/**
* 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 - 2^222 - 2^94 + 2^62
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 31 1s } { 1 0s } { 128 1s } { 31 0s } { 1 1s } { 62 0s}
*
* We use an addition chain for the beginning: [1], 2, 3, 6, 12, [24], 30, [31]
*/
uint[] x1 = this.x;
if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat256.Create();
SM2P256V1Field.Square(x1, x2);
SM2P256V1Field.Multiply(x2, x1, x2);
uint[] x4 = Nat256.Create();
SM2P256V1Field.SquareN(x2, 2, x4);
SM2P256V1Field.Multiply(x4, x2, x4);
uint[] x6 = Nat256.Create();
SM2P256V1Field.SquareN(x4, 2, x6);
SM2P256V1Field.Multiply(x6, x2, x6);
uint[] x12 = x2;
SM2P256V1Field.SquareN(x6, 6, x12);
SM2P256V1Field.Multiply(x12, x6, x12);
uint[] x24 = Nat256.Create();
SM2P256V1Field.SquareN(x12, 12, x24);
SM2P256V1Field.Multiply(x24, x12, x24);
uint[] x30 = x12;
SM2P256V1Field.SquareN(x24, 6, x30);
SM2P256V1Field.Multiply(x30, x6, x30);
uint[] x31 = x6;
SM2P256V1Field.Square(x30, x31);
SM2P256V1Field.Multiply(x31, x1, x31);
uint[] t1 = x24;
SM2P256V1Field.SquareN(x31, 31, t1);
uint[] x62 = x30;
SM2P256V1Field.Multiply(t1, x31, x62);
SM2P256V1Field.SquareN(t1, 32, t1);
SM2P256V1Field.Multiply(t1, x62, t1);
SM2P256V1Field.SquareN(t1, 62, t1);
SM2P256V1Field.Multiply(t1, x62, t1);
SM2P256V1Field.SquareN(t1, 4, t1);
SM2P256V1Field.Multiply(t1, x4, t1);
SM2P256V1Field.SquareN(t1, 32, t1);
SM2P256V1Field.Multiply(t1, x1, t1);
SM2P256V1Field.SquareN(t1, 62, t1);
uint[] t2 = x4;
SM2P256V1Field.Square(t1, t2);
return(Nat256.Eq(x1, t2) ? new SM2P256V1FieldElement(t1) : null);
}
public override ECFieldElement Divide(ECFieldElement b)
{
//return Multiply(b.Invert());
uint[] z = Nat256.Create();
Mod.Invert(SM2P256V1Field.P, ((SM2P256V1FieldElement)b).x, z);
SM2P256V1Field.Multiply(z, x, z);
return(new SM2P256V1FieldElement(z));
}
public SM2P256V1FieldElement(BigInteger x)
{
if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
{
throw new ArgumentException("value invalid for SM2P256V1FieldElement", "x");
}
this.x = SM2P256V1Field.FromBigInteger(x);
}
public override ECFieldElement Multiply(ECFieldElement b)
{
uint[] z = Nat256.Create();
SM2P256V1Field.Multiply(x, ((SM2P256V1FieldElement)b).x, z);
return(new SM2P256V1FieldElement(z));
}
public override ECFieldElement Subtract(ECFieldElement b)
{
uint[] z = Nat256.Create();
SM2P256V1Field.Subtract(x, ((SM2P256V1FieldElement)b).x, z);
return(new SM2P256V1FieldElement(z));
}
public override ECFieldElement AddOne()
{
uint[] z = Nat256.Create();
SM2P256V1Field.AddOne(x, z);
return(new SM2P256V1FieldElement(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;
SM2P256V1FieldElement X1 = (SM2P256V1FieldElement)this.RawXCoord, Y1 = (SM2P256V1FieldElement)this.RawYCoord;
SM2P256V1FieldElement X2 = (SM2P256V1FieldElement)b.RawXCoord, Y2 = (SM2P256V1FieldElement)b.RawYCoord;
SM2P256V1FieldElement Z1 = (SM2P256V1FieldElement)this.RawZCoords[0];
SM2P256V1FieldElement Z2 = (SM2P256V1FieldElement)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;
SM2P256V1Field.Square(Z1.x, S2);
U2 = t2;
SM2P256V1Field.Multiply(S2, X2.x, U2);
SM2P256V1Field.Multiply(S2, Z1.x, S2);
SM2P256V1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SM2P256V1Field.Square(Z2.x, S1);
U1 = tt1;
SM2P256V1Field.Multiply(S1, X1.x, U1);
SM2P256V1Field.Multiply(S1, Z2.x, S1);
SM2P256V1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat256.Create();
SM2P256V1Field.Subtract(U1, U2, H);
uint[] R = t2;
SM2P256V1Field.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;
SM2P256V1Field.Square(H, HSquared);
uint[] G = Nat256.Create();
SM2P256V1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SM2P256V1Field.Multiply(HSquared, U1, V);
SM2P256V1Field.Negate(G, G);
Nat256.Mul(S1, G, tt1);
c = Nat256.AddBothTo(V, V, G);
SM2P256V1Field.Reduce32(c, G);
SM2P256V1FieldElement X3 = new SM2P256V1FieldElement(t4);
SM2P256V1Field.Square(R, X3.x);
SM2P256V1Field.Subtract(X3.x, G, X3.x);
SM2P256V1FieldElement Y3 = new SM2P256V1FieldElement(G);
SM2P256V1Field.Subtract(V, X3.x, Y3.x);
SM2P256V1Field.MultiplyAddToExt(Y3.x, R, tt1);
SM2P256V1Field.Reduce(tt1, Y3.x);
SM2P256V1FieldElement Z3 = new SM2P256V1FieldElement(H);
if (!Z1IsOne)
{
SM2P256V1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SM2P256V1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return(new SM2P256V1Point(curve, X3, Y3, zs, IsCompressed));
}
public override ECPoint Twice()
{
if (this.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
SM2P256V1FieldElement Y1 = (SM2P256V1FieldElement)this.RawYCoord;
if (Y1.IsZero)
{
return(curve.Infinity);
}
SM2P256V1FieldElement X1 = (SM2P256V1FieldElement)this.RawXCoord, Z1 = (SM2P256V1FieldElement)this.RawZCoords[0];
uint c;
uint[] t1 = Nat256.Create();
uint[] t2 = Nat256.Create();
uint[] Y1Squared = Nat256.Create();
SM2P256V1Field.Square(Y1.x, Y1Squared);
uint[] T = Nat256.Create();
SM2P256V1Field.Square(Y1Squared, T);
bool Z1IsOne = Z1.IsOne;
uint[] Z1Squared = Z1.x;
if (!Z1IsOne)
{
Z1Squared = t2;
SM2P256V1Field.Square(Z1.x, Z1Squared);
}
SM2P256V1Field.Subtract(X1.x, Z1Squared, t1);
uint[] M = t2;
SM2P256V1Field.Add(X1.x, Z1Squared, M);
SM2P256V1Field.Multiply(M, t1, M);
c = Nat256.AddBothTo(M, M, M);
SM2P256V1Field.Reduce32(c, M);
uint[] S = Y1Squared;
SM2P256V1Field.Multiply(Y1Squared, X1.x, S);
c = Nat.ShiftUpBits(8, S, 2, 0);
SM2P256V1Field.Reduce32(c, S);
c = Nat.ShiftUpBits(8, T, 3, 0, t1);
SM2P256V1Field.Reduce32(c, t1);
SM2P256V1FieldElement X3 = new SM2P256V1FieldElement(T);
SM2P256V1Field.Square(M, X3.x);
SM2P256V1Field.Subtract(X3.x, S, X3.x);
SM2P256V1Field.Subtract(X3.x, S, X3.x);
SM2P256V1FieldElement Y3 = new SM2P256V1FieldElement(S);
SM2P256V1Field.Subtract(S, X3.x, Y3.x);
SM2P256V1Field.Multiply(Y3.x, M, Y3.x);
SM2P256V1Field.Subtract(Y3.x, t1, Y3.x);
SM2P256V1FieldElement Z3 = new SM2P256V1FieldElement(M);
SM2P256V1Field.Twice(Y1.x, Z3.x);
if (!Z1IsOne)
{
SM2P256V1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
return(new SM2P256V1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed));
}