public override ECFieldElement Multiply(ECFieldElement b) { uint[] z = Nat256.Create(); Curve25519Field.Multiply(x, ((Curve25519FieldElement)b).x, z); return(new Curve25519FieldElement(z)); }
public override ECFieldElement AddOne() { uint[] z = Nat256.Create(); Curve25519Field.AddOne(x, z); return(new Curve25519FieldElement(z)); }
public override ECFieldElement Subtract(ECFieldElement b) { uint[] z = Nat256.Create(); Curve25519Field.Subtract(x, ((Curve25519FieldElement)b).x, z); return(new Curve25519FieldElement(z)); }
public override ECPoint Add(ECPoint b) { if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(Twice()); } ECCurve curve = Curve; Curve25519FieldElement curve25519FieldElement = (Curve25519FieldElement)base.RawXCoord; Curve25519FieldElement curve25519FieldElement2 = (Curve25519FieldElement)base.RawYCoord; Curve25519FieldElement curve25519FieldElement3 = (Curve25519FieldElement)base.RawZCoords[0]; Curve25519FieldElement curve25519FieldElement4 = (Curve25519FieldElement)b.RawXCoord; Curve25519FieldElement curve25519FieldElement5 = (Curve25519FieldElement)b.RawYCoord; Curve25519FieldElement curve25519FieldElement6 = (Curve25519FieldElement)b.RawZCoords[0]; uint[] array = Nat256.CreateExt(); uint[] array2 = Nat256.Create(); uint[] array3 = Nat256.Create(); uint[] array4 = Nat256.Create(); bool isOne = curve25519FieldElement3.IsOne; uint[] array5; uint[] array6; if (isOne) { array5 = curve25519FieldElement4.x; array6 = curve25519FieldElement5.x; } else { array6 = array3; Curve25519Field.Square(curve25519FieldElement3.x, array6); array5 = array2; Curve25519Field.Multiply(array6, curve25519FieldElement4.x, array5); Curve25519Field.Multiply(array6, curve25519FieldElement3.x, array6); Curve25519Field.Multiply(array6, curve25519FieldElement5.x, array6); } bool isOne2 = curve25519FieldElement6.IsOne; uint[] array7; uint[] array8; if (isOne2) { array7 = curve25519FieldElement.x; array8 = curve25519FieldElement2.x; } else { array8 = array4; Curve25519Field.Square(curve25519FieldElement6.x, array8); array7 = array; Curve25519Field.Multiply(array8, curve25519FieldElement.x, array7); Curve25519Field.Multiply(array8, curve25519FieldElement6.x, array8); Curve25519Field.Multiply(array8, curve25519FieldElement2.x, array8); } uint[] array9 = Nat256.Create(); Curve25519Field.Subtract(array7, array5, array9); uint[] array10 = array2; Curve25519Field.Subtract(array8, array6, array10); if (Nat256.IsZero(array9)) { if (Nat256.IsZero(array10)) { return(Twice()); } return(curve.Infinity); } uint[] array11 = Nat256.Create(); Curve25519Field.Square(array9, array11); uint[] array12 = Nat256.Create(); Curve25519Field.Multiply(array11, array9, array12); uint[] array13 = array3; Curve25519Field.Multiply(array11, array7, array13); Curve25519Field.Negate(array12, array12); Nat256.Mul(array8, array12, array); uint x = Nat256.AddBothTo(array13, array13, array12); Curve25519Field.Reduce27(x, array12); Curve25519FieldElement curve25519FieldElement7 = new Curve25519FieldElement(array4); Curve25519Field.Square(array10, curve25519FieldElement7.x); Curve25519Field.Subtract(curve25519FieldElement7.x, array12, curve25519FieldElement7.x); Curve25519FieldElement curve25519FieldElement8 = new Curve25519FieldElement(array12); Curve25519Field.Subtract(array13, curve25519FieldElement7.x, curve25519FieldElement8.x); Curve25519Field.MultiplyAddToExt(curve25519FieldElement8.x, array10, array); Curve25519Field.Reduce(array, curve25519FieldElement8.x); Curve25519FieldElement curve25519FieldElement9 = new Curve25519FieldElement(array9); if (!isOne) { Curve25519Field.Multiply(curve25519FieldElement9.x, curve25519FieldElement3.x, curve25519FieldElement9.x); } if (!isOne2) { Curve25519Field.Multiply(curve25519FieldElement9.x, curve25519FieldElement6.x, curve25519FieldElement9.x); } uint[] zSquared = (!isOne || !isOne2) ? null : array11; Curve25519FieldElement curve25519FieldElement10 = CalculateJacobianModifiedW(curve25519FieldElement9, zSquared); ECFieldElement[] zs = new ECFieldElement[2] { curve25519FieldElement9, curve25519FieldElement10 }; return(new Curve25519Point(curve, curve25519FieldElement7, curve25519FieldElement8, zs, base.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() { /* * Q == 8m + 5, so we use Pocklington's method for this case. * * First, raise this element to the exponent 2^252 - 2^1 (i.e. m + 1) * * Breaking up the exponent's binary representation into "repunits", we get: * { 251 1s } { 1 0s } * * Therefore we need an addition chain containing 251 (the lengths of the repunits) * We use: 1, 2, 3, 4, 7, 11, 15, 30, 60, 120, 131, [251] */ uint[] x1 = this.x; if (Nat256.IsZero(x1) || Nat256.IsOne(x1)) { return(this); } uint[] x2 = Nat256.Create(); Curve25519Field.Square(x1, x2); Curve25519Field.Multiply(x2, x1, x2); uint[] x3 = x2; Curve25519Field.Square(x2, x3); Curve25519Field.Multiply(x3, x1, x3); uint[] x4 = Nat256.Create(); Curve25519Field.Square(x3, x4); Curve25519Field.Multiply(x4, x1, x4); uint[] x7 = Nat256.Create(); Curve25519Field.SquareN(x4, 3, x7); Curve25519Field.Multiply(x7, x3, x7); uint[] x11 = x3; Curve25519Field.SquareN(x7, 4, x11); Curve25519Field.Multiply(x11, x4, x11); uint[] x15 = x7; Curve25519Field.SquareN(x11, 4, x15); Curve25519Field.Multiply(x15, x4, x15); uint[] x30 = x4; Curve25519Field.SquareN(x15, 15, x30); Curve25519Field.Multiply(x30, x15, x30); uint[] x60 = x15; Curve25519Field.SquareN(x30, 30, x60); Curve25519Field.Multiply(x60, x30, x60); uint[] x120 = x30; Curve25519Field.SquareN(x60, 60, x120); Curve25519Field.Multiply(x120, x60, x120); uint[] x131 = x60; Curve25519Field.SquareN(x120, 11, x131); Curve25519Field.Multiply(x131, x11, x131); uint[] x251 = x11; Curve25519Field.SquareN(x131, 120, x251); Curve25519Field.Multiply(x251, x120, x251); uint[] t1 = x251; Curve25519Field.Square(t1, t1); uint[] t2 = x120; Curve25519Field.Square(t1, t2); if (Nat256.Eq(x1, t2)) { return(new Curve25519FieldElement(t1)); } /* * If the first guess is incorrect, we multiply by a precomputed power of 2 to get the second guess, * which is ((4x)^(m + 1))/2 mod Q */ Curve25519Field.Multiply(t1, PRECOMP_POW2, t1); Curve25519Field.Square(t1, t2); if (Nat256.Eq(x1, t2)) { return(new Curve25519FieldElement(t1)); } return(null); }
public override ECFieldElement Add(ECFieldElement b) { uint[] z = Nat256.Create(); Curve25519Field.Add(this.x, ((Curve25519FieldElement)b).x, z); return(new Curve25519FieldElement(z)); }
public override ECFieldElement Negate() { uint[] z = Nat256.Create(); Curve25519Field.Negate(this.x, z); return(new Curve25519FieldElement(z)); }
public override ECFieldElement RandomFieldElement(SecureRandom r) { uint[] x = Nat256.Create(); Curve25519Field.Random(r, x); return(new Curve25519FieldElement(x)); }
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; Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord, Z1 = (Curve25519FieldElement)this.RawZCoords[0]; Curve25519FieldElement X2 = (Curve25519FieldElement)b.RawXCoord, Y2 = (Curve25519FieldElement)b.RawYCoord, Z2 = (Curve25519FieldElement)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; Curve25519Field.Square(Z1.x, S2); U2 = t2; Curve25519Field.Multiply(S2, X2.x, U2); Curve25519Field.Multiply(S2, Z1.x, S2); Curve25519Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; Curve25519Field.Square(Z2.x, S1); U1 = tt1; Curve25519Field.Multiply(S1, X1.x, U1); Curve25519Field.Multiply(S1, Z2.x, S1); Curve25519Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat256.Create(); Curve25519Field.Subtract(U1, U2, H); uint[] R = t2; Curve25519Field.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 = Nat256.Create(); Curve25519Field.Square(H, HSquared); uint[] G = Nat256.Create(); Curve25519Field.Multiply(HSquared, H, G); uint[] V = t3; Curve25519Field.Multiply(HSquared, U1, V); Curve25519Field.Negate(G, G); Nat256.Mul(S1, G, tt1); c = Nat256.AddBothTo(V, V, G); Curve25519Field.Reduce27(c, G); Curve25519FieldElement X3 = new Curve25519FieldElement(t4); Curve25519Field.Square(R, X3.x); Curve25519Field.Subtract(X3.x, G, X3.x); Curve25519FieldElement Y3 = new Curve25519FieldElement(G); Curve25519Field.Subtract(V, X3.x, Y3.x); Curve25519Field.MultiplyAddToExt(Y3.x, R, tt1); Curve25519Field.Reduce(tt1, Y3.x); Curve25519FieldElement Z3 = new Curve25519FieldElement(H); if (!Z1IsOne) { Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { Curve25519Field.Multiply(Z3.x, Z2.x, Z3.x); } uint[] Z3Squared = (Z1IsOne && Z2IsOne) ? HSquared : null; // TODO If the result will only be used in a subsequent addition, we don't need W3 Curve25519FieldElement W3 = CalculateJacobianModifiedW((Curve25519FieldElement)Z3, Z3Squared); ECFieldElement[] zs = new ECFieldElement[] { Z3, W3 }; return(new Curve25519Point(curve, X3, Y3, zs, IsCompressed)); }
public static void Multiply(uint[] x, uint[] y, uint[] z) { uint[] array = Nat256.CreateExt(); Nat256.Mul(x, y, array); Curve25519Field.Reduce(array, z); }
public static void Square(uint[] x, uint[] z) { uint[] array = Nat256.CreateExt(); Nat256.Square(x, array); Curve25519Field.Reduce(array, z); }
public override ECPoint Add(ECPoint b) { uint[] numArray5; uint[] numArray6; uint[] numArray7; uint[] numArray8; if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(this.Twice()); } ECCurve curve = this.Curve; Curve25519FieldElement rawXCoord = (Curve25519FieldElement)base.RawXCoord; Curve25519FieldElement rawYCoord = (Curve25519FieldElement)base.RawYCoord; Curve25519FieldElement element3 = (Curve25519FieldElement)base.RawZCoords[0]; Curve25519FieldElement element4 = (Curve25519FieldElement)b.RawXCoord; Curve25519FieldElement element5 = (Curve25519FieldElement)b.RawYCoord; Curve25519FieldElement element6 = (Curve25519FieldElement)b.RawZCoords[0]; uint[] zz = Nat256.CreateExt(); uint[] numArray2 = Nat256.Create(); uint[] numArray3 = Nat256.Create(); uint[] x = Nat256.Create(); bool isOne = element3.IsOne; if (isOne) { numArray5 = element4.x; numArray6 = element5.x; } else { numArray6 = numArray3; Curve25519Field.Square(element3.x, numArray6); numArray5 = numArray2; Curve25519Field.Multiply(numArray6, element4.x, numArray5); Curve25519Field.Multiply(numArray6, element3.x, numArray6); Curve25519Field.Multiply(numArray6, element5.x, numArray6); } bool flag2 = element6.IsOne; if (flag2) { numArray7 = rawXCoord.x; numArray8 = rawYCoord.x; } else { numArray8 = x; Curve25519Field.Square(element6.x, numArray8); numArray7 = zz; Curve25519Field.Multiply(numArray8, rawXCoord.x, numArray7); Curve25519Field.Multiply(numArray8, element6.x, numArray8); Curve25519Field.Multiply(numArray8, rawYCoord.x, numArray8); } uint[] z = Nat256.Create(); Curve25519Field.Subtract(numArray7, numArray5, z); uint[] numArray10 = numArray2; Curve25519Field.Subtract(numArray8, numArray6, numArray10); if (Nat256.IsZero(z)) { if (Nat256.IsZero(numArray10)) { return(this.Twice()); } return(curve.Infinity); } uint[] numArray11 = Nat256.Create(); Curve25519Field.Square(z, numArray11); uint[] numArray12 = Nat256.Create(); Curve25519Field.Multiply(numArray11, z, numArray12); uint[] numArray13 = numArray3; Curve25519Field.Multiply(numArray11, numArray7, numArray13); Curve25519Field.Negate(numArray12, numArray12); Nat256.Mul(numArray8, numArray12, zz); Curve25519Field.Reduce27(Nat256.AddBothTo(numArray13, numArray13, numArray12), numArray12); Curve25519FieldElement element7 = new Curve25519FieldElement(x); Curve25519Field.Square(numArray10, element7.x); Curve25519Field.Subtract(element7.x, numArray12, element7.x); Curve25519FieldElement y = new Curve25519FieldElement(numArray12); Curve25519Field.Subtract(numArray13, element7.x, y.x); Curve25519Field.MultiplyAddToExt(y.x, numArray10, zz); Curve25519Field.Reduce(zz, y.x); Curve25519FieldElement element9 = new Curve25519FieldElement(z); if (!isOne) { Curve25519Field.Multiply(element9.x, element3.x, element9.x); } if (!flag2) { Curve25519Field.Multiply(element9.x, element6.x, element9.x); } uint[] zSquared = (!isOne || !flag2) ? null : numArray11; Curve25519FieldElement element10 = this.CalculateJacobianModifiedW(element9, zSquared); ECFieldElement[] zs = new ECFieldElement[] { element9, element10 }; return(new Curve25519Point(curve, element7, y, zs, base.IsCompressed)); }