protected BigInteger modInverse(BigInteger x) { int bits = getFieldSize(); int len = (bits + 31) >> 5; int[] p = Nat.fromBigInteger(bits, q); int[] n = Nat.fromBigInteger(bits, x); int[] z = Nat.create(len); Mod.invert(p, n, z); return Nat.toBigInteger(len, z); }
public static void squareN(long[] x, int n, long[] z) { // assert n > 0; long[] tt = Nat.create64(5); implSquare(x, tt); reduce(tt, z); while (--n > 0) { implSquare(z, tt); reduce(tt, z); } }
public ECPoint add(ECPoint b) { if (this.isInfinity()) { return b; } if (b.isInfinity()) { return this; } if (this == b) { return twice(); } ECCurve curve = this.getCurve(); SecP521R1FieldElement X1 = (SecP521R1FieldElement) this.x, Y1 = (SecP521R1FieldElement) this.y; SecP521R1FieldElement X2 = (SecP521R1FieldElement) b.getXCoord(), Y2 = (SecP521R1FieldElement) b.getYCoord(); SecP521R1FieldElement Z1 = (SecP521R1FieldElement) this.zs[0]; SecP521R1FieldElement Z2 = (SecP521R1FieldElement) b.getZCoord(0); int[] t1 = Nat.create(17); int[] t2 = Nat.create(17); int[] t3 = Nat.create(17); int[] t4 = Nat.create(17); boolean Z1IsOne = Z1.isOne(); int[] U2, S2; if (Z1IsOne) { U2 = X2.x; S2 = Y2.x; } else { S2 = t3; SecP521R1Field.square(Z1.x, S2); U2 = t2; SecP521R1Field.multiply(S2, X2.x, U2); SecP521R1Field.multiply(S2, Z1.x, S2); SecP521R1Field.multiply(S2, Y2.x, S2); } boolean Z2IsOne = Z2.isOne(); int[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP521R1Field.square(Z2.x, S1); U1 = t1; SecP521R1Field.multiply(S1, X1.x, U1); SecP521R1Field.multiply(S1, Z2.x, S1); SecP521R1Field.multiply(S1, Y1.x, S1); } int[] H = Nat.create(17); SecP521R1Field.subtract(U1, U2, H); int[] R = t2; SecP521R1Field.subtract(S1, S2, R); // Check if b == this or b == -this if (Nat.isZero(17, H)) { if (Nat.isZero(17, R)) { // this == b, i.e. this must be doubled return this.twice(); } // this == -b, i.e. the result is the point at infinity return curve.getInfinity(); } int[] HSquared = t3; SecP521R1Field.square(H, HSquared); int[] G = Nat.create(17); SecP521R1Field.multiply(HSquared, H, G); int[] V = t3; SecP521R1Field.multiply(HSquared, U1, V); SecP521R1Field.multiply(S1, G, t1); SecP521R1FieldElement X3 = new SecP521R1FieldElement(t4); SecP521R1Field.square(R, X3.x); SecP521R1Field.add(X3.x, G, X3.x); SecP521R1Field.subtract(X3.x, V, X3.x); SecP521R1Field.subtract(X3.x, V, X3.x); SecP521R1FieldElement Y3 = new SecP521R1FieldElement(G); SecP521R1Field.subtract(V, X3.x, Y3.x); SecP521R1Field.multiply(Y3.x, R, t2); SecP521R1Field.subtract(t2, t1, Y3.x); SecP521R1FieldElement Z3 = new SecP521R1FieldElement(H); if (!Z1IsOne) { SecP521R1Field.multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP521R1Field.multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] {Z3}; return new SecP521R1Point(curve, X3, Y3, zs, this.withCompression); }
public ECPoint twice() { if (this.isInfinity()) { return this; } ECCurve curve = this.getCurve(); SecP521R1FieldElement Y1 = (SecP521R1FieldElement) this.y; if (Y1.isZero()) { return curve.getInfinity(); } SecP521R1FieldElement X1 = (SecP521R1FieldElement) this.x, Z1 = (SecP521R1FieldElement) this.zs[0]; int[] t1 = Nat.create(17); int[] t2 = Nat.create(17); int[] Y1Squared = Nat.create(17); SecP521R1Field.square(Y1.x, Y1Squared); int[] T = Nat.create(17); SecP521R1Field.square(Y1Squared, T); boolean Z1IsOne = Z1.isOne(); int[] Z1Squared = Z1.x; if (!Z1IsOne) { Z1Squared = t2; SecP521R1Field.square(Z1.x, Z1Squared); } SecP521R1Field.subtract(X1.x, Z1Squared, t1); int[] M = t2; SecP521R1Field.add(X1.x, Z1Squared, M); SecP521R1Field.multiply(M, t1, M); Nat.addBothTo(17, M, M, M); SecP521R1Field.reduce23(M); int[] S = Y1Squared; SecP521R1Field.multiply(Y1Squared, X1.x, S); Nat.shiftUpBits(17, S, 2, 0); SecP521R1Field.reduce23(S); Nat.shiftUpBits(17, T, 3, 0, t1); SecP521R1Field.reduce23(t1); SecP521R1FieldElement X3 = new SecP521R1FieldElement(T); SecP521R1Field.square(M, X3.x); SecP521R1Field.subtract(X3.x, S, X3.x); SecP521R1Field.subtract(X3.x, S, X3.x); SecP521R1FieldElement Y3 = new SecP521R1FieldElement(S); SecP521R1Field.subtract(S, X3.x, Y3.x); SecP521R1Field.multiply(Y3.x, M, Y3.x); SecP521R1Field.subtract(Y3.x, t1, Y3.x); SecP521R1FieldElement Z3 = new SecP521R1FieldElement(M); SecP521R1Field.twice(Y1.x, Z3.x); if (!Z1IsOne) { SecP521R1Field.multiply(Z3.x, Z1.x, Z3.x); } return new SecP521R1Point(curve, X3, Y3, new ECFieldElement[] {Z3}, this.withCompression); }
public static void squareAddToExt(long[] x, long[] zz) { long[] tt = Nat.create64(5); implSquare(x, tt); addExt(zz, tt, zz); }
public static void square(long[] x, long[] z) { long[] tt = Nat.create64(5); implSquare(x, tt); reduce(tt, z); }