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package org.bouncycastle.math.ec.custom.sec;
import java.math.BigInteger;
import java.security.SecureRandom;
import org.bouncycastle.math.raw.Nat;
import org.bouncycastle.math.raw.Nat256;
import org.bouncycastle.util.Pack;
public class SecP256R1Field
{
private static final long M = 0xFFFFFFFFL;
// 2^256 - 2^224 + 2^192 + 2^96 - 1
static final int[] P = new int[]{ 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000000, 0x00000000,
0x00000001, 0xFFFFFFFF };
static final int[] PExt = new int[]{ 0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF,
0xFFFFFFFF, 0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001, 0x00000001, 0xFFFFFFFE,
0x00000002, 0xFFFFFFFE };
private static final int P7 = 0xFFFFFFFF;
private static final int PExt15s1 = 0xFFFFFFFE >>> 1;
public static void add(int[] x, int[] y, int[] z)
{
int c = Nat256.add(x, y, z);
if (c != 0 || (z[7] == P7 && Nat256.gte(z, P)))
{
addPInvTo(z);
}
}
public static void addExt(int[] xx, int[] yy, int[] zz)
{
int c = Nat.add(16, xx, yy, zz);
if (c != 0 || ((zz[15] >>> 1) >= PExt15s1 && Nat.gte(16, zz, PExt)))
{
Nat.subFrom(16, PExt, zz);
}
}
public static void addOne(int[] x, int[] z)
{
int c = Nat.inc(8, x, z);
if (c != 0 || (z[7] == P7 && Nat256.gte(z, P)))
{
addPInvTo(z);
}
}
public static int[] fromBigInteger(BigInteger x)
{
int[] z = Nat256.fromBigInteger(x);
if (z[7] == P7 && Nat256.gte(z, P))
{
Nat256.subFrom(P, z);
}
return z;
}
public static void half(int[] x, int[] z)
{
if ((x[0] & 1) == 0)
{
Nat.shiftDownBit(8, x, 0, z);
}
else
{
int c = Nat256.add(x, P, z);
Nat.shiftDownBit(8, z, c);
}
}
public static void inv(int[] x, int[] z)
{
/*
* Raise this element to the exponent 2^256 - 2^224 + 2^192 + 2^96 - 3
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 32 1s } { 31 0s } { 1 1s } { 96 0s } { 94 1s } { 1 0s} { 1 1s}
*
* Therefore we need an addition chain containing 1, 32, 94 (the lengths of the repunits)
* We use: [1], 2, 4, 8, 16, [32], 64, 80, 88, 92, [94]
*/
if (0 != isZero(x))
{
throw new IllegalArgumentException("'x' cannot be 0");
}
int[] x1 = x;
int[] x2 = Nat256.create();
square(x1, x2);
multiply(x2, x1, x2);
int[] x4 = Nat256.create();
squareN(x2, 2, x4);
multiply(x4, x2, x4);
int[] x8 = Nat256.create();
squareN(x4, 4, x8);
multiply(x8, x4, x8);
int[] x16 = Nat256.create();
squareN(x8, 8, x16);
multiply(x16, x8, x16);
int[] x32 = Nat256.create();
squareN(x16, 16, x32);
multiply(x32, x16, x32);
int[] x64 = Nat256.create();
squareN(x32, 32, x64);
multiply(x64, x32, x64);
int[] x80 = x64;
squareN(x64, 16, x80);
multiply(x80, x16, x80);
int[] x88 = x16;
squareN(x80, 8, x88);
multiply(x88, x8, x88);
int[] x92 = x8;
squareN(x88, 4, x92);
multiply(x92, x4, x92);
int[] x94 = x4;
squareN(x92, 2, x94);
multiply(x94, x2, x94);
int[] t = x32;
squareN(t, 32, t);
multiply(t, x1, t);
squareN(t, 190, t);
multiply(t, x94, t);
squareN(t, 2, t);
// NOTE that x1 and z could be the same array
multiply(x1, t, z);
}
public static int isZero(int[] x)
{
int d = 0;
for (int i = 0; i < 8; ++i)
{
d |= x[i];
}
d = (d >>> 1) | (d & 1);
return (d - 1) >> 31;
}
public static void multiply(int[] x, int[] y, int[] z)
{
int[] tt = Nat256.createExt();
Nat256.mul(x, y, tt);
reduce(tt, z);
}
public static void multiplyAddToExt(int[] x, int[] y, int[] zz)
{
int c = Nat256.mulAddTo(x, y, zz);
if (c != 0 || ((zz[15] >>> 1) >= PExt15s1 && Nat.gte(16, zz, PExt)))
{
Nat.subFrom(16, PExt, zz);
}
}
public static void negate(int[] x, int[] z)
{
if (0 != isZero(x))
{
Nat256.sub(P, P, z);
}
else
{
Nat256.sub(P, x, z);
}
}
public static void random(SecureRandom r, int[] z)
{
byte[] bb = new byte[8 * 4];
do
{
r.nextBytes(bb);
Pack.littleEndianToInt(bb, 0, z, 0, 8);
}
while (0 == Nat.lessThan(8, z, P));
}
public static void randomMult(SecureRandom r, int[] z)
{
do
{
random(r, z);
}
while (0 != isZero(z));
}
public static void reduce(int[] xx, int[] z)
{
long xx08 = xx[8] & M, xx09 = xx[9] & M, xx10 = xx[10] & M, xx11 = xx[11] & M;
long xx12 = xx[12] & M, xx13 = xx[13] & M, xx14 = xx[14] & M, xx15 = xx[15] & M;
final long n = 6;
xx08 -= n;
long t0 = xx08 + xx09;
long t1 = xx09 + xx10;
long t2 = xx10 + xx11 - xx15;
long t3 = xx11 + xx12;
long t4 = xx12 + xx13;
long t5 = xx13 + xx14;
long t6 = xx14 + xx15;
long t7 = t5 - t0;
long cc = 0;
cc += (xx[0] & M) - t3 - t7;
z[0] = (int)cc;
cc >>= 32;
cc += (xx[1] & M) + t1 - t4 - t6;
z[1] = (int)cc;
cc >>= 32;
cc += (xx[2] & M) + t2 - t5;
z[2] = (int)cc;
cc >>= 32;
cc += (xx[3] & M) + (t3 << 1) + t7 - t6;
z[3] = (int)cc;
cc >>= 32;
cc += (xx[4] & M) + (t4 << 1) + xx14 - t1;
z[4] = (int)cc;
cc >>= 32;
cc += (xx[5] & M) + (t5 << 1) - t2;
z[5] = (int)cc;
cc >>= 32;
cc += (xx[6] & M) + (t6 << 1) + t7;
z[6] = (int)cc;
cc >>= 32;
cc += (xx[7] & M) + (xx15 << 1) + xx08 - t2 - t4;
z[7] = (int)cc;
cc >>= 32;
cc += n;
// assert cc >= 0;
reduce32((int)cc, z);
}
public static void reduce32(int x, int[] z)
{
long cc = 0;
if (x != 0)
{
long xx08 = x & M;
cc += (z[0] & M) + xx08;
z[0] = (int)cc;
cc >>= 32;
if (cc != 0)
{
cc += (z[1] & M);
z[1] = (int)cc;
cc >>= 32;
cc += (z[2] & M);
z[2] = (int)cc;
cc >>= 32;
}
cc += (z[3] & M) - xx08;
z[3] = (int)cc;
cc >>= 32;
if (cc != 0)
{
cc += (z[4] & M);
z[4] = (int)cc;
cc >>= 32;
cc += (z[5] & M);
z[5] = (int)cc;
cc >>= 32;
}
cc += (z[6] & M) - xx08;
z[6] = (int)cc;
cc >>= 32;
cc += (z[7] & M) + xx08;
z[7] = (int)cc;
cc >>= 32;
// assert cc == 0 || cc == 1;
}
if (cc != 0 || (z[7] == P7 && Nat256.gte(z, P)))
{
addPInvTo(z);
}
}
public static void square(int[] x, int[] z)
{
int[] tt = Nat256.createExt();
Nat256.square(x, tt);
reduce(tt, z);
}
public static void squareN(int[] x, int n, int[] z)
{
// assert n > 0;
int[] tt = Nat256.createExt();
Nat256.square(x, tt);
reduce(tt, z);
while (--n > 0)
{
Nat256.square(z, tt);
reduce(tt, z);
}
}
public static void subtract(int[] x, int[] y, int[] z)
{
int c = Nat256.sub(x, y, z);
if (c != 0)
{
subPInvFrom(z);
}
}
public static void subtractExt(int[] xx, int[] yy, int[] zz)
{
int c = Nat.sub(16, xx, yy, zz);
if (c != 0)
{
Nat.addTo(16, PExt, zz);
}
}
public static void twice(int[] x, int[] z)
{
int c = Nat.shiftUpBit(8, x, 0, z);
if (c != 0 || (z[7] == P7 && Nat256.gte(z, P)))
{
addPInvTo(z);
}
}
private static void addPInvTo(int[] z)
{
long c = (z[0] & M) + 1;
z[0] = (int)c;
c >>= 32;
if (c != 0)
{
c += (z[1] & M);
z[1] = (int)c;
c >>= 32;
c += (z[2] & M);
z[2] = (int)c;
c >>= 32;
}
c += (z[3] & M) - 1;
z[3] = (int)c;
c >>= 32;
if (c != 0)
{
c += (z[4] & M);
z[4] = (int)c;
c >>= 32;
c += (z[5] & M);
z[5] = (int)c;
c >>= 32;
}
c += (z[6] & M) - 1;
z[6] = (int)c;
c >>= 32;
c += (z[7] & M) + 1;
z[7] = (int)c;
// c >>= 32;
}
private static void subPInvFrom(int[] z)
{
long c = (z[0] & M) - 1;
z[0] = (int)c;
c >>= 32;
if (c != 0)
{
c += (z[1] & M);
z[1] = (int)c;
c >>= 32;
c += (z[2] & M);
z[2] = (int)c;
c >>= 32;
}
c += (z[3] & M) + 1;
z[3] = (int)c;
c >>= 32;
if (c != 0)
{
c += (z[4] & M);
z[4] = (int)c;
c >>= 32;
c += (z[5] & M);
z[5] = (int)c;
c >>= 32;
}
c += (z[6] & M) + 1;
z[6] = (int)c;
c >>= 32;
c += (z[7] & M) - 1;
z[7] = (int)c;
// c >>= 32;
}
}