public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat256.IsZero(y) || Nat256.IsOne(y))
{
return(this);
}
uint[] array = Nat256.Create();
uint[] array2 = Nat256.Create();
SecP256R1Field.Square(y, array);
SecP256R1Field.Multiply(array, y, array);
SecP256R1Field.SquareN(array, 2, array2);
SecP256R1Field.Multiply(array2, array, array2);
SecP256R1Field.SquareN(array2, 4, array);
SecP256R1Field.Multiply(array, array2, array);
SecP256R1Field.SquareN(array, 8, array2);
SecP256R1Field.Multiply(array2, array, array2);
SecP256R1Field.SquareN(array2, 16, array);
SecP256R1Field.Multiply(array, array2, array);
SecP256R1Field.SquareN(array, 32, array);
SecP256R1Field.Multiply(array, y, array);
SecP256R1Field.SquareN(array, 96, array);
SecP256R1Field.Multiply(array, y, array);
SecP256R1Field.SquareN(array, 94, array);
SecP256R1Field.Multiply(array, array, array2);
if (!Nat256.Eq(y, array2))
{
return(null);
}
return(new SecP256R1FieldElement(array));
}
/**
* 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);
}
protected virtual Curve25519Point TwiceJacobianModified(bool calculateW)
{
Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord,
Z1 = (Curve25519FieldElement)this.RawZCoords[0], W1 = GetJacobianModifiedW();
uint c;
uint[] M = Nat256.Create();
Curve25519Field.Square(X1.x, M);
c = Nat256.AddBothTo(M, M, M);
c += Nat256.AddTo(W1.x, M);
Curve25519Field.Reduce27(c, M);
uint[] _2Y1 = Nat256.Create();
Curve25519Field.Twice(Y1.x, _2Y1);
uint[] _2Y1Squared = Nat256.Create();
Curve25519Field.Multiply(_2Y1, Y1.x, _2Y1Squared);
uint[] S = Nat256.Create();
Curve25519Field.Multiply(_2Y1Squared, X1.x, S);
Curve25519Field.Twice(S, S);
uint[] _8T = Nat256.Create();
Curve25519Field.Square(_2Y1Squared, _8T);
Curve25519Field.Twice(_8T, _8T);
Curve25519FieldElement X3 = new Curve25519FieldElement(_2Y1Squared);
Curve25519Field.Square(M, X3.x);
Curve25519Field.Subtract(X3.x, S, X3.x);
Curve25519Field.Subtract(X3.x, S, X3.x);
Curve25519FieldElement Y3 = new Curve25519FieldElement(S);
Curve25519Field.Subtract(S, X3.x, Y3.x);
Curve25519Field.Multiply(Y3.x, M, Y3.x);
Curve25519Field.Subtract(Y3.x, _8T, Y3.x);
Curve25519FieldElement Z3 = new Curve25519FieldElement(_2Y1);
if (!Nat256.IsOne(Z1.x))
{
Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x);
}
Curve25519FieldElement W3 = null;
if (calculateW)
{
W3 = new Curve25519FieldElement(_8T);
Curve25519Field.Multiply(W3.x, W1.x, W3.x);
Curve25519Field.Twice(W3.x, W3.x);
}
return(new Curve25519Point(this.Curve, X3, Y3, new ECFieldElement[] { Z3, W3 }, IsCompressed));
}
public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat256.IsZero(y) || Nat256.IsOne(y))
{
return(this);
}
uint[] array = Nat256.Create();
Curve25519Field.Square(y, array);
Curve25519Field.Multiply(array, y, array);
uint[] array2 = array;
Curve25519Field.Square(array, array2);
Curve25519Field.Multiply(array2, y, array2);
uint[] array3 = Nat256.Create();
Curve25519Field.Square(array2, array3);
Curve25519Field.Multiply(array3, y, array3);
uint[] array4 = Nat256.Create();
Curve25519Field.SquareN(array3, 3, array4);
Curve25519Field.Multiply(array4, array2, array4);
uint[] array5 = array2;
Curve25519Field.SquareN(array4, 4, array5);
Curve25519Field.Multiply(array5, array3, array5);
uint[] array6 = array4;
Curve25519Field.SquareN(array5, 4, array6);
Curve25519Field.Multiply(array6, array3, array6);
uint[] array7 = array3;
Curve25519Field.SquareN(array6, 15, array7);
Curve25519Field.Multiply(array7, array6, array7);
uint[] array8 = array6;
Curve25519Field.SquareN(array7, 30, array8);
Curve25519Field.Multiply(array8, array7, array8);
uint[] array9 = array7;
Curve25519Field.SquareN(array8, 60, array9);
Curve25519Field.Multiply(array9, array8, array9);
uint[] z = array8;
Curve25519Field.SquareN(array9, 11, z);
Curve25519Field.Multiply(z, array5, z);
uint[] array10 = array5;
Curve25519Field.SquareN(z, 120, array10);
Curve25519Field.Multiply(array10, array9, array10);
uint[] z2 = array10;
Curve25519Field.Square(z2, z2);
uint[] array11 = array9;
Curve25519Field.Square(z2, array11);
if (Nat256.Eq(y, array11))
{
return(new Curve25519FieldElement(z2));
}
Curve25519Field.Multiply(z2, PRECOMP_POW2, z2);
Curve25519Field.Square(z2, array11);
if (Nat256.Eq(y, array11))
{
return(new Curve25519FieldElement(z2));
}
return(null);
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat256.IsZero(x) || Nat256.IsOne(x))
{
return(this);
}
uint[] z = Nat256.Create();
Curve25519Field.Square(x, z);
Curve25519Field.Multiply(z, x, z);
uint[] numArray3 = z;
Curve25519Field.Square(z, numArray3);
Curve25519Field.Multiply(numArray3, x, numArray3);
uint[] numArray4 = Nat256.Create();
Curve25519Field.Square(numArray3, numArray4);
Curve25519Field.Multiply(numArray4, x, numArray4);
uint[] numArray5 = Nat256.Create();
Curve25519Field.SquareN(numArray4, 3, numArray5);
Curve25519Field.Multiply(numArray5, numArray3, numArray5);
uint[] numArray6 = numArray3;
Curve25519Field.SquareN(numArray5, 4, numArray6);
Curve25519Field.Multiply(numArray6, numArray4, numArray6);
uint[] numArray7 = numArray5;
Curve25519Field.SquareN(numArray6, 4, numArray7);
Curve25519Field.Multiply(numArray7, numArray4, numArray7);
uint[] numArray8 = numArray4;
Curve25519Field.SquareN(numArray7, 15, numArray8);
Curve25519Field.Multiply(numArray8, numArray7, numArray8);
uint[] numArray9 = numArray7;
Curve25519Field.SquareN(numArray8, 30, numArray9);
Curve25519Field.Multiply(numArray9, numArray8, numArray9);
uint[] numArray10 = numArray8;
Curve25519Field.SquareN(numArray9, 60, numArray10);
Curve25519Field.Multiply(numArray10, numArray9, numArray10);
uint[] numArray11 = numArray9;
Curve25519Field.SquareN(numArray10, 11, numArray11);
Curve25519Field.Multiply(numArray11, numArray6, numArray11);
uint[] numArray12 = numArray6;
Curve25519Field.SquareN(numArray11, 120, numArray12);
Curve25519Field.Multiply(numArray12, numArray10, numArray12);
uint[] numArray13 = numArray12;
Curve25519Field.Square(numArray13, numArray13);
uint[] numArray14 = numArray10;
Curve25519Field.Square(numArray13, numArray14);
if (Nat256.Eq(x, numArray14))
{
return(new Curve25519FieldElement(numArray13));
}
Curve25519Field.Multiply(numArray13, PRECOMP_POW2, numArray13);
Curve25519Field.Square(numArray13, numArray14);
if (Nat256.Eq(x, numArray14))
{
return(new Curve25519FieldElement(numArray13));
}
return(null);
}
public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat256.IsZero(y) || Nat256.IsOne(y))
{
return(this);
}
uint[] array = Nat256.Create();
SecP256K1Field.Square(y, array);
SecP256K1Field.Multiply(array, y, array);
uint[] array2 = Nat256.Create();
SecP256K1Field.Square(array, array2);
SecP256K1Field.Multiply(array2, y, array2);
uint[] array3 = Nat256.Create();
SecP256K1Field.SquareN(array2, 3, array3);
SecP256K1Field.Multiply(array3, array2, array3);
uint[] array4 = array3;
SecP256K1Field.SquareN(array3, 3, array4);
SecP256K1Field.Multiply(array4, array2, array4);
uint[] array5 = array4;
SecP256K1Field.SquareN(array4, 2, array5);
SecP256K1Field.Multiply(array5, array, array5);
uint[] array6 = Nat256.Create();
SecP256K1Field.SquareN(array5, 11, array6);
SecP256K1Field.Multiply(array6, array5, array6);
uint[] array7 = array5;
SecP256K1Field.SquareN(array6, 22, array7);
SecP256K1Field.Multiply(array7, array6, array7);
uint[] array8 = Nat256.Create();
SecP256K1Field.SquareN(array7, 44, array8);
SecP256K1Field.Multiply(array8, array7, array8);
uint[] z = Nat256.Create();
SecP256K1Field.SquareN(array8, 88, z);
SecP256K1Field.Multiply(z, array8, z);
uint[] z2 = array8;
SecP256K1Field.SquareN(z, 44, z2);
SecP256K1Field.Multiply(z2, array7, z2);
uint[] array9 = array7;
SecP256K1Field.SquareN(z2, 3, array9);
SecP256K1Field.Multiply(array9, array2, array9);
uint[] z3 = array9;
SecP256K1Field.SquareN(z3, 23, z3);
SecP256K1Field.Multiply(z3, array6, z3);
SecP256K1Field.SquareN(z3, 6, z3);
SecP256K1Field.Multiply(z3, array, z3);
SecP256K1Field.SquareN(z3, 2, z3);
uint[] array10 = array;
SecP256K1Field.Square(z3, array10);
if (!Nat256.Eq(y, array10))
{
return(null);
}
return(new SecP256K1FieldElement(z3));
}
protected virtual Curve25519Point TwiceJacobianModified(bool calculateW)
{
Curve25519FieldElement curve25519FieldElement = (Curve25519FieldElement)base.RawXCoord;
Curve25519FieldElement curve25519FieldElement2 = (Curve25519FieldElement)base.RawYCoord;
Curve25519FieldElement curve25519FieldElement3 = (Curve25519FieldElement)base.RawZCoords[0];
Curve25519FieldElement jacobianModifiedW = GetJacobianModifiedW();
uint[] array = Nat256.Create();
Curve25519Field.Square(curve25519FieldElement.x, array);
uint num = Nat256.AddBothTo(array, array, array);
num += Nat256.AddTo(jacobianModifiedW.x, array);
Curve25519Field.Reduce27(num, array);
uint[] array2 = Nat256.Create();
Curve25519Field.Twice(curve25519FieldElement2.x, array2);
uint[] array3 = Nat256.Create();
Curve25519Field.Multiply(array2, curve25519FieldElement2.x, array3);
uint[] array4 = Nat256.Create();
Curve25519Field.Multiply(array3, curve25519FieldElement.x, array4);
Curve25519Field.Twice(array4, array4);
uint[] array5 = Nat256.Create();
Curve25519Field.Square(array3, array5);
Curve25519Field.Twice(array5, array5);
Curve25519FieldElement curve25519FieldElement4 = new Curve25519FieldElement(array3);
Curve25519Field.Square(array, curve25519FieldElement4.x);
Curve25519Field.Subtract(curve25519FieldElement4.x, array4, curve25519FieldElement4.x);
Curve25519Field.Subtract(curve25519FieldElement4.x, array4, curve25519FieldElement4.x);
Curve25519FieldElement curve25519FieldElement5 = new Curve25519FieldElement(array4);
Curve25519Field.Subtract(array4, curve25519FieldElement4.x, curve25519FieldElement5.x);
Curve25519Field.Multiply(curve25519FieldElement5.x, array, curve25519FieldElement5.x);
Curve25519Field.Subtract(curve25519FieldElement5.x, array5, curve25519FieldElement5.x);
Curve25519FieldElement curve25519FieldElement6 = new Curve25519FieldElement(array2);
if (!Nat256.IsOne(curve25519FieldElement3.x))
{
Curve25519Field.Multiply(curve25519FieldElement6.x, curve25519FieldElement3.x, curve25519FieldElement6.x);
}
Curve25519FieldElement curve25519FieldElement7 = null;
if (calculateW)
{
curve25519FieldElement7 = new Curve25519FieldElement(array5);
Curve25519Field.Multiply(curve25519FieldElement7.x, jacobianModifiedW.x, curve25519FieldElement7.x);
Curve25519Field.Twice(curve25519FieldElement7.x, curve25519FieldElement7.x);
}
return(new Curve25519Point(Curve, curve25519FieldElement4, curve25519FieldElement5, new ECFieldElement[2]
{
curve25519FieldElement6,
curve25519FieldElement7
}, base.IsCompressed));
}
protected virtual Curve25519Point TwiceJacobianModified(bool calculateW)
{
Curve25519FieldElement rawXCoord = (Curve25519FieldElement)base.RawXCoord;
Curve25519FieldElement rawYCoord = (Curve25519FieldElement)base.RawYCoord;
Curve25519FieldElement element3 = (Curve25519FieldElement)base.RawZCoords[0];
Curve25519FieldElement jacobianModifiedW = this.GetJacobianModifiedW();
uint[] z = Nat256.Create();
Curve25519Field.Square(rawXCoord.x, z);
uint x = Nat256.AddBothTo(z, z, z) + Nat256.AddTo(jacobianModifiedW.x, z);
Curve25519Field.Reduce27(x, z);
uint[] numArray2 = Nat256.Create();
Curve25519Field.Twice(rawYCoord.x, numArray2);
uint[] numArray3 = Nat256.Create();
Curve25519Field.Multiply(numArray2, rawYCoord.x, numArray3);
uint[] numArray4 = Nat256.Create();
Curve25519Field.Multiply(numArray3, rawXCoord.x, numArray4);
Curve25519Field.Twice(numArray4, numArray4);
uint[] numArray5 = Nat256.Create();
Curve25519Field.Square(numArray3, numArray5);
Curve25519Field.Twice(numArray5, numArray5);
Curve25519FieldElement element5 = new Curve25519FieldElement(numArray3);
Curve25519Field.Square(z, element5.x);
Curve25519Field.Subtract(element5.x, numArray4, element5.x);
Curve25519Field.Subtract(element5.x, numArray4, element5.x);
Curve25519FieldElement y = new Curve25519FieldElement(numArray4);
Curve25519Field.Subtract(numArray4, element5.x, y.x);
Curve25519Field.Multiply(y.x, z, y.x);
Curve25519Field.Subtract(y.x, numArray5, y.x);
Curve25519FieldElement element7 = new Curve25519FieldElement(numArray2);
if (!Nat256.IsOne(element3.x))
{
Curve25519Field.Multiply(element7.x, element3.x, element7.x);
}
Curve25519FieldElement element8 = null;
if (calculateW)
{
element8 = new Curve25519FieldElement(numArray5);
Curve25519Field.Multiply(element8.x, jacobianModifiedW.x, element8.x);
Curve25519Field.Twice(element8.x, element8.x);
}
return(new Curve25519Point(this.Curve, element5, y, new ECFieldElement[] { element7, element8 }, 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()
{
// Raise this element to the exponent 2^254 - 2^222 + 2^190 + 2^94
uint[] x1 = this.x;
if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
{
return(this);
}
uint[] t1 = Nat256.Create();
uint[] t2 = Nat256.Create();
SecP256R1Field.Square(x1, t1);
SecP256R1Field.Multiply(t1, x1, t1);
SecP256R1Field.SquareN(t1, 2, t2);
SecP256R1Field.Multiply(t2, t1, t2);
SecP256R1Field.SquareN(t2, 4, t1);
SecP256R1Field.Multiply(t1, t2, t1);
SecP256R1Field.SquareN(t1, 8, t2);
SecP256R1Field.Multiply(t2, t1, t2);
SecP256R1Field.SquareN(t2, 16, t1);
SecP256R1Field.Multiply(t1, t2, t1);
SecP256R1Field.SquareN(t1, 32, t1);
SecP256R1Field.Multiply(t1, x1, t1);
SecP256R1Field.SquareN(t1, 96, t1);
SecP256R1Field.Multiply(t1, x1, t1);
SecP256R1Field.SquareN(t1, 94, t1);
SecP256R1Field.Multiply(t1, t1, t2);
return(Nat256.Eq(x1, t2) ? new SecP256R1FieldElement(t1) : null);
}
/**
* 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 - 2^30 - 2^7 - 2^6 - 2^5 - 2^4 - 2^2
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 223 1s } { 1 0s } { 22 1s } { 4 0s } { 2 1s } { 2 0s}
*
* Therefore we need an addition chain containing 2, 22, 223 (the lengths of the repunits)
* We use: 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
*/
uint[] x1 = this.x;
if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat256.Create();
SecP256K1Field.Square(x1, x2);
SecP256K1Field.Multiply(x2, x1, x2);
uint[] x3 = Nat256.Create();
SecP256K1Field.Square(x2, x3);
SecP256K1Field.Multiply(x3, x1, x3);
uint[] x6 = Nat256.Create();
SecP256K1Field.SquareN(x3, 3, x6);
SecP256K1Field.Multiply(x6, x3, x6);
uint[] x9 = x6;
SecP256K1Field.SquareN(x6, 3, x9);
SecP256K1Field.Multiply(x9, x3, x9);
uint[] x11 = x9;
SecP256K1Field.SquareN(x9, 2, x11);
SecP256K1Field.Multiply(x11, x2, x11);
uint[] x22 = Nat256.Create();
SecP256K1Field.SquareN(x11, 11, x22);
SecP256K1Field.Multiply(x22, x11, x22);
uint[] x44 = x11;
SecP256K1Field.SquareN(x22, 22, x44);
SecP256K1Field.Multiply(x44, x22, x44);
uint[] x88 = Nat256.Create();
SecP256K1Field.SquareN(x44, 44, x88);
SecP256K1Field.Multiply(x88, x44, x88);
uint[] x176 = Nat256.Create();
SecP256K1Field.SquareN(x88, 88, x176);
SecP256K1Field.Multiply(x176, x88, x176);
uint[] x220 = x88;
SecP256K1Field.SquareN(x176, 44, x220);
SecP256K1Field.Multiply(x220, x44, x220);
uint[] x223 = x44;
SecP256K1Field.SquareN(x220, 3, x223);
SecP256K1Field.Multiply(x223, x3, x223);
uint[] t1 = x223;
SecP256K1Field.SquareN(t1, 23, t1);
SecP256K1Field.Multiply(t1, x22, t1);
SecP256K1Field.SquareN(t1, 6, t1);
SecP256K1Field.Multiply(t1, x2, t1);
SecP256K1Field.SquareN(t1, 2, t1);
uint[] t2 = x2;
SecP256K1Field.Square(t1, t2);
return(Nat256.Eq(x1, t2) ? new SecP256K1FieldElement(t1) : null);
}
/**
* 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 2^252 - 2^1 (i.e. m + 1)
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 251 1s } { 1 0s }
*
* Therefore we need an addition chain containing 251 (the lengths of the repunits)
* We use: 1, 2, 3, 4, 7, 11, 15, 30, 60, 120, 131, [251]
*/
uint[] x1 = this.x;
if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat256.Create();
Curve25519Field.Square(x1, x2);
Curve25519Field.Multiply(x2, x1, x2);
uint[] x3 = x2;
Curve25519Field.Square(x2, x3);
Curve25519Field.Multiply(x3, x1, x3);
uint[] x4 = Nat256.Create();
Curve25519Field.Square(x3, x4);
Curve25519Field.Multiply(x4, x1, x4);
uint[] x7 = Nat256.Create();
Curve25519Field.SquareN(x4, 3, x7);
Curve25519Field.Multiply(x7, x3, x7);
uint[] x11 = x3;
Curve25519Field.SquareN(x7, 4, x11);
Curve25519Field.Multiply(x11, x4, x11);
uint[] x15 = x7;
Curve25519Field.SquareN(x11, 4, x15);
Curve25519Field.Multiply(x15, x4, x15);
uint[] x30 = x4;
Curve25519Field.SquareN(x15, 15, x30);
Curve25519Field.Multiply(x30, x15, x30);
uint[] x60 = x15;
Curve25519Field.SquareN(x30, 30, x60);
Curve25519Field.Multiply(x60, x30, x60);
uint[] x120 = x30;
Curve25519Field.SquareN(x60, 60, x120);
Curve25519Field.Multiply(x120, x60, x120);
uint[] x131 = x60;
Curve25519Field.SquareN(x120, 11, x131);
Curve25519Field.Multiply(x131, x11, x131);
uint[] x251 = x11;
Curve25519Field.SquareN(x131, 120, x251);
Curve25519Field.Multiply(x251, x120, x251);
uint[] t1 = x251;
Curve25519Field.Square(t1, t1);
uint[] t2 = x120;
Curve25519Field.Square(t1, t2);
if (Nat256.Eq(x1, t2))
{
return(new Curve25519FieldElement(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
*/
Curve25519Field.Multiply(t1, PRECOMP_POW2, t1);
Curve25519Field.Square(t1, t2);
if (Nat256.Eq(x1, t2))
{
return(new Curve25519FieldElement(t1));
}
return(null);
}
