public override ECFieldElement Multiply(ECFieldElement b)
{
ulong[] z = Nat192.Create64();
SecT131Field.Multiply(x, ((SecT131FieldElement)b).x, z);
return(new SecT131FieldElement(z));
}
public override ECFieldElement Add(ECFieldElement b)
{
ulong[] z = Nat192.Create64();
SecT163Field.Add(x, ((SecT163FieldElement)b).x, z);
return(new SecT163FieldElement(z));
}
public static void Multiply(uint[] x, uint[] y, uint[] z)
{
uint[] tt = Nat192.CreateExt();
Nat192.Mul(x, y, tt);
Reduce(tt, z);
}
public override BigInteger ToBigInteger()
{
return(Nat192.ToBigInteger64(x));
}
public override ECFieldElement Subtract(ECFieldElement b)
{
uint[] z = Nat192.Create();
SecP192K1Field.Subtract(x, ((SecP192K1FieldElement)b).x, z);
return(new SecP192K1FieldElement(z));
}
public static void Reduce(uint[] xx, uint[] z)
{
ulong xx06 = xx[6], xx07 = xx[7], xx08 = xx[8];
ulong xx09 = xx[9], xx10 = xx[10], xx11 = xx[11];
ulong t0 = xx06 + xx10;
ulong t1 = xx07 + xx11;
ulong cc = 0;
cc += (ulong)xx[0] + t0;
uint z0 = (uint)cc;
cc >>= 32;
cc += (ulong)xx[1] + t1;
z[1] = (uint)cc;
cc >>= 32;
t0 += xx08;
t1 += xx09;
cc += (ulong)xx[2] + t0;
ulong z2 = (uint)cc;
cc >>= 32;
cc += (ulong)xx[3] + t1;
z[3] = (uint)cc;
cc >>= 32;
t0 -= xx06;
t1 -= xx07;
cc += (ulong)xx[4] + t0;
z[4] = (uint)cc;
cc >>= 32;
cc += (ulong)xx[5] + t1;
z[5] = (uint)cc;
cc >>= 32;
z2 += cc;
cc += z0;
z[0] = (uint)cc;
cc >>= 32;
if (cc != 0)
{
cc += z[1];
z[1] = (uint)cc;
z2 += cc >> 32;
}
z[2] = (uint)z2;
cc = z2 >> 32;
Debug.Assert(cc == 0 || cc == 1);
if ((cc != 0 && Nat.IncAt(6, z, 3) != 0) ||
(z[5] == P5 && Nat192.Gte(z, P)))
{
AddPInvTo(z);
}
}
public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
{
ulong[] tt = Nat192.CreateExt64();
ImplMultiply(x, y, tt);
Reduce(tt, z);
}
public override bool TestBitZero()
{
return(Nat192.GetBit(x, 0) == 1);
}
public static void SquareAddToExt(ulong[] x, ulong[] zz)
{
ulong[] tt = Nat192.CreateExt64();
ImplSquare(x, tt);
AddExt(zz, tt, zz);
}
public static ulong[] FromBigInteger(BigInteger x)
{
ulong[] z = Nat192.FromBigInteger64(x);
Reduce29(z, 0);
return(z);
}
public static void Square(ulong[] x, ulong[] z)
{
ulong[] tt = Nat192.CreateExt64();
ImplSquare(x, tt);
Reduce(tt, z);
}
public override ECPoint Twice()
{
if (base.IsInfinity)
{
return(this);
}
ECCurve curve = Curve;
SecP192R1FieldElement secP192R1FieldElement = (SecP192R1FieldElement)base.RawYCoord;
if (secP192R1FieldElement.IsZero)
{
return(curve.Infinity);
}
SecP192R1FieldElement secP192R1FieldElement2 = (SecP192R1FieldElement)base.RawXCoord;
SecP192R1FieldElement secP192R1FieldElement3 = (SecP192R1FieldElement)base.RawZCoords[0];
uint[] array = Nat192.Create();
uint[] array2 = Nat192.Create();
uint[] array3 = Nat192.Create();
SecP192R1Field.Square(secP192R1FieldElement.x, array3);
uint[] array4 = Nat192.Create();
SecP192R1Field.Square(array3, array4);
bool isOne = secP192R1FieldElement3.IsOne;
uint[] array5 = secP192R1FieldElement3.x;
if (!isOne)
{
array5 = array2;
SecP192R1Field.Square(secP192R1FieldElement3.x, array5);
}
SecP192R1Field.Subtract(secP192R1FieldElement2.x, array5, array);
uint[] array6 = array2;
SecP192R1Field.Add(secP192R1FieldElement2.x, array5, array6);
SecP192R1Field.Multiply(array6, array, array6);
uint x = Nat192.AddBothTo(array6, array6, array6);
SecP192R1Field.Reduce32(x, array6);
uint[] array7 = array3;
SecP192R1Field.Multiply(array3, secP192R1FieldElement2.x, array7);
x = Nat.ShiftUpBits(6, array7, 2, 0u);
SecP192R1Field.Reduce32(x, array7);
x = Nat.ShiftUpBits(6, array4, 3, 0u, array);
SecP192R1Field.Reduce32(x, array);
SecP192R1FieldElement secP192R1FieldElement4 = new SecP192R1FieldElement(array4);
SecP192R1Field.Square(array6, secP192R1FieldElement4.x);
SecP192R1Field.Subtract(secP192R1FieldElement4.x, array7, secP192R1FieldElement4.x);
SecP192R1Field.Subtract(secP192R1FieldElement4.x, array7, secP192R1FieldElement4.x);
SecP192R1FieldElement secP192R1FieldElement5 = new SecP192R1FieldElement(array7);
SecP192R1Field.Subtract(array7, secP192R1FieldElement4.x, secP192R1FieldElement5.x);
SecP192R1Field.Multiply(secP192R1FieldElement5.x, array6, secP192R1FieldElement5.x);
SecP192R1Field.Subtract(secP192R1FieldElement5.x, array, secP192R1FieldElement5.x);
SecP192R1FieldElement secP192R1FieldElement6 = new SecP192R1FieldElement(array6);
SecP192R1Field.Twice(secP192R1FieldElement.x, secP192R1FieldElement6.x);
if (!isOne)
{
SecP192R1Field.Multiply(secP192R1FieldElement6.x, secP192R1FieldElement3.x, secP192R1FieldElement6.x);
}
return(new SecP192R1Point(curve, secP192R1FieldElement4, secP192R1FieldElement5, new ECFieldElement[1]
{
secP192R1FieldElement6
}, base.IsCompressed));
}
public static void Reduce32(uint x, uint[] z)
{
if ((x != 0 && Nat192.Mul33WordAdd(4553u, x, z, 0) != 0) || (z[5] == uint.MaxValue && Nat192.Gte(z, P)))
{
Nat.Add33To(6, 4553u, 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 2^190 - 2^30 - 2^10 - 2^6 - 2^5 - 2^4 - 2^1
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 159 1s } { 1 0s } { 19 1s } { 1 0s } { 3 1s } { 3 0s} { 3 1s } { 1 0s }
*
* Therefore we need an addition chain containing 3, 19, 159 (the lengths of the repunits)
* We use: 1, 2, [3], 6, 8, 16, [19], 35, 70, 140, [159]
*/
uint[] x1 = this.x;
if (Nat192.IsZero(x1) || Nat192.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat192.Create();
SecP192K1Field.Square(x1, x2);
SecP192K1Field.Multiply(x2, x1, x2);
uint[] x3 = Nat192.Create();
SecP192K1Field.Square(x2, x3);
SecP192K1Field.Multiply(x3, x1, x3);
uint[] x6 = Nat192.Create();
SecP192K1Field.SquareN(x3, 3, x6);
SecP192K1Field.Multiply(x6, x3, x6);
uint[] x8 = x6;
SecP192K1Field.SquareN(x6, 2, x8);
SecP192K1Field.Multiply(x8, x2, x8);
uint[] x16 = x2;
SecP192K1Field.SquareN(x8, 8, x16);
SecP192K1Field.Multiply(x16, x8, x16);
uint[] x19 = x8;
SecP192K1Field.SquareN(x16, 3, x19);
SecP192K1Field.Multiply(x19, x3, x19);
uint[] x35 = Nat192.Create();
SecP192K1Field.SquareN(x19, 16, x35);
SecP192K1Field.Multiply(x35, x16, x35);
uint[] x70 = x16;
SecP192K1Field.SquareN(x35, 35, x70);
SecP192K1Field.Multiply(x70, x35, x70);
uint[] x140 = x35;
SecP192K1Field.SquareN(x70, 70, x140);
SecP192K1Field.Multiply(x140, x70, x140);
uint[] x159 = x70;
SecP192K1Field.SquareN(x140, 19, x159);
SecP192K1Field.Multiply(x159, x19, x159);
uint[] t1 = x159;
SecP192K1Field.SquareN(t1, 20, t1);
SecP192K1Field.Multiply(t1, x19, t1);
SecP192K1Field.SquareN(t1, 4, t1);
SecP192K1Field.Multiply(t1, x3, t1);
SecP192K1Field.SquareN(t1, 6, t1);
SecP192K1Field.Multiply(t1, x3, t1);
SecP192K1Field.Square(t1, t1);
uint[] t2 = x3;
SecP192K1Field.Square(t1, t2);
return(Nat192.Eq(x1, t2) ? new SecP192K1FieldElement(t1) : null);
}
public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
{
ulong[] tt = Nat192.CreateExt64();
ImplMultiply(x, y, tt);
AddExt(zz, tt, zz);
}
public SecP192K1FieldElement()
{
this.x = Nat192.Create();
}
public override ECFieldElement Square()
{
uint[] z = Nat192.Create();
SecP192R1Field.Square(x, z);
return(new SecP192R1FieldElement(z));
}
public override ECFieldElement AddOne()
{
uint[] z = Nat192.Create();
SecP192K1Field.AddOne(x, z);
return(new SecP192K1FieldElement(z));
}
public override ECFieldElement Add(ECFieldElement b)
{
uint[] z = Nat192.Create();
SecP192R1Field.Add(x, ((SecP192R1FieldElement)b).x, z);
return(new SecP192R1FieldElement(z));
}
public override ECFieldElement Multiply(ECFieldElement b)
{
uint[] z = Nat192.Create();
SecP192K1Field.Multiply(x, ((SecP192K1FieldElement)b).x, z);
return(new SecP192K1FieldElement(z));
}
public static void Square(uint[] x, uint[] z)
{
uint[] array = Nat192.CreateExt();
Nat192.Square(x, array);
Reduce(array, z);
}
public static void Square(uint[] x, uint[] z)
{
uint[] tt = Nat192.CreateExt();
Nat192.Square(x, tt);
Reduce(tt, z);
}
public static void Multiply(uint[] x, uint[] y, uint[] z)
{
uint[] array = Nat192.CreateExt();
Nat192.Mul(x, y, array);
Reduce(array, z);
}
public SecT131FieldElement()
{
this.x = Nat192.Create64();
}
public override ECPoint Twice()
{
if (this.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
SecP192K1FieldElement Y1 = (SecP192K1FieldElement)this.RawYCoord;
if (Y1.IsZero)
{
return(curve.Infinity);
}
SecP192K1FieldElement X1 = (SecP192K1FieldElement)this.RawXCoord, Z1 = (SecP192K1FieldElement)this.RawZCoords[0];
uint c;
uint[] Y1Squared = Nat192.Create();
SecP192K1Field.Square(Y1.x, Y1Squared);
uint[] T = Nat192.Create();
SecP192K1Field.Square(Y1Squared, T);
uint[] M = Nat192.Create();
SecP192K1Field.Square(X1.x, M);
c = Nat192.AddBothTo(M, M, M);
SecP192K1Field.Reduce32(c, M);
uint[] S = Y1Squared;
SecP192K1Field.Multiply(Y1Squared, X1.x, S);
c = Nat.ShiftUpBits(6, S, 2, 0);
SecP192K1Field.Reduce32(c, S);
uint[] t1 = Nat192.Create();
c = Nat.ShiftUpBits(6, T, 3, 0, t1);
SecP192K1Field.Reduce32(c, t1);
SecP192K1FieldElement X3 = new SecP192K1FieldElement(T);
SecP192K1Field.Square(M, X3.x);
SecP192K1Field.Subtract(X3.x, S, X3.x);
SecP192K1Field.Subtract(X3.x, S, X3.x);
SecP192K1FieldElement Y3 = new SecP192K1FieldElement(S);
SecP192K1Field.Subtract(S, X3.x, Y3.x);
SecP192K1Field.Multiply(Y3.x, M, Y3.x);
SecP192K1Field.Subtract(Y3.x, t1, Y3.x);
SecP192K1FieldElement Z3 = new SecP192K1FieldElement(M);
SecP192K1Field.Twice(Y1.x, Z3.x);
if (!Z1.IsOne)
{
SecP192K1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
return(new SecP192K1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed));
}
public override ECFieldElement AddOne()
{
ulong[] z = Nat192.Create64();
SecT131Field.AddOne(x, z);
return(new SecT131FieldElement(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;
SecP192K1FieldElement X1 = (SecP192K1FieldElement)this.RawXCoord, Y1 = (SecP192K1FieldElement)this.RawYCoord;
SecP192K1FieldElement X2 = (SecP192K1FieldElement)b.RawXCoord, Y2 = (SecP192K1FieldElement)b.RawYCoord;
SecP192K1FieldElement Z1 = (SecP192K1FieldElement)this.RawZCoords[0];
SecP192K1FieldElement Z2 = (SecP192K1FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat192.CreateExt();
uint[] t2 = Nat192.Create();
uint[] t3 = Nat192.Create();
uint[] t4 = Nat192.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
SecP192K1Field.Square(Z1.x, S2);
U2 = t2;
SecP192K1Field.Multiply(S2, X2.x, U2);
SecP192K1Field.Multiply(S2, Z1.x, S2);
SecP192K1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP192K1Field.Square(Z2.x, S1);
U1 = tt1;
SecP192K1Field.Multiply(S1, X1.x, U1);
SecP192K1Field.Multiply(S1, Z2.x, S1);
SecP192K1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat192.Create();
SecP192K1Field.Subtract(U1, U2, H);
uint[] R = t2;
SecP192K1Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat192.IsZero(H))
{
if (Nat192.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;
SecP192K1Field.Square(H, HSquared);
uint[] G = Nat192.Create();
SecP192K1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP192K1Field.Multiply(HSquared, U1, V);
SecP192K1Field.Negate(G, G);
Nat192.Mul(S1, G, tt1);
c = Nat192.AddBothTo(V, V, G);
SecP192K1Field.Reduce32(c, G);
SecP192K1FieldElement X3 = new SecP192K1FieldElement(t4);
SecP192K1Field.Square(R, X3.x);
SecP192K1Field.Subtract(X3.x, G, X3.x);
SecP192K1FieldElement Y3 = new SecP192K1FieldElement(G);
SecP192K1Field.Subtract(V, X3.x, Y3.x);
SecP192K1Field.MultiplyAddToExt(Y3.x, R, tt1);
SecP192K1Field.Reduce(tt1, Y3.x);
SecP192K1FieldElement Z3 = new SecP192K1FieldElement(H);
if (!Z1IsOne)
{
SecP192K1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP192K1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return(new SecP192K1Point(curve, X3, Y3, zs, 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;
SecP192K1FieldElement secP192K1FieldElement = (SecP192K1FieldElement)base.RawXCoord;
SecP192K1FieldElement secP192K1FieldElement2 = (SecP192K1FieldElement)base.RawYCoord;
SecP192K1FieldElement secP192K1FieldElement3 = (SecP192K1FieldElement)b.RawXCoord;
SecP192K1FieldElement secP192K1FieldElement4 = (SecP192K1FieldElement)b.RawYCoord;
SecP192K1FieldElement secP192K1FieldElement5 = (SecP192K1FieldElement)base.RawZCoords[0];
SecP192K1FieldElement secP192K1FieldElement6 = (SecP192K1FieldElement)b.RawZCoords[0];
uint[] array = Nat192.CreateExt();
uint[] array2 = Nat192.Create();
uint[] array3 = Nat192.Create();
uint[] array4 = Nat192.Create();
bool isOne = secP192K1FieldElement5.IsOne;
uint[] array5;
uint[] array6;
if (isOne)
{
array5 = secP192K1FieldElement3.x;
array6 = secP192K1FieldElement4.x;
}
else
{
array6 = array3;
SecP192K1Field.Square(secP192K1FieldElement5.x, array6);
array5 = array2;
SecP192K1Field.Multiply(array6, secP192K1FieldElement3.x, array5);
SecP192K1Field.Multiply(array6, secP192K1FieldElement5.x, array6);
SecP192K1Field.Multiply(array6, secP192K1FieldElement4.x, array6);
}
bool isOne2 = secP192K1FieldElement6.IsOne;
uint[] array7;
uint[] array8;
if (isOne2)
{
array7 = secP192K1FieldElement.x;
array8 = secP192K1FieldElement2.x;
}
else
{
array8 = array4;
SecP192K1Field.Square(secP192K1FieldElement6.x, array8);
array7 = array;
SecP192K1Field.Multiply(array8, secP192K1FieldElement.x, array7);
SecP192K1Field.Multiply(array8, secP192K1FieldElement6.x, array8);
SecP192K1Field.Multiply(array8, secP192K1FieldElement2.x, array8);
}
uint[] array9 = Nat192.Create();
SecP192K1Field.Subtract(array7, array5, array9);
uint[] array10 = array2;
SecP192K1Field.Subtract(array8, array6, array10);
if (Nat192.IsZero(array9))
{
if (Nat192.IsZero(array10))
{
return(Twice());
}
return(curve.Infinity);
}
uint[] array11 = array3;
SecP192K1Field.Square(array9, array11);
uint[] array12 = Nat192.Create();
SecP192K1Field.Multiply(array11, array9, array12);
uint[] array13 = array3;
SecP192K1Field.Multiply(array11, array7, array13);
SecP192K1Field.Negate(array12, array12);
Nat192.Mul(array8, array12, array);
uint x = Nat192.AddBothTo(array13, array13, array12);
SecP192K1Field.Reduce32(x, array12);
SecP192K1FieldElement secP192K1FieldElement7 = new SecP192K1FieldElement(array4);
SecP192K1Field.Square(array10, secP192K1FieldElement7.x);
SecP192K1Field.Subtract(secP192K1FieldElement7.x, array12, secP192K1FieldElement7.x);
SecP192K1FieldElement secP192K1FieldElement8 = new SecP192K1FieldElement(array12);
SecP192K1Field.Subtract(array13, secP192K1FieldElement7.x, secP192K1FieldElement8.x);
SecP192K1Field.MultiplyAddToExt(secP192K1FieldElement8.x, array10, array);
SecP192K1Field.Reduce(array, secP192K1FieldElement8.x);
SecP192K1FieldElement secP192K1FieldElement9 = new SecP192K1FieldElement(array9);
if (!isOne)
{
SecP192K1Field.Multiply(secP192K1FieldElement9.x, secP192K1FieldElement5.x, secP192K1FieldElement9.x);
}
if (!isOne2)
{
SecP192K1Field.Multiply(secP192K1FieldElement9.x, secP192K1FieldElement6.x, secP192K1FieldElement9.x);
}
ECFieldElement[] zs = new ECFieldElement[1]
{
secP192K1FieldElement9
};
return(new SecP192K1Point(curve, secP192K1FieldElement7, secP192K1FieldElement8, zs, base.IsCompressed));
}
public override ECFieldElement Sqrt()
{
ulong[] z = Nat192.Create64();
SecT163Field.Sqrt(x, z);
return(new SecT163FieldElement(z));
}
