public override BigInteger ToBigInteger()
{
return(Nat224.ToBigInteger(x));
}
public SecP224R1FieldElement()
{
this.x = Nat224.Create();
}
public override bool TestBitZero()
{
return(Nat224.GetBit(x, 0) == 1);
}
public static void Square(uint[] x, uint[] z)
{
uint[] tt = Nat224.CreateExt();
Nat224.Square(x, tt);
Reduce(tt, z);
}
public static void Multiply(uint[] x, uint[] y, uint[] z)
{
uint[] tt = Nat224.CreateExt();
Nat224.Mul(x, y, tt);
Reduce(tt, z);
}
public override ECFieldElement Multiply(ECFieldElement b)
{
uint[] z = Nat224.Create();
SecP224R1Field.Multiply(x, ((SecP224R1FieldElement)b).x, z);
return(new SecP224R1FieldElement(z));
}
public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat224.IsZero(y) || Nat224.IsOne(y))
{
return(this);
}
uint[] array = Nat224.Create();
SecP224K1Field.Square(y, array);
SecP224K1Field.Multiply(array, y, array);
uint[] array2 = array;
SecP224K1Field.Square(array, array2);
SecP224K1Field.Multiply(array2, y, array2);
uint[] array3 = Nat224.Create();
SecP224K1Field.Square(array2, array3);
SecP224K1Field.Multiply(array3, y, array3);
uint[] array4 = Nat224.Create();
SecP224K1Field.SquareN(array3, 4, array4);
SecP224K1Field.Multiply(array4, array3, array4);
uint[] array5 = Nat224.Create();
SecP224K1Field.SquareN(array4, 3, array5);
SecP224K1Field.Multiply(array5, array2, array5);
uint[] array6 = array5;
SecP224K1Field.SquareN(array5, 8, array6);
SecP224K1Field.Multiply(array6, array4, array6);
uint[] array7 = array4;
SecP224K1Field.SquareN(array6, 4, array7);
SecP224K1Field.Multiply(array7, array3, array7);
uint[] array8 = array3;
SecP224K1Field.SquareN(array7, 19, array8);
SecP224K1Field.Multiply(array8, array6, array8);
uint[] array9 = Nat224.Create();
SecP224K1Field.SquareN(array8, 42, array9);
SecP224K1Field.Multiply(array9, array8, array9);
uint[] z = array8;
SecP224K1Field.SquareN(array9, 23, z);
SecP224K1Field.Multiply(z, array7, z);
uint[] array10 = array7;
SecP224K1Field.SquareN(z, 84, array10);
SecP224K1Field.Multiply(array10, array9, array10);
uint[] z2 = array10;
SecP224K1Field.SquareN(z2, 20, z2);
SecP224K1Field.Multiply(z2, array6, z2);
SecP224K1Field.SquareN(z2, 3, z2);
SecP224K1Field.Multiply(z2, y, z2);
SecP224K1Field.SquareN(z2, 2, z2);
SecP224K1Field.Multiply(z2, y, z2);
SecP224K1Field.SquareN(z2, 4, z2);
SecP224K1Field.Multiply(z2, array2, z2);
SecP224K1Field.Square(z2, z2);
uint[] array11 = array9;
SecP224K1Field.Square(z2, array11);
if (Nat224.Eq(y, array11))
{
return(new SecP224K1FieldElement(z2));
}
SecP224K1Field.Multiply(z2, PRECOMP_POW2, z2);
SecP224K1Field.Square(z2, array11);
if (Nat224.Eq(y, array11))
{
return(new SecP224K1FieldElement(z2));
}
return(null);
}
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;
SecP224R1FieldElement X1 = (SecP224R1FieldElement)this.RawXCoord, Y1 = (SecP224R1FieldElement)this.RawYCoord;
SecP224R1FieldElement X2 = (SecP224R1FieldElement)b.RawXCoord, Y2 = (SecP224R1FieldElement)b.RawYCoord;
SecP224R1FieldElement Z1 = (SecP224R1FieldElement)this.RawZCoords[0];
SecP224R1FieldElement Z2 = (SecP224R1FieldElement)b.RawZCoords[0];
uint c;
uint[] tt1 = Nat224.CreateExt();
uint[] t2 = Nat224.Create();
uint[] t3 = Nat224.Create();
uint[] t4 = Nat224.Create();
bool Z1IsOne = Z1.IsOne;
uint[] U2, S2;
if (Z1IsOne)
{
U2 = X2.x;
S2 = Y2.x;
}
else
{
S2 = t3;
SecP224R1Field.Square(Z1.x, S2);
U2 = t2;
SecP224R1Field.Multiply(S2, X2.x, U2);
SecP224R1Field.Multiply(S2, Z1.x, S2);
SecP224R1Field.Multiply(S2, Y2.x, S2);
}
bool Z2IsOne = Z2.IsOne;
uint[] U1, S1;
if (Z2IsOne)
{
U1 = X1.x;
S1 = Y1.x;
}
else
{
S1 = t4;
SecP224R1Field.Square(Z2.x, S1);
U1 = tt1;
SecP224R1Field.Multiply(S1, X1.x, U1);
SecP224R1Field.Multiply(S1, Z2.x, S1);
SecP224R1Field.Multiply(S1, Y1.x, S1);
}
uint[] H = Nat224.Create();
SecP224R1Field.Subtract(U1, U2, H);
uint[] R = t2;
SecP224R1Field.Subtract(S1, S2, R);
// Check if b == this or b == -this
if (Nat224.IsZero(H))
{
if (Nat224.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;
SecP224R1Field.Square(H, HSquared);
uint[] G = Nat224.Create();
SecP224R1Field.Multiply(HSquared, H, G);
uint[] V = t3;
SecP224R1Field.Multiply(HSquared, U1, V);
SecP224R1Field.Negate(G, G);
Nat224.Mul(S1, G, tt1);
c = Nat224.AddBothTo(V, V, G);
SecP224R1Field.Reduce32(c, G);
SecP224R1FieldElement X3 = new SecP224R1FieldElement(t4);
SecP224R1Field.Square(R, X3.x);
SecP224R1Field.Subtract(X3.x, G, X3.x);
SecP224R1FieldElement Y3 = new SecP224R1FieldElement(G);
SecP224R1Field.Subtract(V, X3.x, Y3.x);
SecP224R1Field.MultiplyAddToExt(Y3.x, R, tt1);
SecP224R1Field.Reduce(tt1, Y3.x);
SecP224R1FieldElement Z3 = new SecP224R1FieldElement(H);
if (!Z1IsOne)
{
SecP224R1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
if (!Z2IsOne)
{
SecP224R1Field.Multiply(Z3.x, Z2.x, Z3.x);
}
ECFieldElement[] zs = new ECFieldElement[] { Z3 };
return(new SecP224R1Point(curve, X3, Y3, zs, IsCompressed));
}
public override ECFieldElement Square()
{
uint[] z = Nat224.Create();
SecP224K1Field.Square(x, z);
return(new SecP224K1FieldElement(z));
}
public static void Square(uint[] x, uint[] z)
{
uint[] array = Nat224.CreateExt();
Nat224.Square(x, array);
Reduce(array, z);
}
public override ECPoint Twice()
{
if (this.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
SecP224R1FieldElement Y1 = (SecP224R1FieldElement)this.RawYCoord;
if (Y1.IsZero)
{
return(curve.Infinity);
}
SecP224R1FieldElement X1 = (SecP224R1FieldElement)this.RawXCoord, Z1 = (SecP224R1FieldElement)this.RawZCoords[0];
uint c;
uint[] t1 = Nat224.Create();
uint[] t2 = Nat224.Create();
uint[] Y1Squared = Nat224.Create();
SecP224R1Field.Square(Y1.x, Y1Squared);
uint[] T = Nat224.Create();
SecP224R1Field.Square(Y1Squared, T);
bool Z1IsOne = Z1.IsOne;
uint[] Z1Squared = Z1.x;
if (!Z1IsOne)
{
Z1Squared = t2;
SecP224R1Field.Square(Z1.x, Z1Squared);
}
SecP224R1Field.Subtract(X1.x, Z1Squared, t1);
uint[] M = t2;
SecP224R1Field.Add(X1.x, Z1Squared, M);
SecP224R1Field.Multiply(M, t1, M);
c = Nat224.AddBothTo(M, M, M);
SecP224R1Field.Reduce32(c, M);
uint[] S = Y1Squared;
SecP224R1Field.Multiply(Y1Squared, X1.x, S);
c = Nat.ShiftUpBits(7, S, 2, 0);
SecP224R1Field.Reduce32(c, S);
c = Nat.ShiftUpBits(7, T, 3, 0, t1);
SecP224R1Field.Reduce32(c, t1);
SecP224R1FieldElement X3 = new SecP224R1FieldElement(T);
SecP224R1Field.Square(M, X3.x);
SecP224R1Field.Subtract(X3.x, S, X3.x);
SecP224R1Field.Subtract(X3.x, S, X3.x);
SecP224R1FieldElement Y3 = new SecP224R1FieldElement(S);
SecP224R1Field.Subtract(S, X3.x, Y3.x);
SecP224R1Field.Multiply(Y3.x, M, Y3.x);
SecP224R1Field.Subtract(Y3.x, t1, Y3.x);
SecP224R1FieldElement Z3 = new SecP224R1FieldElement(M);
SecP224R1Field.Twice(Y1.x, Z3.x);
if (!Z1IsOne)
{
SecP224R1Field.Multiply(Z3.x, Z1.x, Z3.x);
}
return(new SecP224R1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed));
}
public static void Reduce32(uint x, uint[] z)
{
if ((x != 0 && Nat224.Mul33WordAdd(6803u, x, z, 0) != 0) || (z[6] == uint.MaxValue && Nat224.Gte(z, P)))
{
Nat.Add33To(7, 6803u, z);
}
}
public static void Multiply(uint[] x, uint[] y, uint[] z)
{
uint[] array = Nat224.CreateExt();
Nat224.Mul(x, y, array);
Reduce(array, z);
}
public SecP224K1FieldElement()
{
x = Nat224.Create();
}
public override ECFieldElement AddOne()
{
uint[] z = Nat224.Create();
SecP224R1Field.AddOne(x, z);
return(new SecP224R1FieldElement(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()
{
/*
* Q == 8m + 5, so we use Pocklington's method for this case.
*
* First, raise this element to the exponent 2^221 - 2^29 - 2^9 - 2^8 - 2^6 - 2^4 - 2^1 (i.e. m + 1)
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 191 1s } { 1 0s } { 19 1s } { 2 0s } { 1 1s } { 1 0s} { 1 1s } { 1 0s} { 3 1s } { 1 0s}
*
* Therefore we need an addition chain containing 1, 3, 19, 191 (the lengths of the repunits)
* We use: [1], 2, [3], 4, 8, 11, [19], 23, 42, 84, 107, [191]
*/
uint[] x1 = this.x;
if (Nat224.IsZero(x1) || Nat224.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat224.Create();
SecP224K1Field.Square(x1, x2);
SecP224K1Field.Multiply(x2, x1, x2);
uint[] x3 = x2;
SecP224K1Field.Square(x2, x3);
SecP224K1Field.Multiply(x3, x1, x3);
uint[] x4 = Nat224.Create();
SecP224K1Field.Square(x3, x4);
SecP224K1Field.Multiply(x4, x1, x4);
uint[] x8 = Nat224.Create();
SecP224K1Field.SquareN(x4, 4, x8);
SecP224K1Field.Multiply(x8, x4, x8);
uint[] x11 = Nat224.Create();
SecP224K1Field.SquareN(x8, 3, x11);
SecP224K1Field.Multiply(x11, x3, x11);
uint[] x19 = x11;
SecP224K1Field.SquareN(x11, 8, x19);
SecP224K1Field.Multiply(x19, x8, x19);
uint[] x23 = x8;
SecP224K1Field.SquareN(x19, 4, x23);
SecP224K1Field.Multiply(x23, x4, x23);
uint[] x42 = x4;
SecP224K1Field.SquareN(x23, 19, x42);
SecP224K1Field.Multiply(x42, x19, x42);
uint[] x84 = Nat224.Create();
SecP224K1Field.SquareN(x42, 42, x84);
SecP224K1Field.Multiply(x84, x42, x84);
uint[] x107 = x42;
SecP224K1Field.SquareN(x84, 23, x107);
SecP224K1Field.Multiply(x107, x23, x107);
uint[] x191 = x23;
SecP224K1Field.SquareN(x107, 84, x191);
SecP224K1Field.Multiply(x191, x84, x191);
uint[] t1 = x191;
SecP224K1Field.SquareN(t1, 20, t1);
SecP224K1Field.Multiply(t1, x19, t1);
SecP224K1Field.SquareN(t1, 3, t1);
SecP224K1Field.Multiply(t1, x1, t1);
SecP224K1Field.SquareN(t1, 2, t1);
SecP224K1Field.Multiply(t1, x1, t1);
SecP224K1Field.SquareN(t1, 4, t1);
SecP224K1Field.Multiply(t1, x3, t1);
SecP224K1Field.Square(t1, t1);
uint[] t2 = x84;
SecP224K1Field.Square(t1, t2);
if (Nat224.Eq(x1, t2))
{
return(new SecP224K1FieldElement(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
*/
SecP224K1Field.Multiply(t1, PRECOMP_POW2, t1);
SecP224K1Field.Square(t1, t2);
if (Nat224.Eq(x1, t2))
{
return(new SecP224K1FieldElement(t1));
}
return(null);
}
public override ECFieldElement Subtract(ECFieldElement b)
{
uint[] z = Nat224.Create();
SecP224R1Field.Subtract(x, ((SecP224R1FieldElement)b).x, z);
return(new SecP224R1FieldElement(z));
}
public override ECFieldElement Add(ECFieldElement b)
{
uint[] z = Nat224.Create();
SecP224K1Field.Add(x, ((SecP224K1FieldElement)b).x, z);
return(new SecP224K1FieldElement(z));
}
public static void Reduce(uint[] xx, uint[] z)
{
long xx10 = xx[10], xx11 = xx[11], xx12 = xx[12], xx13 = xx[13];
const long n = 1;
long t0 = (long)xx[7] + xx11 - n;
long t1 = (long)xx[8] + xx12;
long t2 = (long)xx[9] + xx13;
long cc = 0;
cc += (long)xx[0] - t0;
long z0 = (uint)cc;
cc >>= 32;
cc += (long)xx[1] - t1;
z[1] = (uint)cc;
cc >>= 32;
cc += (long)xx[2] - t2;
z[2] = (uint)cc;
cc >>= 32;
cc += (long)xx[3] + t0 - xx10;
long z3 = (uint)cc;
cc >>= 32;
cc += (long)xx[4] + t1 - xx11;
z[4] = (uint)cc;
cc >>= 32;
cc += (long)xx[5] + t2 - xx12;
z[5] = (uint)cc;
cc >>= 32;
cc += (long)xx[6] + xx10 - xx13;
z[6] = (uint)cc;
cc >>= 32;
cc += n;
Debug.Assert(cc >= 0);
z3 += cc;
z0 -= cc;
z[0] = (uint)z0;
cc = z0 >> 32;
if (cc != 0)
{
cc += (long)z[1];
z[1] = (uint)cc;
cc >>= 32;
cc += (long)z[2];
z[2] = (uint)cc;
z3 += cc >> 32;
}
z[3] = (uint)z3;
cc = z3 >> 32;
Debug.Assert(cc == 0 || cc == 1);
if ((cc != 0 && Nat.IncAt(7, z, 4) != 0) ||
(z[6] == P6 && Nat224.Gte(z, P)))
{
AddPInvTo(z);
}
}
public override ECFieldElement Invert()
{
uint[] z = Nat224.Create();
Mod.Invert(SecP224K1Field.P, x, z);
return(new SecP224K1FieldElement(z));
}