public override ECFieldElement Subtract(ECFieldElement b)
{
uint[] z = Nat256.Create();
SecP256R1Field.Subtract(x, ((SecP256R1FieldElement)b).x, z);
return(new SecP256R1FieldElement(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;
SecP256K1FieldElement secP256K1FieldElement = (SecP256K1FieldElement)base.RawXCoord;
SecP256K1FieldElement secP256K1FieldElement2 = (SecP256K1FieldElement)base.RawYCoord;
SecP256K1FieldElement secP256K1FieldElement3 = (SecP256K1FieldElement)b.RawXCoord;
SecP256K1FieldElement secP256K1FieldElement4 = (SecP256K1FieldElement)b.RawYCoord;
SecP256K1FieldElement secP256K1FieldElement5 = (SecP256K1FieldElement)base.RawZCoords[0];
SecP256K1FieldElement secP256K1FieldElement6 = (SecP256K1FieldElement)b.RawZCoords[0];
uint[] array = Nat256.CreateExt();
uint[] array2 = Nat256.Create();
uint[] array3 = Nat256.Create();
uint[] array4 = Nat256.Create();
bool isOne = secP256K1FieldElement5.IsOne;
uint[] array5;
uint[] array6;
if (isOne)
{
array5 = secP256K1FieldElement3.x;
array6 = secP256K1FieldElement4.x;
}
else
{
array6 = array3;
SecP256K1Field.Square(secP256K1FieldElement5.x, array6);
array5 = array2;
SecP256K1Field.Multiply(array6, secP256K1FieldElement3.x, array5);
SecP256K1Field.Multiply(array6, secP256K1FieldElement5.x, array6);
SecP256K1Field.Multiply(array6, secP256K1FieldElement4.x, array6);
}
bool isOne2 = secP256K1FieldElement6.IsOne;
uint[] array7;
uint[] array8;
if (isOne2)
{
array7 = secP256K1FieldElement.x;
array8 = secP256K1FieldElement2.x;
}
else
{
array8 = array4;
SecP256K1Field.Square(secP256K1FieldElement6.x, array8);
array7 = array;
SecP256K1Field.Multiply(array8, secP256K1FieldElement.x, array7);
SecP256K1Field.Multiply(array8, secP256K1FieldElement6.x, array8);
SecP256K1Field.Multiply(array8, secP256K1FieldElement2.x, array8);
}
uint[] array9 = Nat256.Create();
SecP256K1Field.Subtract(array7, array5, array9);
uint[] array10 = array2;
SecP256K1Field.Subtract(array8, array6, array10);
if (Nat256.IsZero(array9))
{
if (Nat256.IsZero(array10))
{
return(Twice());
}
return(curve.Infinity);
}
uint[] array11 = array3;
SecP256K1Field.Square(array9, array11);
uint[] array12 = Nat256.Create();
SecP256K1Field.Multiply(array11, array9, array12);
uint[] array13 = array3;
SecP256K1Field.Multiply(array11, array7, array13);
SecP256K1Field.Negate(array12, array12);
Nat256.Mul(array8, array12, array);
uint x = Nat256.AddBothTo(array13, array13, array12);
SecP256K1Field.Reduce32(x, array12);
SecP256K1FieldElement secP256K1FieldElement7 = new SecP256K1FieldElement(array4);
SecP256K1Field.Square(array10, secP256K1FieldElement7.x);
SecP256K1Field.Subtract(secP256K1FieldElement7.x, array12, secP256K1FieldElement7.x);
SecP256K1FieldElement secP256K1FieldElement8 = new SecP256K1FieldElement(array12);
SecP256K1Field.Subtract(array13, secP256K1FieldElement7.x, secP256K1FieldElement8.x);
SecP256K1Field.MultiplyAddToExt(secP256K1FieldElement8.x, array10, array);
SecP256K1Field.Reduce(array, secP256K1FieldElement8.x);
SecP256K1FieldElement secP256K1FieldElement9 = new SecP256K1FieldElement(array9);
if (!isOne)
{
SecP256K1Field.Multiply(secP256K1FieldElement9.x, secP256K1FieldElement5.x, secP256K1FieldElement9.x);
}
if (!isOne2)
{
SecP256K1Field.Multiply(secP256K1FieldElement9.x, secP256K1FieldElement6.x, secP256K1FieldElement9.x);
}
ECFieldElement[] zs = new ECFieldElement[1] {
secP256K1FieldElement9
};
return(new SecP256K1Point(curve, secP256K1FieldElement7, secP256K1FieldElement8, zs, base.IsCompressed));
}
public SecP256R1FieldElement()
{
this.x = Nat256.Create();
}
public override ECFieldElement AddOne()
{
uint[] z = Nat256.Create();
SecP256R1Field.AddOne(x, z);
return(new SecP256R1FieldElement(z));
}
public override ECPoint Twice()
{
if (base.IsInfinity)
{
return(this);
}
ECCurve curve = Curve;
SecP256R1FieldElement secP256R1FieldElement = (SecP256R1FieldElement)base.RawYCoord;
if (secP256R1FieldElement.IsZero)
{
return(curve.Infinity);
}
SecP256R1FieldElement secP256R1FieldElement2 = (SecP256R1FieldElement)base.RawXCoord;
SecP256R1FieldElement secP256R1FieldElement3 = (SecP256R1FieldElement)base.RawZCoords[0];
uint[] array = Nat256.Create();
uint[] array2 = Nat256.Create();
uint[] array3 = Nat256.Create();
SecP256R1Field.Square(secP256R1FieldElement.x, array3);
uint[] array4 = Nat256.Create();
SecP256R1Field.Square(array3, array4);
bool isOne = secP256R1FieldElement3.IsOne;
uint[] array5 = secP256R1FieldElement3.x;
if (!isOne)
{
array5 = array2;
SecP256R1Field.Square(secP256R1FieldElement3.x, array5);
}
SecP256R1Field.Subtract(secP256R1FieldElement2.x, array5, array);
uint[] array6 = array2;
SecP256R1Field.Add(secP256R1FieldElement2.x, array5, array6);
SecP256R1Field.Multiply(array6, array, array6);
uint x = Nat256.AddBothTo(array6, array6, array6);
SecP256R1Field.Reduce32(x, array6);
uint[] array7 = array3;
SecP256R1Field.Multiply(array3, secP256R1FieldElement2.x, array7);
x = Nat.ShiftUpBits(8, array7, 2, 0u);
SecP256R1Field.Reduce32(x, array7);
x = Nat.ShiftUpBits(8, array4, 3, 0u, array);
SecP256R1Field.Reduce32(x, array);
SecP256R1FieldElement secP256R1FieldElement4 = new SecP256R1FieldElement(array4);
SecP256R1Field.Square(array6, secP256R1FieldElement4.x);
SecP256R1Field.Subtract(secP256R1FieldElement4.x, array7, secP256R1FieldElement4.x);
SecP256R1Field.Subtract(secP256R1FieldElement4.x, array7, secP256R1FieldElement4.x);
SecP256R1FieldElement secP256R1FieldElement5 = new SecP256R1FieldElement(array7);
SecP256R1Field.Subtract(array7, secP256R1FieldElement4.x, secP256R1FieldElement5.x);
SecP256R1Field.Multiply(secP256R1FieldElement5.x, array6, secP256R1FieldElement5.x);
SecP256R1Field.Subtract(secP256R1FieldElement5.x, array, secP256R1FieldElement5.x);
SecP256R1FieldElement secP256R1FieldElement6 = new SecP256R1FieldElement(array6);
SecP256R1Field.Twice(secP256R1FieldElement.x, secP256R1FieldElement6.x);
if (!isOne)
{
SecP256R1Field.Multiply(secP256R1FieldElement6.x, secP256R1FieldElement3.x, secP256R1FieldElement6.x);
}
return(new SecP256R1Point(curve, secP256R1FieldElement4, secP256R1FieldElement5, new ECFieldElement[1] {
secP256R1FieldElement6
}, base.IsCompressed));
}
public override ECFieldElement Multiply(ECFieldElement b)
{
uint[] z = Nat256.Create();
SecP256R1Field.Multiply(x, ((SecP256R1FieldElement)b).x, z);
return(new SecP256R1FieldElement(z));
}
/**
* 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);
}
public override ECFieldElement Add(ECFieldElement b)
{
uint[] z = Nat256.Create();
SecP256K1Field.Add(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;
SecP256R1FieldElement X1 = (SecP256R1FieldElement)this.RawXCoord, Y1 = (SecP256R1FieldElement)this.RawYCoord;
SecP256R1FieldElement X2 = (SecP256R1FieldElement)b.RawXCoord, Y2 = (SecP256R1FieldElement)b.RawYCoord;
SecP256R1FieldElement Z1 = (SecP256R1FieldElement)this.RawZCoords[0];
SecP256R1FieldElement Z2 = (SecP256R1FieldElement)b.RawZCoords[0];
uint[] tt1 = Nat256.CreateExt();
uint[] tt2 = Nat256.CreateExt();
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;
SecP256R1Field.Square(Z1.x, S2);
U2 = tt2;
SecP256R1Field.Multiply(S2, X2.x, U2);
SecP256R1Field.Multiply(S2, Z1.x, S2);
SecP256R1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP256R1Field.Square(Z2.x, S1);
U1 = tt1;
SecP256R1Field.Multiply(S1, X1.x, U1);
SecP256R1Field.Multiply(S1, Z2.x, S1);
SecP256R1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat256.Create();
SecP256R1Field.Subtract(U1, U2, H);
uint[] R = tt2;
SecP256R1Field.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;
SecP256R1Field.Square(H, HSquared);
uint[] G = Nat256.Create();
SecP256R1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP256R1Field.Multiply(HSquared, U1, V);
Nat256.Mul(S1, G, tt1);
SecP256R1FieldElement X3 = new SecP256R1FieldElement(t4);
SecP256R1Field.Square(R, X3.x);
SecP256R1Field.Add(X3.x, G, X3.x);
SecP256R1Field.Subtract(X3.x, V, X3.x);
SecP256R1Field.Subtract(X3.x, V, X3.x);
SecP256R1FieldElement Y3 = new SecP256R1FieldElement(G);
SecP256R1Field.Subtract(V, X3.x, Y3.x);
Nat256.Mul(Y3.x, R, tt2);
SecP256R1Field.SubtractExt(tt2, tt1, tt2);
SecP256R1Field.Reduce(tt2, Y3.x);
SecP256R1FieldElement Z3 = new SecP256R1FieldElement(H);
if (!Z1IsOne)
{
SecP256R1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP256R1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return(new SecP256R1Point(curve, X3, Y3, zs, IsCompressed));
}
public override ECFieldElement Square()
{
uint[] z = Nat256.Create();
SecP256K1Field.Square(x, z);
return(new SecP256K1FieldElement(z));
}
public override ECPoint Twice()
{
if (this.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
SecP256R1FieldElement Y1 = (SecP256R1FieldElement)this.RawYCoord;
if (Y1.IsZero)
{
return(curve.Infinity);
}
SecP256R1FieldElement X1 = (SecP256R1FieldElement)this.RawXCoord, Z1 = (SecP256R1FieldElement)this.RawZCoords[0];
uint[] t1 = Nat256.Create();
uint[] t2 = Nat256.Create();
uint[] Y1Squared = Nat256.Create();
SecP256R1Field.Square(Y1.x, Y1Squared);
uint[] T = Nat256.Create();
SecP256R1Field.Square(Y1Squared, T);
bool Z1IsOne = Z1.IsOne;
uint[] Z1Squared = Z1.x;
if (!Z1IsOne)
{
Z1Squared = t2;
SecP256R1Field.Square(Z1.x, Z1Squared);
}
SecP256R1Field.Subtract(X1.x, Z1Squared, t1);
uint[] M = t2;
SecP256R1Field.Add(X1.x, Z1Squared, M);
SecP256R1Field.Multiply(M, t1, M);
SecP256R1Field.Twice(M, t1);
SecP256R1Field.Add(M, t1, M);
uint[] S = Y1Squared;
SecP256R1Field.Multiply(Y1Squared, X1.x, S);
uint c = Nat.ShiftUpBits(8, S, 2, 0);
SecP256R1Field.Reduce32(c, S);
c = Nat.ShiftUpBits(8, T, 3, 0, t1);
SecP256R1Field.Reduce32(c, t1);
SecP256R1FieldElement X3 = new SecP256R1FieldElement(T);
SecP256R1Field.Square(M, X3.x);
SecP256R1Field.Subtract(X3.x, S, X3.x);
SecP256R1Field.Subtract(X3.x, S, X3.x);
SecP256R1FieldElement Y3 = new SecP256R1FieldElement(S);
SecP256R1Field.Subtract(S, X3.x, Y3.x);
SecP256R1Field.Multiply(Y3.x, M, Y3.x);
SecP256R1Field.Subtract(Y3.x, t1, Y3.x);
SecP256R1FieldElement Z3 = new SecP256R1FieldElement(M);
SecP256R1Field.Twice(Y1.x, Z3.x);
if (!Z1IsOne)
{
SecP256R1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
return(new SecP256R1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, 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;
SecP256K1FieldElement rawXCoord = (SecP256K1FieldElement)base.RawXCoord;
SecP256K1FieldElement rawYCoord = (SecP256K1FieldElement)base.RawYCoord;
SecP256K1FieldElement element3 = (SecP256K1FieldElement)b.RawXCoord;
SecP256K1FieldElement element4 = (SecP256K1FieldElement)b.RawYCoord;
SecP256K1FieldElement element5 = (SecP256K1FieldElement)base.RawZCoords[0];
SecP256K1FieldElement element6 = (SecP256K1FieldElement)b.RawZCoords[0];
uint[] zz = Nat256.CreateExt();
uint[] numArray2 = Nat256.Create();
uint[] numArray3 = Nat256.Create();
uint[] x = Nat256.Create();
bool isOne = element5.IsOne;
if (isOne)
{
numArray5 = element3.x;
numArray6 = element4.x;
}
else
{
numArray6 = numArray3;
SecP256K1Field.Square(element5.x, numArray6);
numArray5 = numArray2;
SecP256K1Field.Multiply(numArray6, element3.x, numArray5);
SecP256K1Field.Multiply(numArray6, element5.x, numArray6);
SecP256K1Field.Multiply(numArray6, element4.x, numArray6);
}
bool flag2 = element6.IsOne;
if (flag2)
{
numArray7 = rawXCoord.x;
numArray8 = rawYCoord.x;
}
else
{
numArray8 = x;
SecP256K1Field.Square(element6.x, numArray8);
numArray7 = zz;
SecP256K1Field.Multiply(numArray8, rawXCoord.x, numArray7);
SecP256K1Field.Multiply(numArray8, element6.x, numArray8);
SecP256K1Field.Multiply(numArray8, rawYCoord.x, numArray8);
}
uint[] z = Nat256.Create();
SecP256K1Field.Subtract(numArray7, numArray5, z);
uint[] numArray10 = numArray2;
SecP256K1Field.Subtract(numArray8, numArray6, numArray10);
if (Nat256.IsZero(z))
{
if (Nat256.IsZero(numArray10))
{
return(this.Twice());
}
return(curve.Infinity);
}
uint[] numArray11 = numArray3;
SecP256K1Field.Square(z, numArray11);
uint[] numArray12 = Nat256.Create();
SecP256K1Field.Multiply(numArray11, z, numArray12);
uint[] numArray13 = numArray3;
SecP256K1Field.Multiply(numArray11, numArray7, numArray13);
SecP256K1Field.Negate(numArray12, numArray12);
Nat256.Mul(numArray8, numArray12, zz);
SecP256K1Field.Reduce32(Nat256.AddBothTo(numArray13, numArray13, numArray12), numArray12);
SecP256K1FieldElement element7 = new SecP256K1FieldElement(x);
SecP256K1Field.Square(numArray10, element7.x);
SecP256K1Field.Subtract(element7.x, numArray12, element7.x);
SecP256K1FieldElement y = new SecP256K1FieldElement(numArray12);
SecP256K1Field.Subtract(numArray13, element7.x, y.x);
SecP256K1Field.MultiplyAddToExt(y.x, numArray10, zz);
SecP256K1Field.Reduce(zz, y.x);
SecP256K1FieldElement element9 = new SecP256K1FieldElement(z);
if (!isOne)
{
SecP256K1Field.Multiply(element9.x, element5.x, element9.x);
}
if (!flag2)
{
SecP256K1Field.Multiply(element9.x, element6.x, element9.x);
}
ECFieldElement[] zs = new ECFieldElement[] { element9 };
return(new SecP256K1Point(curve, element7, y, zs, base.IsCompressed));
}
public static void Inv(uint[] x, uint[] z)
{
/*
* Raise this element to the exponent 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 3
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 223 1s } { 1 0s } { 22 1s } { 4 0s } { 1 1s } { 1 0s } { 2 1s } { 1 0s } { 1 1s }
*
* Therefore we need an addition chain containing 1, 2, 22, 223 (the lengths of the repunits)
* We use: [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
*/
if (0 != IsZero(x))
{
throw new ArgumentException("cannot be 0", "x");
}
uint[] x1 = x;
uint[] x2 = Nat256.Create();
Square(x1, x2);
Multiply(x2, x1, x2);
uint[] x3 = Nat256.Create();
Square(x2, x3);
Multiply(x3, x1, x3);
uint[] x6 = Nat256.Create();
SquareN(x3, 3, x6);
Multiply(x6, x3, x6);
uint[] x9 = x6;
SquareN(x6, 3, x9);
Multiply(x9, x3, x9);
uint[] x11 = x9;
SquareN(x9, 2, x11);
Multiply(x11, x2, x11);
uint[] x22 = Nat256.Create();
SquareN(x11, 11, x22);
Multiply(x22, x11, x22);
uint[] x44 = x11;
SquareN(x22, 22, x44);
Multiply(x44, x22, x44);
uint[] x88 = Nat256.Create();
SquareN(x44, 44, x88);
Multiply(x88, x44, x88);
uint[] x176 = Nat256.Create();
SquareN(x88, 88, x176);
Multiply(x176, x88, x176);
uint[] x220 = x88;
SquareN(x176, 44, x220);
Multiply(x220, x44, x220);
uint[] x223 = x44;
SquareN(x220, 3, x223);
Multiply(x223, x3, x223);
uint[] t = x223;
SquareN(t, 23, t);
Multiply(t, x22, t);
SquareN(t, 5, t);
Multiply(t, x1, t);
SquareN(t, 3, t);
Multiply(t, x2, t);
SquareN(t, 2, t);
// NOTE that x1 and z could be the same array
Multiply(x1, t, z);
}
public override ECFieldElement Negate()
{
uint[] z = Nat256.Create();
SecP256R1Field.Negate(this.x, z);
return(new SecP256R1FieldElement(z));
}
public override ECFieldElement Invert()
{
uint[] z = Nat256.Create();
Mod.Invert(SecP256R1Field.P, this.x, z);
return(new SecP256R1FieldElement(z));
}
