1d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Rootpackage org.bouncycastle.math.ec.custom.sec; 2d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 3d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Rootimport org.bouncycastle.math.ec.ECCurve; 4d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Rootimport org.bouncycastle.math.ec.ECFieldElement; 5d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Rootimport org.bouncycastle.math.ec.ECPoint; 6d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Rootimport org.bouncycastle.math.raw.Nat; 7d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Rootimport org.bouncycastle.math.raw.Nat256; 8d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 9d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Rootpublic class SecP256K1Point extends ECPoint.AbstractFp 10d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root{ 11d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root /** 12d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * Create a point which encodes with point compression. 1379d3bf2425a53baab7feb744dad710b6c15533c9Sergio Giro * 14d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @param curve 15d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * the curve to use 16d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @param x 17d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * affine x co-ordinate 18d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @param y 19d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * affine y co-ordinate 2079d3bf2425a53baab7feb744dad710b6c15533c9Sergio Giro * 21d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @deprecated Use ECCurve.createPoint to construct points 22d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root */ 23d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root public SecP256K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y) 24d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 25d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root this(curve, x, y, false); 26d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 27d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 28d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root /** 29d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * Create a point that encodes with or without point compresion. 3079d3bf2425a53baab7feb744dad710b6c15533c9Sergio Giro * 31d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @param curve 32d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * the curve to use 33d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @param x 34d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * affine x co-ordinate 35d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @param y 36d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * affine y co-ordinate 37d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @param withCompression 38d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * if true encode with point compression 3979d3bf2425a53baab7feb744dad710b6c15533c9Sergio Giro * 40d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * @deprecated per-point compression property will be removed, refer 41d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root * {@link #getEncoded(boolean)} 42d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root */ 43d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root public SecP256K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, boolean withCompression) 44d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 45d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root super(curve, x, y); 46d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 47d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if ((x == null) != (y == null)) 48d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 49d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root throw new IllegalArgumentException("Exactly one of the field elements is null"); 50d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 51d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 52d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root this.withCompression = withCompression; 53d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 54d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 55d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, 56d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root boolean withCompression) 57d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 58d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root super(curve, x, y, zs); 59d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 60d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root this.withCompression = withCompression; 61d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 62d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 63d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root protected ECPoint detach() 64d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 65d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return new SecP256K1Point(null, getAffineXCoord(), getAffineYCoord()); 66d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 67d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 68d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root // B.3 pg 62 69d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root public ECPoint add(ECPoint b) 70d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 71d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (this.isInfinity()) 72d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 73d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return b; 74d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 75d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (b.isInfinity()) 76d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 77d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return this; 78d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 79d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (this == b) 80d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 81d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return twice(); 82d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 83d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 84d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root ECCurve curve = this.getCurve(); 85d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 86d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.x, Y1 = (SecP256K1FieldElement)this.y; 87d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement X2 = (SecP256K1FieldElement)b.getXCoord(), Y2 = (SecP256K1FieldElement)b.getYCoord(); 88d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 89d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement Z1 = (SecP256K1FieldElement)this.zs[0]; 90d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement Z2 = (SecP256K1FieldElement)b.getZCoord(0); 91d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 92d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int c; 93d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] tt1 = Nat256.createExt(); 94d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] t2 = Nat256.create(); 95d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] t3 = Nat256.create(); 96d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] t4 = Nat256.create(); 97d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 98d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root boolean Z1IsOne = Z1.isOne(); 99d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] U2, S2; 100d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (Z1IsOne) 101d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 102d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root U2 = X2.x; 103d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root S2 = Y2.x; 104d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 105d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root else 106d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 107d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root S2 = t3; 108d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.square(Z1.x, S2); 109d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 110d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root U2 = t2; 111d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(S2, X2.x, U2); 112d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 113d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(S2, Z1.x, S2); 114d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(S2, Y2.x, S2); 115d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 116d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 117d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root boolean Z2IsOne = Z2.isOne(); 118d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] U1, S1; 119d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (Z2IsOne) 120d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 121d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root U1 = X1.x; 122d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root S1 = Y1.x; 123d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 124d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root else 125d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 126d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root S1 = t4; 127d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.square(Z2.x, S1); 128d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 129d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root U1 = tt1; 130d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(S1, X1.x, U1); 131d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 132d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(S1, Z2.x, S1); 133d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(S1, Y1.x, S1); 134d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 135d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 136d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] H = Nat256.create(); 137d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.subtract(U1, U2, H); 138d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 139d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] R = t2; 140d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.subtract(S1, S2, R); 141d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 142d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root // Check if b == this or b == -this 143d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (Nat256.isZero(H)) 144d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 145d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (Nat256.isZero(R)) 146d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 147d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root // this == b, i.e. this must be doubled 148d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return this.twice(); 149d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 150d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 151d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root // this == -b, i.e. the result is the point at infinity 152d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return curve.getInfinity(); 153d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 154d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 155d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] HSquared = t3; 156d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.square(H, HSquared); 157d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 158d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] G = Nat256.create(); 159d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(HSquared, H, G); 160d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 161d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] V = t3; 162d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(HSquared, U1, V); 163d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 164d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.negate(G, G); 165d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root Nat256.mul(S1, G, tt1); 166d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 167d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root c = Nat256.addBothTo(V, V, G); 168d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.reduce32(c, G); 169d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 170d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement X3 = new SecP256K1FieldElement(t4); 171d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.square(R, X3.x); 172d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.subtract(X3.x, G, X3.x); 173d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 174d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement Y3 = new SecP256K1FieldElement(G); 175d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.subtract(V, X3.x, Y3.x); 176d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiplyAddToExt(Y3.x, R, tt1); 177d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.reduce(tt1, Y3.x); 178d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 179d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement Z3 = new SecP256K1FieldElement(H); 180d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (!Z1IsOne) 181d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 182d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(Z3.x, Z1.x, Z3.x); 183d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 184d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (!Z2IsOne) 185d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 186d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(Z3.x, Z2.x, Z3.x); 187d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 188d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 189d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root ECFieldElement[] zs = new ECFieldElement[] { Z3 }; 190d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 191d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return new SecP256K1Point(curve, X3, Y3, zs, this.withCompression); 192d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 193d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 194d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root // B.3 pg 62 195d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root public ECPoint twice() 196d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 197d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (this.isInfinity()) 198d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 199d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return this; 200d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 201d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 202d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root ECCurve curve = this.getCurve(); 203d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 204d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement Y1 = (SecP256K1FieldElement)this.y; 205d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (Y1.isZero()) 206d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 207d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return curve.getInfinity(); 208d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 209d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 210d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.x, Z1 = (SecP256K1FieldElement)this.zs[0]; 211d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 212d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int c; 21379d3bf2425a53baab7feb744dad710b6c15533c9Sergio Giro 214d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] Y1Squared = Nat256.create(); 215d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.square(Y1.x, Y1Squared); 216d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 217d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] T = Nat256.create(); 218d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.square(Y1Squared, T); 219d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 220d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] M = Nat256.create(); 221d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.square(X1.x, M); 222d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root c = Nat256.addBothTo(M, M, M); 223d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.reduce32(c, M); 224d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 225d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] S = Y1Squared; 226d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(Y1Squared, X1.x, S); 227d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root c = Nat.shiftUpBits(8, S, 2, 0); 228d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.reduce32(c, S); 229d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 230d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root int[] t1 = Nat256.create(); 231d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root c = Nat.shiftUpBits(8, T, 3, 0, t1); 232d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.reduce32(c, t1); 233d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 234d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement X3 = new SecP256K1FieldElement(T); 235d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.square(M, X3.x); 236d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.subtract(X3.x, S, X3.x); 237d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.subtract(X3.x, S, X3.x); 238d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 239d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement Y3 = new SecP256K1FieldElement(S); 240d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.subtract(S, X3.x, Y3.x); 241d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(Y3.x, M, Y3.x); 242d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.subtract(Y3.x, t1, Y3.x); 243d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 244d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1FieldElement Z3 = new SecP256K1FieldElement(M); 245d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.twice(Y1.x, Z3.x); 246d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (!Z1.isOne()) 247d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 248d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root SecP256K1Field.multiply(Z3.x, Z1.x, Z3.x); 249d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 250d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 251d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return new SecP256K1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, this.withCompression); 252d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 253d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 254d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root public ECPoint twicePlus(ECPoint b) 255d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 256d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (this == b) 257d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 258d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return threeTimes(); 259d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 260d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (this.isInfinity()) 261d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 262d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return b; 263d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 264d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (b.isInfinity()) 265d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 266d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return twice(); 267d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 268d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 269d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root ECFieldElement Y1 = this.y; 270d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (Y1.isZero()) 271d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 272d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return b; 273d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 274d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 275d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return twice().add(b); 276d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 277d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 278d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root public ECPoint threeTimes() 279d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 280d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (this.isInfinity() || this.y.isZero()) 281d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 282d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return this; 283d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 284d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 285d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root // NOTE: Be careful about recursions between twicePlus and threeTimes 286d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return twice().add(this); 287d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 288d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 289d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root public ECPoint negate() 290d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 291d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root if (this.isInfinity()) 292d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root { 293d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return this; 294d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 295d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root 296d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root return new SecP256K1Point(curve, this.x, this.y.negate(), this.zs, this.withCompression); 297d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root } 298d001700a15b8bd733ae344c1fc315b97c43c6590Kenny Root} 299