)x0 * x1_2;
long a2 = (long)x0 * x2_2
+ (long)x1 * x1;
long a3 = (long)x1_2 * x2_2
+ (long)x0 * x3_2;
long a4 = (long)x2 * x2_2
+ (long)x0 * x4_2
+ (long)x1 * x3_2;
long a5 = (long)x1_2 * x4_2
+ (long)x2_2 * x3_2;
long a6 = (long)x2_2 * x4_2
+ (long)x3 * x3;
long a7 = (long)x3 * x4_2;
long a8 = (long)x4 * x4_2;
int u1_2 = u1 * 2;
int u2_2 = u2 * 2;
int u3_2 = u3 * 2;
int u4_2 = u4 * 2;
long b0 = (long)u0 * u0;
long b1 = (long)u0 * u1_2;
long b2 = (long)u0 * u2_2
+ (long)u1 * u1;
long b3 = (long)u1_2 * u2_2
+ (long)u0 * u3_2;
long b4 = (long)u2 * u2_2
+ (long)u0 * u4_2
+ (long)u1 * u3_2;
long b5 = (long)u1_2 * u4_2
+ (long)u2_2 * u3_2;
long b6 = (long)u2_2 * u4_2
+ (long)u3 * u3;
long b7 = (long)u3 * u4_2;
long b8 = (long)u4 * u4_2;
a0 -= b5 * 38;
a1 -= b6 * 38;
a2 -= b7 * 38;
a3 -= b8 * 38;
a5 -= b0;
a6 -= b1;
a7 -= b2;
a8 -= b3;
// long a9 = -b4;
x0 += u0;
x1 += u1;
x2 += u2;
x3 += u3;
x4 += u4;
x1_2 = x1 * 2;
x2_2 = x2 * 2;
x3_2 = x3 * 2;
x4_2 = x4 * 2;
long c0 = (long)x0 * x0;
long c1 = (long)x0 * x1_2;
long c2 = (long)x0 * x2_2
+ (long)x1 * x1;
long c3 = (long)x1_2 * x2_2
+ (long)x0 * x3_2;
long c4 = (long)x2 * x2_2
+ (long)x0 * x4_2
+ (long)x1 * x3_2;
long c5 = (long)x1_2 * x4_2
+ (long)x2_2 * x3_2;
long c6 = (long)x2_2 * x4_2
+ (long)x3 * x3;
long c7 = (long)x3 * x4_2;
long c8 = (long)x4 * x4_2;
int z8, z9;
long t;
t = a8 + (c3 - a3);
z8 = (int)t & M26; t >>= 26;
// t += a9 + (c4 - a4);
t += (c4 - a4) - b4;
// z9 = (int)t & M24; t >>= 24;
// t = a0 + (t + ((c5 - a5) << 1)) * 19;
z9 = (int)t & M25; t >>= 25;
t = a0 + (t + c5 - a5) * 38;
z[0] = (int)t & M26; t >>= 26;
t += a1 + (c6 - a6) * 38;
z[1] = (int)t & M26; t >>= 26;
t += a2 + (c7 - a7) * 38;
z[2] = (int)t & M25; t >>= 25;
t += a3 + (c8 - a8) * 38;
z[3] = (int)t & M26; t >>= 26;
// t += a4 - a9 * 38;
t += a4 + b4 * 38;
z[4] = (int)t & M25; t >>= 25;
t += a5 + (c0 - a0);
z[5] = (int)t & M26; t >>= 26;
t += a6 + (c1 - a1);
z[6] = (int)t & M26; t >>= 26;
t += a7 + (c2 - a2);
z[7] = (int)t & M25; t >>= 25;
t += z8;
z[8] = (int)t & M26; t >>= 26;
z[9] = z9 + (int)t;
}
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[] uv3 = create();
int[] uv7 = create();
mul(u, v, uv3);
sqr(v, uv7);
mul(uv3, uv7, uv3);
sqr(uv7, uv7);
mul(uv7, uv3, uv7);
int[] t = create();
int[] x = create();
powPm5d8(uv7, t, x);
mul(x, uv3, x);
int[] vx2 = create();
sqr(x, vx2);
mul(vx2, v, vx2);
sub(vx2, u, t);
normalize(t);
if (isZeroVar(t))
{
copy(x, 0, z, 0);
return true;
}
add(vx2, u, t);
normalize(t);
if (isZeroVar(t))
{
mul(x, ROOT_NEG_ONE, z);
return true;
}
return false;
}
public static void sub(int[] x, int[] y, int[] z)
{
for (int i = 0; i < SIZE; ++i)
{
z[i] = x[i] - y[i];
}
}
public static void subOne(int[] z)
{
z[0] -= 1;
}
public static void zero(int[] z)
{
for (int i = 0; i < SIZE; ++i)
{
z[i] = 0;
}
}
}