/** * 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 2^382 - 2^126 - 2^94 + 2^30 uint[] x1 = this.x; if (Nat.IsZero(12, x1) || Nat.IsOne(12, x1)) return this; uint[] t1 = Nat.Create(12); uint[] t2 = Nat.Create(12); uint[] t3 = Nat.Create(12); uint[] t4 = Nat.Create(12); SecP384R1Field.Square(x1, t1); SecP384R1Field.Multiply(t1, x1, t1); SecP384R1Field.SquareN(t1, 2, t2); SecP384R1Field.Multiply(t2, t1, t2); SecP384R1Field.Square(t2, t2); SecP384R1Field.Multiply(t2, x1, t2); SecP384R1Field.SquareN(t2, 5, t3); SecP384R1Field.Multiply(t3, t2, t3); SecP384R1Field.SquareN(t3, 5, t4); SecP384R1Field.Multiply(t4, t2, t4); SecP384R1Field.SquareN(t4, 15, t2); SecP384R1Field.Multiply(t2, t4, t2); SecP384R1Field.SquareN(t2, 2, t3); SecP384R1Field.Multiply(t1, t3, t1); SecP384R1Field.SquareN(t3, 28, t3); SecP384R1Field.Multiply(t2, t3, t2); SecP384R1Field.SquareN(t2, 60, t3); SecP384R1Field.Multiply(t3, t2, t3); uint[] r = t2; SecP384R1Field.SquareN(t3, 120, r); SecP384R1Field.Multiply(r, t3, r); SecP384R1Field.SquareN(r, 15, r); SecP384R1Field.Multiply(r, t4, r); SecP384R1Field.SquareN(r, 33, r); SecP384R1Field.Multiply(r, t1, r); SecP384R1Field.SquareN(r, 64, r); SecP384R1Field.Multiply(r, x1, r); SecP384R1Field.SquareN(r, 30, t1); SecP384R1Field.Square(t1, t2); return Nat.Eq(12, x1, t2) ? new SecP384R1FieldElement(t1) : null; }
public static void Negate(uint[] x, uint[] z) { if (Nat.IsZero(17, x)) { Nat.Zero(17, z); return; } Nat.Sub(17, SecP521R1Field.P, x, z); }
public static void Negate(uint[] x, uint[] z) { if (Nat.IsZero(0x11, x)) { Nat.Zero(0x11, z); } else { Nat.Sub(0x11, P, x, z); } }
public override ECFieldElement Sqrt() { uint[] array = x; if (Nat.IsZero(17, array) || Nat.IsOne(17, array)) { return(this); } uint[] z = Nat.Create(17); uint[] array2 = Nat.Create(17); SecP521R1Field.SquareN(array, 519, z); SecP521R1Field.Square(z, array2); return((!Nat.Eq(17, array, array2)) ? null : new SecP521R1FieldElement(z)); }
public override ECFieldElement Sqrt() { uint[] x = this.x; if (Nat.IsZero(0x11, x) || Nat.IsOne(0x11, x)) { return(this); } uint[] z = Nat.Create(0x11); uint[] numArray3 = Nat.Create(0x11); SecP521R1Field.SquareN(x, 0x207, z); SecP521R1Field.Square(z, numArray3); return(!Nat.Eq(0x11, x, numArray3) ? null : new SecP521R1FieldElement(z)); }
public override ECFieldElement Sqrt() { uint[] y = this.x; if (Nat.IsZero(12, y) || Nat.IsOne(12, y)) { return(this); } uint[] array = Nat.Create(12); uint[] array2 = Nat.Create(12); uint[] array3 = Nat.Create(12); uint[] array4 = Nat.Create(12); SecP384R1Field.Square(y, array); SecP384R1Field.Multiply(array, y, array); SecP384R1Field.SquareN(array, 2, array2); SecP384R1Field.Multiply(array2, array, array2); SecP384R1Field.Square(array2, array2); SecP384R1Field.Multiply(array2, y, array2); SecP384R1Field.SquareN(array2, 5, array3); SecP384R1Field.Multiply(array3, array2, array3); SecP384R1Field.SquareN(array3, 5, array4); SecP384R1Field.Multiply(array4, array2, array4); SecP384R1Field.SquareN(array4, 15, array2); SecP384R1Field.Multiply(array2, array4, array2); SecP384R1Field.SquareN(array2, 2, array3); SecP384R1Field.Multiply(array, array3, array); SecP384R1Field.SquareN(array3, 28, array3); SecP384R1Field.Multiply(array2, array3, array2); SecP384R1Field.SquareN(array2, 60, array3); SecP384R1Field.Multiply(array3, array2, array3); uint[] z = array2; SecP384R1Field.SquareN(array3, 120, z); SecP384R1Field.Multiply(z, array3, z); SecP384R1Field.SquareN(z, 15, z); SecP384R1Field.Multiply(z, array4, z); SecP384R1Field.SquareN(z, 33, z); SecP384R1Field.Multiply(z, array, z); SecP384R1Field.SquareN(z, 64, z); SecP384R1Field.Multiply(z, y, z); SecP384R1Field.SquareN(z, 30, array); SecP384R1Field.Square(array, array2); if (!Nat.Eq(12, y, array2)) { return(null); } return(new SecP384R1FieldElement(array)); }
/** * 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 2^519 uint[] x1 = this.x; if (Nat.IsZero(17, x1) || Nat.IsOne(17, x1)) { return(this); } uint[] t1 = Nat.Create(17); uint[] t2 = Nat.Create(17); SecP521R1Field.SquareN(x1, 519, t1); SecP521R1Field.Square(t1, t2); return(Nat.Eq(17, x1, t2) ? new SecP521R1FieldElement(t1) : null); }
public override ECFieldElement Sqrt() { uint[] x = this.x; if (Nat.IsZero(12, x) || Nat.IsOne(12, x)) { return(this); } uint[] z = Nat.Create(12); uint[] numArray3 = Nat.Create(12); uint[] numArray4 = Nat.Create(12); uint[] numArray5 = Nat.Create(12); SecP384R1Field.Square(x, z); SecP384R1Field.Multiply(z, x, z); SecP384R1Field.SquareN(z, 2, numArray3); SecP384R1Field.Multiply(numArray3, z, numArray3); SecP384R1Field.Square(numArray3, numArray3); SecP384R1Field.Multiply(numArray3, x, numArray3); SecP384R1Field.SquareN(numArray3, 5, numArray4); SecP384R1Field.Multiply(numArray4, numArray3, numArray4); SecP384R1Field.SquareN(numArray4, 5, numArray5); SecP384R1Field.Multiply(numArray5, numArray3, numArray5); SecP384R1Field.SquareN(numArray5, 15, numArray3); SecP384R1Field.Multiply(numArray3, numArray5, numArray3); SecP384R1Field.SquareN(numArray3, 2, numArray4); SecP384R1Field.Multiply(z, numArray4, z); SecP384R1Field.SquareN(numArray4, 0x1c, numArray4); SecP384R1Field.Multiply(numArray3, numArray4, numArray3); SecP384R1Field.SquareN(numArray3, 60, numArray4); SecP384R1Field.Multiply(numArray4, numArray3, numArray4); uint[] numArray6 = numArray3; SecP384R1Field.SquareN(numArray4, 120, numArray6); SecP384R1Field.Multiply(numArray6, numArray4, numArray6); SecP384R1Field.SquareN(numArray6, 15, numArray6); SecP384R1Field.Multiply(numArray6, numArray5, numArray6); SecP384R1Field.SquareN(numArray6, 0x21, numArray6); SecP384R1Field.Multiply(numArray6, z, numArray6); SecP384R1Field.SquareN(numArray6, 0x40, numArray6); SecP384R1Field.Multiply(numArray6, x, numArray6); SecP384R1Field.SquareN(numArray6, 30, z); SecP384R1Field.Square(z, numArray3); return(!Nat.Eq(12, x, numArray3) ? null : new SecP384R1FieldElement(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; SecP384R1FieldElement X1 = (SecP384R1FieldElement)this.RawXCoord, Y1 = (SecP384R1FieldElement)this.RawYCoord; SecP384R1FieldElement X2 = (SecP384R1FieldElement)b.RawXCoord, Y2 = (SecP384R1FieldElement)b.RawYCoord; SecP384R1FieldElement Z1 = (SecP384R1FieldElement)this.RawZCoords[0]; SecP384R1FieldElement Z2 = (SecP384R1FieldElement)b.RawZCoords[0]; uint c; uint[] tt1 = Nat.Create(24); uint[] tt2 = Nat.Create(24); uint[] t3 = Nat.Create(12); uint[] t4 = Nat.Create(12); bool Z1IsOne = Z1.IsOne; uint[] U2, S2; if (Z1IsOne) { U2 = X2.x; S2 = Y2.x; } else { S2 = t3; SecP384R1Field.Square(Z1.x, S2); U2 = tt2; SecP384R1Field.Multiply(S2, X2.x, U2); SecP384R1Field.Multiply(S2, Z1.x, S2); SecP384R1Field.Multiply(S2, Y2.x, S2); } bool Z2IsOne = Z2.IsOne; uint[] U1, S1; if (Z2IsOne) { U1 = X1.x; S1 = Y1.x; } else { S1 = t4; SecP384R1Field.Square(Z2.x, S1); U1 = tt1; SecP384R1Field.Multiply(S1, X1.x, U1); SecP384R1Field.Multiply(S1, Z2.x, S1); SecP384R1Field.Multiply(S1, Y1.x, S1); } uint[] H = Nat.Create(12); SecP384R1Field.Subtract(U1, U2, H); uint[] R = Nat.Create(12); SecP384R1Field.Subtract(S1, S2, R); // Check if b == this or b == -this if (Nat.IsZero(12, H)) { if (Nat.IsZero(12, 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; SecP384R1Field.Square(H, HSquared); uint[] G = Nat.Create(12); SecP384R1Field.Multiply(HSquared, H, G); uint[] V = t3; SecP384R1Field.Multiply(HSquared, U1, V); SecP384R1Field.Negate(G, G); Nat384.Mul(S1, G, tt1); c = Nat.AddBothTo(12, V, V, G); SecP384R1Field.Reduce32(c, G); SecP384R1FieldElement X3 = new SecP384R1FieldElement(t4); SecP384R1Field.Square(R, X3.x); SecP384R1Field.Subtract(X3.x, G, X3.x); SecP384R1FieldElement Y3 = new SecP384R1FieldElement(G); SecP384R1Field.Subtract(V, X3.x, Y3.x); Nat384.Mul(Y3.x, R, tt2); SecP384R1Field.AddExt(tt1, tt2, tt1); SecP384R1Field.Reduce(tt1, Y3.x); SecP384R1FieldElement Z3 = new SecP384R1FieldElement(H); if (!Z1IsOne) { SecP384R1Field.Multiply(Z3.x, Z1.x, Z3.x); } if (!Z2IsOne) { SecP384R1Field.Multiply(Z3.x, Z2.x, Z3.x); } ECFieldElement[] zs = new ECFieldElement[] { Z3 }; return new SecP384R1Point(curve, X3, Y3, zs, IsCompressed); }
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; SecP521R1FieldElement rawXCoord = (SecP521R1FieldElement)base.RawXCoord; SecP521R1FieldElement rawYCoord = (SecP521R1FieldElement)base.RawYCoord; SecP521R1FieldElement element3 = (SecP521R1FieldElement)b.RawXCoord; SecP521R1FieldElement element4 = (SecP521R1FieldElement)b.RawYCoord; SecP521R1FieldElement element5 = (SecP521R1FieldElement)base.RawZCoords[0]; SecP521R1FieldElement element6 = (SecP521R1FieldElement)b.RawZCoords[0]; uint[] z = Nat.Create(0x11); uint[] numArray2 = Nat.Create(0x11); uint[] numArray3 = Nat.Create(0x11); uint[] x = Nat.Create(0x11); bool isOne = element5.IsOne; if (isOne) { numArray5 = element3.x; numArray6 = element4.x; } else { numArray6 = numArray3; SecP521R1Field.Square(element5.x, numArray6); numArray5 = numArray2; SecP521R1Field.Multiply(numArray6, element3.x, numArray5); SecP521R1Field.Multiply(numArray6, element5.x, numArray6); SecP521R1Field.Multiply(numArray6, element4.x, numArray6); } bool flag2 = element6.IsOne; if (flag2) { numArray7 = rawXCoord.x; numArray8 = rawYCoord.x; } else { numArray8 = x; SecP521R1Field.Square(element6.x, numArray8); numArray7 = z; SecP521R1Field.Multiply(numArray8, rawXCoord.x, numArray7); SecP521R1Field.Multiply(numArray8, element6.x, numArray8); SecP521R1Field.Multiply(numArray8, rawYCoord.x, numArray8); } uint[] numArray9 = Nat.Create(0x11); SecP521R1Field.Subtract(numArray7, numArray5, numArray9); uint[] numArray10 = numArray2; SecP521R1Field.Subtract(numArray8, numArray6, numArray10); if (Nat.IsZero(0x11, numArray9)) { if (Nat.IsZero(0x11, numArray10)) { return(this.Twice()); } return(curve.Infinity); } uint[] numArray11 = numArray3; SecP521R1Field.Square(numArray9, numArray11); uint[] numArray12 = Nat.Create(0x11); SecP521R1Field.Multiply(numArray11, numArray9, numArray12); uint[] numArray13 = numArray3; SecP521R1Field.Multiply(numArray11, numArray7, numArray13); SecP521R1Field.Multiply(numArray8, numArray12, z); SecP521R1FieldElement element7 = new SecP521R1FieldElement(x); SecP521R1Field.Square(numArray10, element7.x); SecP521R1Field.Add(element7.x, numArray12, element7.x); SecP521R1Field.Subtract(element7.x, numArray13, element7.x); SecP521R1Field.Subtract(element7.x, numArray13, element7.x); SecP521R1FieldElement y = new SecP521R1FieldElement(numArray12); SecP521R1Field.Subtract(numArray13, element7.x, y.x); SecP521R1Field.Multiply(y.x, numArray10, numArray2); SecP521R1Field.Subtract(numArray2, z, y.x); SecP521R1FieldElement element9 = new SecP521R1FieldElement(numArray9); if (!isOne) { SecP521R1Field.Multiply(element9.x, element5.x, element9.x); } if (!flag2) { SecP521R1Field.Multiply(element9.x, element6.x, element9.x); } ECFieldElement[] zs = new ECFieldElement[] { element9 }; return(new SecP521R1Point(curve, element7, y, zs, base.IsCompressed)); }
public override ECPoint Add(ECPoint b) { if (base.IsInfinity) { return(b); } if (b.IsInfinity) { return(this); } if (this == b) { return(Twice()); } ECCurve curve = Curve; SecP384R1FieldElement secP384R1FieldElement = (SecP384R1FieldElement)base.RawXCoord; SecP384R1FieldElement secP384R1FieldElement2 = (SecP384R1FieldElement)base.RawYCoord; SecP384R1FieldElement secP384R1FieldElement3 = (SecP384R1FieldElement)b.RawXCoord; SecP384R1FieldElement secP384R1FieldElement4 = (SecP384R1FieldElement)b.RawYCoord; SecP384R1FieldElement secP384R1FieldElement5 = (SecP384R1FieldElement)base.RawZCoords[0]; SecP384R1FieldElement secP384R1FieldElement6 = (SecP384R1FieldElement)b.RawZCoords[0]; uint[] array = Nat.Create(24); uint[] array2 = Nat.Create(24); uint[] array3 = Nat.Create(12); uint[] array4 = Nat.Create(12); bool isOne = secP384R1FieldElement5.IsOne; uint[] array5; uint[] array6; if (isOne) { array5 = secP384R1FieldElement3.x; array6 = secP384R1FieldElement4.x; } else { array6 = array3; SecP384R1Field.Square(secP384R1FieldElement5.x, array6); array5 = array2; SecP384R1Field.Multiply(array6, secP384R1FieldElement3.x, array5); SecP384R1Field.Multiply(array6, secP384R1FieldElement5.x, array6); SecP384R1Field.Multiply(array6, secP384R1FieldElement4.x, array6); } bool isOne2 = secP384R1FieldElement6.IsOne; uint[] array7; uint[] array8; if (isOne2) { array7 = secP384R1FieldElement.x; array8 = secP384R1FieldElement2.x; } else { array8 = array4; SecP384R1Field.Square(secP384R1FieldElement6.x, array8); array7 = array; SecP384R1Field.Multiply(array8, secP384R1FieldElement.x, array7); SecP384R1Field.Multiply(array8, secP384R1FieldElement6.x, array8); SecP384R1Field.Multiply(array8, secP384R1FieldElement2.x, array8); } uint[] array9 = Nat.Create(12); SecP384R1Field.Subtract(array7, array5, array9); uint[] array10 = Nat.Create(12); SecP384R1Field.Subtract(array8, array6, array10); if (Nat.IsZero(12, array9)) { if (Nat.IsZero(12, array10)) { return(Twice()); } return(curve.Infinity); } uint[] array11 = array3; SecP384R1Field.Square(array9, array11); uint[] array12 = Nat.Create(12); SecP384R1Field.Multiply(array11, array9, array12); uint[] array13 = array3; SecP384R1Field.Multiply(array11, array7, array13); SecP384R1Field.Negate(array12, array12); Nat384.Mul(array8, array12, array); uint x = Nat.AddBothTo(12, array13, array13, array12); SecP384R1Field.Reduce32(x, array12); SecP384R1FieldElement secP384R1FieldElement7 = new SecP384R1FieldElement(array4); SecP384R1Field.Square(array10, secP384R1FieldElement7.x); SecP384R1Field.Subtract(secP384R1FieldElement7.x, array12, secP384R1FieldElement7.x); SecP384R1FieldElement secP384R1FieldElement8 = new SecP384R1FieldElement(array12); SecP384R1Field.Subtract(array13, secP384R1FieldElement7.x, secP384R1FieldElement8.x); Nat384.Mul(secP384R1FieldElement8.x, array10, array2); SecP384R1Field.AddExt(array, array2, array); SecP384R1Field.Reduce(array, secP384R1FieldElement8.x); SecP384R1FieldElement secP384R1FieldElement9 = new SecP384R1FieldElement(array9); if (!isOne) { SecP384R1Field.Multiply(secP384R1FieldElement9.x, secP384R1FieldElement5.x, secP384R1FieldElement9.x); } if (!isOne2) { SecP384R1Field.Multiply(secP384R1FieldElement9.x, secP384R1FieldElement6.x, secP384R1FieldElement9.x); } ECFieldElement[] zs = new ECFieldElement[1] { secP384R1FieldElement9 }; return(new SecP384R1Point(curve, secP384R1FieldElement7, secP384R1FieldElement8, zs, base.IsCompressed)); }
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; SecP521R1FieldElement X1 = (SecP521R1FieldElement)this.RawXCoord, Y1 = (SecP521R1FieldElement)this.RawYCoord; SecP521R1FieldElement X2 = (SecP521R1FieldElement)b.RawXCoord, Y2 = (SecP521R1FieldElement)b.RawYCoord; SecP521R1FieldElement Z1 = (SecP521R1FieldElement)this.RawZCoords[0]; SecP521R1FieldElement Z2 = (SecP521R1FieldElement)b.RawZCoords[0]; uint[] t1 = Nat.Create(17); uint[] t2 = Nat.Create(17); uint[] t3 = Nat.Create(17); uint[] t4 = Nat.Create(17); bool Z1IsOne = Z1.IsOne; uint[] 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); } bool Z2IsOne = Z2.IsOne; uint[] 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); } uint[] H = Nat.Create(17); SecP521R1Field.Subtract(U1, U2, H); uint[] 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.Infinity); } uint[] HSquared = t3; SecP521R1Field.Square(H, HSquared); uint[] G = Nat.Create(17); SecP521R1Field.Multiply(HSquared, H, G); uint[] 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)); }
public static void Invert(uint[] p, uint[] x, uint[] z) { int num = p.Length; if (Nat.IsZero(num, x)) { throw new ArgumentException("cannot be 0", "x"); } if (Nat.IsOne(num, x)) { Array.Copy(x, 0, z, 0, num); return; } uint[] array = Nat.Copy(num, x); uint[] array2 = Nat.Create(num); array2[0] = 1u; int xc = 0; if ((array[0] & 1) == 0) { InversionStep(p, array, num, array2, ref xc); } if (Nat.IsOne(num, array)) { InversionResult(p, xc, array2, z); return; } uint[] array3 = Nat.Copy(num, p); uint[] array4 = Nat.Create(num); int xc2 = 0; int num2 = num; while (true) { if (array[num2 - 1] == 0 && array3[num2 - 1] == 0) { num2--; } else if (Nat.Gte(num, array, array3)) { Nat.SubFrom(num, array3, array); xc += Nat.SubFrom(num, array4, array2) - xc2; InversionStep(p, array, num2, array2, ref xc); if (Nat.IsOne(num, array)) { InversionResult(p, xc, array2, z); return; } } else { Nat.SubFrom(num, array, array3); xc2 += Nat.SubFrom(num, array2, array4) - xc; InversionStep(p, array3, num2, array4, ref xc2); if (Nat.IsOne(num, array3)) { break; } } } InversionResult(p, xc2, array4, z); }