using System; namespace Org.BouncyCastle.Math.EC.Custom.Sec { internal class SecT131R2Point : AbstractF2mPoint { /** * @deprecated Use ECCurve.createPoint to construct points */ public SecT131R2Point(ECCurve curve, ECFieldElement x, ECFieldElement y) : this(curve, x, y, false) { } /** * @deprecated per-point compression property will be removed, refer {@link #getEncoded(bool)} */ public SecT131R2Point(ECCurve curve, ECFieldElement x, ECFieldElement y, bool withCompression) : base(curve, x, y, withCompression) { if ((x == null) != (y == null)) throw new ArgumentException("Exactly one of the field elements is null"); } internal SecT131R2Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, bool withCompression) : base(curve, x, y, zs, withCompression) { } protected override ECPoint Detach() { return new SecT131R2Point(null, AffineXCoord, AffineYCoord); } public override ECFieldElement YCoord { get { ECFieldElement X = RawXCoord, L = RawYCoord; if (this.IsInfinity || X.IsZero) return L; // Y is actually Lambda (X + Y/X) here; convert to affine value on the fly ECFieldElement Y = L.Add(X).Multiply(X); ECFieldElement Z = RawZCoords[0]; if (!Z.IsOne) { Y = Y.Divide(Z); } return Y; } } protected internal override bool CompressionYTilde { get { ECFieldElement X = this.RawXCoord; if (X.IsZero) return false; ECFieldElement Y = this.RawYCoord; // Y is actually Lambda (X + Y/X) here return Y.TestBitZero() != X.TestBitZero(); } } public override ECPoint Add(ECPoint b) { if (this.IsInfinity) return b; if (b.IsInfinity) return this; ECCurve curve = this.Curve; ECFieldElement X1 = this.RawXCoord; ECFieldElement X2 = b.RawXCoord; if (X1.IsZero) { if (X2.IsZero) return curve.Infinity; return b.Add(this); } ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0]; ECFieldElement L2 = b.RawYCoord, Z2 = b.RawZCoords[0]; bool Z1IsOne = Z1.IsOne; ECFieldElement U2 = X2, S2 = L2; if (!Z1IsOne) { U2 = U2.Multiply(Z1); S2 = S2.Multiply(Z1); } bool Z2IsOne = Z2.IsOne; ECFieldElement U1 = X1, S1 = L1; if (!Z2IsOne) { U1 = U1.Multiply(Z2); S1 = S1.Multiply(Z2); } ECFieldElement A = S1.Add(S2); ECFieldElement B = U1.Add(U2); if (B.IsZero) { if (A.IsZero) return Twice(); return curve.Infinity; } ECFieldElement X3, L3, Z3; if (X2.IsZero) { // TODO This can probably be optimized quite a bit ECPoint p = this.Normalize(); X1 = p.XCoord; ECFieldElement Y1 = p.YCoord; ECFieldElement Y2 = L2; ECFieldElement L = Y1.Add(Y2).Divide(X1); X3 = L.Square().Add(L).Add(X1).Add(curve.A); if (X3.IsZero) { return new SecT131R2Point(curve, X3, curve.B.Sqrt(), IsCompressed); } ECFieldElement Y3 = L.Multiply(X1.Add(X3)).Add(X3).Add(Y1); L3 = Y3.Divide(X3).Add(X3); Z3 = curve.FromBigInteger(BigInteger.One); } else { B = B.Square(); ECFieldElement AU1 = A.Multiply(U1); ECFieldElement AU2 = A.Multiply(U2); X3 = AU1.Multiply(AU2); if (X3.IsZero) { return new SecT131R2Point(curve, X3, curve.B.Sqrt(), IsCompressed); } ECFieldElement ABZ2 = A.Multiply(B); if (!Z2IsOne) { ABZ2 = ABZ2.Multiply(Z2); } L3 = AU2.Add(B).SquarePlusProduct(ABZ2, L1.Add(Z1)); Z3 = ABZ2; if (!Z1IsOne) { Z3 = Z3.Multiply(Z1); } } return new SecT131R2Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed); } public override ECPoint Twice() { if (this.IsInfinity) { return this; } ECCurve curve = this.Curve; ECFieldElement X1 = this.RawXCoord; if (X1.IsZero) { // A point with X == 0 is its own additive inverse return curve.Infinity; } ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0]; bool Z1IsOne = Z1.IsOne; ECFieldElement L1Z1 = Z1IsOne ? L1 : L1.Multiply(Z1); ECFieldElement Z1Sq = Z1IsOne ? Z1 : Z1.Square(); ECFieldElement a = curve.A; ECFieldElement aZ1Sq = Z1IsOne ? a : a.Multiply(Z1Sq); ECFieldElement T = L1.Square().Add(L1Z1).Add(aZ1Sq); if (T.IsZero) { return new SecT131R2Point(curve, T, curve.B.Sqrt(), IsCompressed); } ECFieldElement X3 = T.Square(); ECFieldElement Z3 = Z1IsOne ? T : T.Multiply(Z1Sq); ECFieldElement X1Z1 = Z1IsOne ? X1 : X1.Multiply(Z1); ECFieldElement L3 = X1Z1.SquarePlusProduct(T, L1Z1).Add(X3).Add(Z3); return new SecT131R2Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed); } public override ECPoint TwicePlus(ECPoint b) { if (this.IsInfinity) return b; if (b.IsInfinity) return Twice(); ECCurve curve = this.Curve; ECFieldElement X1 = this.RawXCoord; if (X1.IsZero) { // A point with X == 0 is its own additive inverse return b; } ECFieldElement X2 = b.RawXCoord, Z2 = b.RawZCoords[0]; if (X2.IsZero || !Z2.IsOne) { return Twice().Add(b); } ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0]; ECFieldElement L2 = b.RawYCoord; ECFieldElement X1Sq = X1.Square(); ECFieldElement L1Sq = L1.Square(); ECFieldElement Z1Sq = Z1.Square(); ECFieldElement L1Z1 = L1.Multiply(Z1); ECFieldElement T = curve.A.Multiply(Z1Sq).Add(L1Sq).Add(L1Z1); ECFieldElement L2plus1 = L2.AddOne(); ECFieldElement A = curve.A.Add(L2plus1).Multiply(Z1Sq).Add(L1Sq).MultiplyPlusProduct(T, X1Sq, Z1Sq); ECFieldElement X2Z1Sq = X2.Multiply(Z1Sq); ECFieldElement B = X2Z1Sq.Add(T).Square(); if (B.IsZero) { if (A.IsZero) return b.Twice(); return curve.Infinity; } if (A.IsZero) { return new SecT131R2Point(curve, A, curve.B.Sqrt(), IsCompressed); } ECFieldElement X3 = A.Square().Multiply(X2Z1Sq); ECFieldElement Z3 = A.Multiply(B).Multiply(Z1Sq); ECFieldElement L3 = A.Add(B).Square().MultiplyPlusProduct(T, L2plus1, Z3); return new SecT131R2Point(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed); } public override ECPoint Negate() { if (IsInfinity) return this; ECFieldElement X = this.RawXCoord; if (X.IsZero) return this; // L is actually Lambda (X + Y/X) here ECFieldElement L = this.RawYCoord, Z = this.RawZCoords[0]; return new SecT131R2Point(Curve, X, L.Add(Z), new ECFieldElement[] { Z }, IsCompressed); } } }