public override ECFieldElement Divide(ECFieldElement b)
{
uint[] z = Nat224.Create();
Mod.Invert(SecP224K1Field.P, ((SecP224K1FieldElement)b).x, z);
SecP224K1Field.Multiply(z, this.x, z);
return(new SecP224K1FieldElement(z));
}
public override ECFieldElement Invert()
{
//return new SecP224K1FieldElement(ToBigInteger().ModInverse(Q));
uint[] z = Nat224.Create();
Mod.Invert(SecP224K1Field.P, x, z);
return(new SecP224K1FieldElement(z));
}
public override ECFieldElement Divide(ECFieldElement b)
{
//return Multiply(b.Invert());
uint[] z = Nat224.Create();
SecP224K1Field.Inv(((SecP224K1FieldElement)b).x, z);
SecP224K1Field.Multiply(z, x, z);
return(new SecP224K1FieldElement(z));
}
public override ECPoint Twice()
{
if (base.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
SecP224R1FieldElement rawYCoord = (SecP224R1FieldElement)base.RawYCoord;
if (rawYCoord.IsZero)
{
return(curve.Infinity);
}
SecP224R1FieldElement rawXCoord = (SecP224R1FieldElement)base.RawXCoord;
SecP224R1FieldElement element3 = (SecP224R1FieldElement)base.RawZCoords[0];
uint[] z = Nat224.Create();
uint[] numArray2 = Nat224.Create();
uint[] numArray3 = Nat224.Create();
SecP224R1Field.Square(rawYCoord.x, numArray3);
uint[] numArray4 = Nat224.Create();
SecP224R1Field.Square(numArray3, numArray4);
bool isOne = element3.IsOne;
uint[] x = element3.x;
if (!isOne)
{
x = numArray2;
SecP224R1Field.Square(element3.x, x);
}
SecP224R1Field.Subtract(rawXCoord.x, x, z);
uint[] numArray6 = numArray2;
SecP224R1Field.Add(rawXCoord.x, x, numArray6);
SecP224R1Field.Multiply(numArray6, z, numArray6);
SecP224R1Field.Reduce32(Nat224.AddBothTo(numArray6, numArray6, numArray6), numArray6);
uint[] numArray7 = numArray3;
SecP224R1Field.Multiply(numArray3, rawXCoord.x, numArray7);
SecP224R1Field.Reduce32(Nat.ShiftUpBits(7, numArray7, 2, 0), numArray7);
SecP224R1Field.Reduce32(Nat.ShiftUpBits(7, numArray4, 3, 0, z), z);
SecP224R1FieldElement element4 = new SecP224R1FieldElement(numArray4);
SecP224R1Field.Square(numArray6, element4.x);
SecP224R1Field.Subtract(element4.x, numArray7, element4.x);
SecP224R1Field.Subtract(element4.x, numArray7, element4.x);
SecP224R1FieldElement y = new SecP224R1FieldElement(numArray7);
SecP224R1Field.Subtract(numArray7, element4.x, y.x);
SecP224R1Field.Multiply(y.x, numArray6, y.x);
SecP224R1Field.Subtract(y.x, z, y.x);
SecP224R1FieldElement element6 = new SecP224R1FieldElement(numArray6);
SecP224R1Field.Twice(rawYCoord.x, element6.x);
if (!isOne)
{
SecP224R1Field.Multiply(element6.x, element3.x, element6.x);
}
return(new SecP224R1Point(curve, element4, y, new ECFieldElement[] { element6 }, base.IsCompressed));
}
public override ECPoint Twice()
{
if (base.IsInfinity)
{
return(this);
}
ECCurve curve = Curve;
SecP224K1FieldElement secP224K1FieldElement = (SecP224K1FieldElement)base.RawYCoord;
if (secP224K1FieldElement.IsZero)
{
return(curve.Infinity);
}
SecP224K1FieldElement secP224K1FieldElement2 = (SecP224K1FieldElement)base.RawXCoord;
SecP224K1FieldElement secP224K1FieldElement3 = (SecP224K1FieldElement)base.RawZCoords[0];
uint[] array = Nat224.Create();
SecP224K1Field.Square(secP224K1FieldElement.x, array);
uint[] array2 = Nat224.Create();
SecP224K1Field.Square(array, array2);
uint[] array3 = Nat224.Create();
SecP224K1Field.Square(secP224K1FieldElement2.x, array3);
uint x = Nat224.AddBothTo(array3, array3, array3);
SecP224K1Field.Reduce32(x, array3);
uint[] array4 = array;
SecP224K1Field.Multiply(array, secP224K1FieldElement2.x, array4);
x = Nat.ShiftUpBits(7, array4, 2, 0u);
SecP224K1Field.Reduce32(x, array4);
uint[] array5 = Nat224.Create();
x = Nat.ShiftUpBits(7, array2, 3, 0u, array5);
SecP224K1Field.Reduce32(x, array5);
SecP224K1FieldElement secP224K1FieldElement4 = new SecP224K1FieldElement(array2);
SecP224K1Field.Square(array3, secP224K1FieldElement4.x);
SecP224K1Field.Subtract(secP224K1FieldElement4.x, array4, secP224K1FieldElement4.x);
SecP224K1Field.Subtract(secP224K1FieldElement4.x, array4, secP224K1FieldElement4.x);
SecP224K1FieldElement secP224K1FieldElement5 = new SecP224K1FieldElement(array4);
SecP224K1Field.Subtract(array4, secP224K1FieldElement4.x, secP224K1FieldElement5.x);
SecP224K1Field.Multiply(secP224K1FieldElement5.x, array3, secP224K1FieldElement5.x);
SecP224K1Field.Subtract(secP224K1FieldElement5.x, array5, secP224K1FieldElement5.x);
SecP224K1FieldElement secP224K1FieldElement6 = new SecP224K1FieldElement(array3);
SecP224K1Field.Twice(secP224K1FieldElement.x, secP224K1FieldElement6.x);
if (!secP224K1FieldElement3.IsOne)
{
SecP224K1Field.Multiply(secP224K1FieldElement6.x, secP224K1FieldElement3.x, secP224K1FieldElement6.x);
}
return(new SecP224K1Point(curve, secP224K1FieldElement4, secP224K1FieldElement5, new ECFieldElement[1]
{
secP224K1FieldElement6
}, base.IsCompressed));
}
private static void RS(uint[] d, uint[] e, uint[] f)
{
SecP224R1Field.Multiply(e, d, e);
uint[] t = Nat224.Create();
SecP224R1Field.Square(d, t);
SecP224R1Field.Add(f, t, d);
SecP224R1Field.Twice(e, e);
SecP224R1Field.Multiply(f, t, f);
uint c = Nat.ShiftUpBits(7, f, 2, 0);
SecP224R1Field.Reduce32(c, f);
}
public static void Inv(uint[] x, uint[] z)
{
/*
* Raise this element to the exponent 2^224 - 2^96 - 1
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 127 1s } { 1 0s } { 96 1s }
*
* Therefore we need an addition chain containing 96, 127 (the lengths of the repunits)
* We use: 1, 2, 3, 6, 12, 24, 48, [96], 120, 126, [127]
*/
if (0 != IsZero(x))
{
throw new ArgumentException("cannot be 0", "x");
}
uint[] x1 = x;
uint[] x2 = Nat224.Create();
Square(x1, x2);
Multiply(x2, x1, x2);
uint[] x3 = x2;
Square(x2, x3);
Multiply(x3, x1, x3);
uint[] x6 = Nat224.Create();
SquareN(x3, 3, x6);
Multiply(x6, x3, x6);
uint[] x12 = x3;
SquareN(x6, 6, x12);
Multiply(x12, x6, x12);
uint[] x24 = Nat224.Create();
SquareN(x12, 12, x24);
Multiply(x24, x12, x24);
uint[] x48 = x12;
SquareN(x24, 24, x48);
Multiply(x48, x24, x48);
uint[] x96 = Nat224.Create();
SquareN(x48, 48, x96);
Multiply(x96, x48, x96);
uint[] x120 = x48;
SquareN(x96, 24, x120);
Multiply(x120, x24, x120);
uint[] x126 = x24;
SquareN(x120, 6, x126);
Multiply(x126, x6, x126);
uint[] x127 = x6;
Square(x126, x127);
Multiply(x127, x1, x127);
uint[] t = x127;
SquareN(t, 97, t);
Multiply(t, x96, z);
}
public override ECPoint LookupVar(int index)
{
uint[] x = Nat224.Create(), y = Nat224.Create();
int pos = index * SECP224R1_FE_INTS * 2;
for (int j = 0; j < SECP224R1_FE_INTS; ++j)
{
x[j] = m_table[pos + j];
y[j] = m_table[pos + SECP224R1_FE_INTS + j];
}
return(CreatePoint(x, y));
}
private static bool IsSquare(uint[] x)
{
uint[] z = Nat224.Create();
uint[] array = Nat224.Create();
Nat224.Copy(x, z);
for (int i = 0; i < 7; i++)
{
Nat224.Copy(z, array);
SecP224R1Field.SquareN(z, 1 << i, z);
SecP224R1Field.Multiply(z, array, z);
}
SecP224R1Field.SquareN(z, 95, z);
return(Nat224.IsOne(z));
}
private static bool IsSquare(uint[] x)
{
uint[] z = Nat224.Create();
uint[] numArray2 = Nat224.Create();
Nat224.Copy(x, z);
for (int i = 0; i < 7; i++)
{
Nat224.Copy(z, numArray2);
SecP224R1Field.SquareN(z, ((int)1) << i, z);
SecP224R1Field.Multiply(z, numArray2, z);
}
SecP224R1Field.SquareN(z, 0x5f, z);
return(Nat224.IsOne(z));
}
private static void RM(uint[] nc, uint[] d0, uint[] e0, uint[] d1, uint[] e1, uint[] f1)
{
uint[] t = Nat224.Create();
SecP224R1Field.Multiply(e1, e0, t);
SecP224R1Field.Multiply(t, nc, t);
SecP224R1Field.Multiply(d1, d0, f1);
SecP224R1Field.Add(f1, t, f1);
SecP224R1Field.Multiply(d1, e0, t);
Nat224.Copy(f1, d1);
SecP224R1Field.Multiply(e1, d0, e1);
SecP224R1Field.Add(e1, t, e1);
SecP224R1Field.Square(e1, f1);
SecP224R1Field.Multiply(f1, nc, f1);
}
private static bool IsSquare(uint[] x)
{
uint[] t1 = Nat224.Create();
uint[] t2 = Nat224.Create();
Nat224.Copy(x, t1);
for (int i = 0; i < 7; ++i)
{
Nat224.Copy(t1, t2);
SecP224R1Field.SquareN(t1, 1 << i, t1);
SecP224R1Field.Multiply(t1, t2, t1);
}
SecP224R1Field.SquareN(t1, 95, t1);
return(Nat224.IsOne(t1));
}
/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
uint[] c = this.x;
if (Nat224.IsZero(c) || Nat224.IsOne(c))
{
return(this);
}
uint[] nc = Nat224.Create();
SecP224R1Field.Negate(c, nc);
uint[] r = Mod.Random(SecP224R1Field.P);
for (;;)
{
uint[] d1 = Nat224.Create();
Nat224.Copy(r, d1);
uint[] e1 = Nat224.Create();
e1[0] = 1;
uint[] f1 = Nat224.Create();
RP(nc, d1, e1, f1);
uint[] d0 = Nat224.Create();
uint[] e0 = Nat224.Create();
for (int k = 1; k < 96; ++k)
{
Nat224.Copy(d1, d0);
Nat224.Copy(e1, e0);
RS(d1, e1, f1);
if (Nat224.IsZero(d1))
{
Mod.Invert(SecP224R1Field.P, e0, f1);
SecP224R1Field.Multiply(f1, d0, f1);
SecP224R1Field.Square(f1, d1);
return(Nat224.Eq(c, d1) ? new SecP224R1FieldElement(f1) : null);
}
}
// Avoid any possible infinite loop due to a bad random number generator
SecP224R1Field.AddOne(r, r);
}
}
public override ECPoint Twice()
{
if (base.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
SecP224K1FieldElement rawYCoord = (SecP224K1FieldElement)base.RawYCoord;
if (rawYCoord.IsZero)
{
return(curve.Infinity);
}
SecP224K1FieldElement rawXCoord = (SecP224K1FieldElement)base.RawXCoord;
SecP224K1FieldElement element3 = (SecP224K1FieldElement)base.RawZCoords[0];
uint[] z = Nat224.Create();
SecP224K1Field.Square(rawYCoord.x, z);
uint[] numArray2 = Nat224.Create();
SecP224K1Field.Square(z, numArray2);
uint[] numArray3 = Nat224.Create();
SecP224K1Field.Square(rawXCoord.x, numArray3);
SecP224K1Field.Reduce32(Nat224.AddBothTo(numArray3, numArray3, numArray3), numArray3);
uint[] numArray4 = z;
SecP224K1Field.Multiply(z, rawXCoord.x, numArray4);
SecP224K1Field.Reduce32(Nat.ShiftUpBits(7, numArray4, 2, 0), numArray4);
uint[] numArray5 = Nat224.Create();
SecP224K1Field.Reduce32(Nat.ShiftUpBits(7, numArray2, 3, 0, numArray5), numArray5);
SecP224K1FieldElement x = new SecP224K1FieldElement(numArray2);
SecP224K1Field.Square(numArray3, x.x);
SecP224K1Field.Subtract(x.x, numArray4, x.x);
SecP224K1Field.Subtract(x.x, numArray4, x.x);
SecP224K1FieldElement y = new SecP224K1FieldElement(numArray4);
SecP224K1Field.Subtract(numArray4, x.x, y.x);
SecP224K1Field.Multiply(y.x, numArray3, y.x);
SecP224K1Field.Subtract(y.x, numArray5, y.x);
SecP224K1FieldElement element6 = new SecP224K1FieldElement(numArray3);
SecP224K1Field.Twice(rawYCoord.x, element6.x);
if (!element3.IsOne)
{
SecP224K1Field.Multiply(element6.x, element3.x, element6.x);
}
return(new SecP224K1Point(curve, x, y, new ECFieldElement[] { element6 }, base.IsCompressed));
}
private static void RP(uint[] nc, uint[] d1, uint[] e1, uint[] f1, uint[] t)
{
Nat224.Copy(nc, f1);
uint[] z = Nat224.Create();
uint[] numArray2 = Nat224.Create();
for (int i = 0; i < 7; i++)
{
Nat224.Copy(d1, z);
Nat224.Copy(e1, numArray2);
int num2 = ((int)1) << i;
while (--num2 >= 0)
{
RS(d1, e1, f1, t);
}
RM(nc, z, numArray2, d1, e1, f1, t);
}
}
private static void RP(uint[] nc, uint[] d1, uint[] e1, uint[] f1, uint[] t)
{
Nat224.Copy(nc, f1);
uint[] array = Nat224.Create();
uint[] array2 = Nat224.Create();
for (int i = 0; i < 7; i++)
{
Nat224.Copy(d1, array);
Nat224.Copy(e1, array2);
int num = 1 << i;
while (--num >= 0)
{
SecP224R1FieldElement.RS(d1, e1, f1, t);
}
SecP224R1FieldElement.RM(nc, array, array2, d1, e1, f1, t);
}
}
public override ECPoint Lookup(int index)
{
uint[] x = Nat224.Create(), y = Nat224.Create();
int pos = 0;
for (int i = 0; i < m_size; ++i)
{
uint MASK = (uint)(((i ^ index) - 1) >> 31);
for (int j = 0; j < SECP224R1_FE_INTS; ++j)
{
x[j] ^= m_table[pos + j] & MASK;
y[j] ^= m_table[pos + SECP224R1_FE_INTS + j] & MASK;
}
pos += (SECP224R1_FE_INTS * 2);
}
return(CreatePoint(x, y));
}
public virtual ECPoint Lookup(int index)
{
uint[] x = Nat224.Create(), y = Nat224.Create();
int pos = 0;
for (int i = 0; i < m_size; ++i)
{
uint MASK = (uint)(((i ^ index) - 1) >> 31);
for (int j = 0; j < SECP224K1_FE_INTS; ++j)
{
x[j] ^= m_table[pos + j] & MASK;
y[j] ^= m_table[pos + SECP224K1_FE_INTS + j] & MASK;
}
pos += (SECP224K1_FE_INTS * 2);
}
return(m_outer.CreateRawPoint(new SecP224K1FieldElement(x), new SecP224K1FieldElement(y), false));
}
private static void RP(uint[] nc, uint[] d1, uint[] e1, uint[] f1, uint[] t)
{
Nat224.Copy(nc, f1);
uint[] d0 = Nat224.Create();
uint[] e0 = Nat224.Create();
for (int i = 0; i < 7; ++i)
{
Nat224.Copy(d1, d0);
Nat224.Copy(e1, e0);
int j = 1 << i;
while (--j >= 0)
{
RS(d1, e1, f1, t);
}
RM(nc, d0, e0, d1, e1, f1, t);
}
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat224.IsZero(x) || Nat224.IsOne(x))
{
return(this);
}
uint[] z = Nat224.Create();
SecP224R1Field.Negate(x, z);
uint[] r = Mod.Random(SecP224R1Field.P);
uint[] t = Nat224.Create();
if (!IsSquare(x))
{
return(null);
}
while (!TrySqrt(z, r, t))
{
SecP224R1Field.AddOne(r, r);
}
SecP224R1Field.Square(t, r);
return(!Nat224.Eq(x, r) ? null : new SecP224R1FieldElement(t));
}
public override ECFieldElement Sqrt()
{
uint[] array = x;
if (Nat224.IsZero(array) || Nat224.IsOne(array))
{
return(this);
}
uint[] array2 = Nat224.Create();
SecP224R1Field.Negate(array, array2);
uint[] array3 = Mod.Random(SecP224R1Field.P);
uint[] t = Nat224.Create();
if (!IsSquare(array))
{
return(null);
}
while (!TrySqrt(array2, array3, t))
{
SecP224R1Field.AddOne(array3, array3);
}
SecP224R1Field.Square(t, array3);
return((!Nat224.Eq(array, array3)) ? null : new SecP224R1FieldElement(t));
}
/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
uint[] c = this.x;
if (Nat224.IsZero(c) || Nat224.IsOne(c))
return this;
uint[] nc = Nat224.Create();
SecP224R1Field.Negate(c, nc);
uint[] r = Mod.Random(SecP224R1Field.P);
uint[] t = Nat224.Create();
if (!IsSquare(c))
return null;
while (!TrySqrt(nc, r, t))
{
SecP224R1Field.AddOne(r, r);
}
SecP224R1Field.Square(t, r);
return Nat224.Eq(c, r) ? new SecP224R1FieldElement(t) : null;
}
private static bool TrySqrt(uint[] nc, uint[] r, uint[] t)
{
uint[] array = Nat224.Create();
Nat224.Copy(r, array);
uint[] array2 = Nat224.Create();
array2[0] = 1u;
uint[] array3 = Nat224.Create();
SecP224R1FieldElement.RP(nc, array, array2, array3, t);
uint[] array4 = Nat224.Create();
uint[] z = Nat224.Create();
for (int i = 1; i < 96; i++)
{
Nat224.Copy(array, array4);
Nat224.Copy(array2, z);
SecP224R1FieldElement.RS(array, array2, array3, t);
if (Nat224.IsZero(array))
{
Mod.Invert(SecP224R1Field.P, z, t);
SecP224R1Field.Multiply(t, array4, t);
return(true);
}
}
return(false);
}
private static bool TrySqrt(uint[] nc, uint[] r, uint[] t)
{
uint[] z = Nat224.Create();
Nat224.Copy(r, z);
uint[] numArray2 = Nat224.Create();
numArray2[0] = 1;
uint[] numArray3 = Nat224.Create();
RP(nc, z, numArray2, numArray3, t);
uint[] numArray4 = Nat224.Create();
uint[] numArray5 = Nat224.Create();
for (int i = 1; i < 0x60; i++)
{
Nat224.Copy(z, numArray4);
Nat224.Copy(numArray2, numArray5);
RS(z, numArray2, numArray3, t);
if (Nat224.IsZero(z))
{
Mod.Invert(SecP224R1Field.P, numArray5, t);
SecP224R1Field.Multiply(t, numArray4, t);
return(true);
}
}
return(false);
}
public override ECFieldElement Multiply(ECFieldElement b)
{
uint[] z = Nat224.Create();
SecP224R1Field.Multiply(x, ((SecP224R1FieldElement)b).x, z);
return(new SecP224R1FieldElement(z));
}
public override ECFieldElement Subtract(ECFieldElement b)
{
uint[] z = Nat224.Create();
SecP224R1Field.Subtract(x, ((SecP224R1FieldElement)b).x, z);
return(new SecP224R1FieldElement(z));
}
public override ECFieldElement AddOne()
{
uint[] z = Nat224.Create();
SecP224R1Field.AddOne(x, z);
return(new SecP224R1FieldElement(z));
}
public SecP224R1FieldElement()
{
this.x = Nat224.Create();
}
/**
* 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 Add(ECFieldElement b)
{
uint[] z = Nat224.Create();
SecP224K1Field.Add(x, ((SecP224K1FieldElement)b).x, z);
return(new SecP224K1FieldElement(z));
}