public static Multiply ( uint x, uint y, uint z ) : void | ||
x | uint | |
y | uint | |
z | uint | |
Результат | void |
public override ECPoint Twice() { if (this.IsInfinity) { return(this); } ECCurve curve = this.Curve; SecP256K1FieldElement Y1 = (SecP256K1FieldElement)this.RawYCoord; if (Y1.IsZero) { return(curve.Infinity); } SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Z1 = (SecP256K1FieldElement)this.RawZCoords[0]; uint c; uint[] Y1Squared = Nat256.Create(); SecP256K1Field.Square(Y1.x, Y1Squared); uint[] T = Nat256.Create(); SecP256K1Field.Square(Y1Squared, T); uint[] M = Nat256.Create(); SecP256K1Field.Square(X1.x, M); c = Nat256.AddBothTo(M, M, M); SecP256K1Field.Reduce32(c, M); uint[] S = Y1Squared; SecP256K1Field.Multiply(Y1Squared, X1.x, S); c = Nat.ShiftUpBits(8, S, 2, 0); SecP256K1Field.Reduce32(c, S); uint[] t1 = Nat256.Create(); c = Nat.ShiftUpBits(8, T, 3, 0, t1); SecP256K1Field.Reduce32(c, t1); SecP256K1FieldElement X3 = new SecP256K1FieldElement(T); SecP256K1Field.Square(M, X3.x); SecP256K1Field.Subtract(X3.x, S, X3.x); SecP256K1Field.Subtract(X3.x, S, X3.x); SecP256K1FieldElement Y3 = new SecP256K1FieldElement(S); SecP256K1Field.Subtract(S, X3.x, Y3.x); SecP256K1Field.Multiply(Y3.x, M, Y3.x); SecP256K1Field.Subtract(Y3.x, t1, Y3.x); SecP256K1FieldElement Z3 = new SecP256K1FieldElement(M); SecP256K1Field.Twice(Y1.x, Z3.x); if (!Z1.IsOne) { SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x); } return(new SecP256K1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed)); }
public override ECFieldElement Multiply(ECFieldElement b) { uint[] z = Nat256.Create(); SecP256K1Field.Multiply(this.x, ((SecP256K1FieldElement)b).x, z); return(new SecP256K1FieldElement(z)); }
public override ECPoint Add(ECPoint b) { if (this.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(Twice()); } ECCurve curve = this.Curve; SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Y1 = (SecP256K1FieldElement)this.RawYCoord; SecP256K1FieldElement X2 = (SecP256K1FieldElement)b.RawXCoord, Y2 = (SecP256K1FieldElement)b.RawYCoord; SecP256K1FieldElement Z1 = (SecP256K1FieldElement)this.RawZCoords[0]; SecP256K1FieldElement Z2 = (SecP256K1FieldElement)b.RawZCoords[0]; uint c; uint[] tt1 = Nat256.CreateExt(); uint[] t2 = Nat256.Create(); uint[] t3 = Nat256.Create(); uint[] t4 = Nat256.Create(); bool Z1IsOne = Z1.IsOne; uint[] U2, S2; if (Z1IsOne) { U2 = X2.x; S2 = Y2.x; } else { S2 = t3; SecP256K1Field.Square(Z1.x, S2); U2 = t2; SecP256K1Field.Multiply(S2, X2.x, U2); SecP256K1Field.Multiply(S2, Z1.x, S2); SecP256K1Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP256K1Field.Square(Z2.x, S1); U1 = tt1; SecP256K1Field.Multiply(S1, X1.x, U1); SecP256K1Field.Multiply(S1, Z2.x, S1); SecP256K1Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat256.Create(); SecP256K1Field.Subtract(U1, U2, H); uint[] R = t2; SecP256K1Field.Subtract(S1, S2, R); // Check if b == this or b == -this if (Nat256.IsZero(H)) { if (Nat256.IsZero(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.Infinity); } uint[] HSquared = t3; SecP256K1Field.Square(H, HSquared); uint[] G = Nat256.Create(); SecP256K1Field.Multiply(HSquared, H, G); uint[] V = t3; SecP256K1Field.Multiply(HSquared, U1, V); SecP256K1Field.Negate(G, G); Nat256.Mul(S1, G, tt1); c = Nat256.AddBothTo(V, V, G); SecP256K1Field.Reduce32(c, G); SecP256K1FieldElement X3 = new SecP256K1FieldElement(t4); SecP256K1Field.Square(R, X3.x); SecP256K1Field.Subtract(X3.x, G, X3.x); SecP256K1FieldElement Y3 = new SecP256K1FieldElement(G); SecP256K1Field.Subtract(V, X3.x, Y3.x); SecP256K1Field.MultiplyAddToExt(Y3.x, R, tt1); SecP256K1Field.Reduce(tt1, Y3.x); SecP256K1FieldElement Z3 = new SecP256K1FieldElement(H); if (!Z1IsOne) { SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP256K1Field.Multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] { Z3 }; return(new SecP256K1Point(curve, X3, Y3, zs, IsCompressed)); }
/** * return a sqrt root - the routine verifies that the calculation returns the right value - if * none exists it returns null. */ public override ECFieldElement Sqrt() { /* * Raise this element to the exponent 2^254 - 2^30 - 2^7 - 2^6 - 2^5 - 2^4 - 2^2 * * Breaking up the exponent's binary representation into "repunits", we get: * { 223 1s } { 1 0s } { 22 1s } { 4 0s } { 2 1s } { 2 0s} * * Therefore we need an addition chain containing 2, 22, 223 (the lengths of the repunits) * We use: 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] */ uint[] x1 = this.x; if (Nat256.IsZero(x1) || Nat256.IsOne(x1)) { return(this); } uint[] x2 = Nat256.Create(); SecP256K1Field.Square(x1, x2); SecP256K1Field.Multiply(x2, x1, x2); uint[] x3 = Nat256.Create(); SecP256K1Field.Square(x2, x3); SecP256K1Field.Multiply(x3, x1, x3); uint[] x6 = Nat256.Create(); SecP256K1Field.SquareN(x3, 3, x6); SecP256K1Field.Multiply(x6, x3, x6); uint[] x9 = x6; SecP256K1Field.SquareN(x6, 3, x9); SecP256K1Field.Multiply(x9, x3, x9); uint[] x11 = x9; SecP256K1Field.SquareN(x9, 2, x11); SecP256K1Field.Multiply(x11, x2, x11); uint[] x22 = Nat256.Create(); SecP256K1Field.SquareN(x11, 11, x22); SecP256K1Field.Multiply(x22, x11, x22); uint[] x44 = x11; SecP256K1Field.SquareN(x22, 22, x44); SecP256K1Field.Multiply(x44, x22, x44); uint[] x88 = Nat256.Create(); SecP256K1Field.SquareN(x44, 44, x88); SecP256K1Field.Multiply(x88, x44, x88); uint[] x176 = Nat256.Create(); SecP256K1Field.SquareN(x88, 88, x176); SecP256K1Field.Multiply(x176, x88, x176); uint[] x220 = x88; SecP256K1Field.SquareN(x176, 44, x220); SecP256K1Field.Multiply(x220, x44, x220); uint[] x223 = x44; SecP256K1Field.SquareN(x220, 3, x223); SecP256K1Field.Multiply(x223, x3, x223); uint[] t1 = x223; SecP256K1Field.SquareN(t1, 23, t1); SecP256K1Field.Multiply(t1, x22, t1); SecP256K1Field.SquareN(t1, 6, t1); SecP256K1Field.Multiply(t1, x2, t1); SecP256K1Field.SquareN(t1, 2, t1); uint[] t2 = x2; SecP256K1Field.Square(t1, t2); return(Nat256.Eq(x1, t2) ? new SecP256K1FieldElement(t1) : null); }