public override ECFieldElement Divide(ECFieldElement b)
{
uint[] z = Nat224.Create();
Mod.Invert(SecP224K1Field.P, ((SecP224K1FieldElement)b).x, z);
SecP224K1Field.Multiply(z, 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));
}
private static bool TrySqrt(uint[] nc, uint[] r, uint[] t)
{
uint[] d1 = Nat224.Create();
Nat224.Copy(r, d1);
uint[] e1 = Nat224.Create();
e1[0] = 1;
uint[] f1 = Nat224.Create();
RP(nc, d1, e1, f1, t);
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, t);
if (Nat224.IsZero(d1))
{
Mod.Invert(SecP224R1Field.P, e0, t);
SecP224R1Field.Multiply(t, d0, t);
return(true);
}
}
return(false);
}
/**
* 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);
}
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));
}
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[] 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));
}
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 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();
}
public override ECFieldElement Invert()
{
uint[] z = Nat224.Create();
Mod.Invert(SecP224K1Field.P, x, z);
return(new SecP224K1FieldElement(z));
}
public override ECFieldElement Add(ECFieldElement b)
{
uint[] z = Nat224.Create();
SecP224K1Field.Add(x, ((SecP224K1FieldElement)b).x, z);
return(new SecP224K1FieldElement(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 SecP224K1FieldElement()
{
x = Nat224.Create();
}
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 override ECFieldElement Square()
{
uint[] z = Nat224.Create();
SecP224K1Field.Square(x, z);
return(new SecP224K1FieldElement(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;
SecP224R1FieldElement secP224R1FieldElement = (SecP224R1FieldElement)base.RawXCoord;
SecP224R1FieldElement secP224R1FieldElement2 = (SecP224R1FieldElement)base.RawYCoord;
SecP224R1FieldElement secP224R1FieldElement3 = (SecP224R1FieldElement)b.RawXCoord;
SecP224R1FieldElement secP224R1FieldElement4 = (SecP224R1FieldElement)b.RawYCoord;
SecP224R1FieldElement secP224R1FieldElement5 = (SecP224R1FieldElement)base.RawZCoords[0];
SecP224R1FieldElement secP224R1FieldElement6 = (SecP224R1FieldElement)b.RawZCoords[0];
uint[] array = Nat224.CreateExt();
uint[] array2 = Nat224.Create();
uint[] array3 = Nat224.Create();
uint[] array4 = Nat224.Create();
bool isOne = secP224R1FieldElement5.IsOne;
uint[] array5;
uint[] array6;
if (isOne)
{
array5 = secP224R1FieldElement3.x;
array6 = secP224R1FieldElement4.x;
}
else
{
array6 = array3;
SecP224R1Field.Square(secP224R1FieldElement5.x, array6);
array5 = array2;
SecP224R1Field.Multiply(array6, secP224R1FieldElement3.x, array5);
SecP224R1Field.Multiply(array6, secP224R1FieldElement5.x, array6);
SecP224R1Field.Multiply(array6, secP224R1FieldElement4.x, array6);
}
bool isOne2 = secP224R1FieldElement6.IsOne;
uint[] array7;
uint[] array8;
if (isOne2)
{
array7 = secP224R1FieldElement.x;
array8 = secP224R1FieldElement2.x;
}
else
{
array8 = array4;
SecP224R1Field.Square(secP224R1FieldElement6.x, array8);
array7 = array;
SecP224R1Field.Multiply(array8, secP224R1FieldElement.x, array7);
SecP224R1Field.Multiply(array8, secP224R1FieldElement6.x, array8);
SecP224R1Field.Multiply(array8, secP224R1FieldElement2.x, array8);
}
uint[] array9 = Nat224.Create();
SecP224R1Field.Subtract(array7, array5, array9);
uint[] array10 = array2;
SecP224R1Field.Subtract(array8, array6, array10);
if (Nat224.IsZero(array9))
{
if (Nat224.IsZero(array10))
{
return(Twice());
}
return(curve.Infinity);
}
uint[] array11 = array3;
SecP224R1Field.Square(array9, array11);
uint[] array12 = Nat224.Create();
SecP224R1Field.Multiply(array11, array9, array12);
uint[] array13 = array3;
SecP224R1Field.Multiply(array11, array7, array13);
SecP224R1Field.Negate(array12, array12);
Nat224.Mul(array8, array12, array);
uint x = Nat224.AddBothTo(array13, array13, array12);
SecP224R1Field.Reduce32(x, array12);
SecP224R1FieldElement secP224R1FieldElement7 = new SecP224R1FieldElement(array4);
SecP224R1Field.Square(array10, secP224R1FieldElement7.x);
SecP224R1Field.Subtract(secP224R1FieldElement7.x, array12, secP224R1FieldElement7.x);
SecP224R1FieldElement secP224R1FieldElement8 = new SecP224R1FieldElement(array12);
SecP224R1Field.Subtract(array13, secP224R1FieldElement7.x, secP224R1FieldElement8.x);
SecP224R1Field.MultiplyAddToExt(secP224R1FieldElement8.x, array10, array);
SecP224R1Field.Reduce(array, secP224R1FieldElement8.x);
SecP224R1FieldElement secP224R1FieldElement9 = new SecP224R1FieldElement(array9);
if (!isOne)
{
SecP224R1Field.Multiply(secP224R1FieldElement9.x, secP224R1FieldElement5.x, secP224R1FieldElement9.x);
}
if (!isOne2)
{
SecP224R1Field.Multiply(secP224R1FieldElement9.x, secP224R1FieldElement6.x, secP224R1FieldElement9.x);
}
ECFieldElement[] zs = new ECFieldElement[1]
{
secP224R1FieldElement9
};
return(new SecP224R1Point(curve, secP224R1FieldElement7, secP224R1FieldElement8, zs, base.IsCompressed));
}
/**
* 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);
}