protected static ECFieldElement[] GetInitialZCoords(ECCurve curve)
{
// Cope with null curve, most commonly used by implicitlyCa
int coord = null == curve ? ECCurve.COORD_AFFINE : curve.CoordinateSystem;
switch (coord)
{
case ECCurve.COORD_AFFINE:
case ECCurve.COORD_LAMBDA_AFFINE:
return EMPTY_ZS;
default:
break;
}
ECFieldElement one = curve.FromBigInteger(BigInteger.One);
switch (coord)
{
case ECCurve.COORD_HOMOGENEOUS:
case ECCurve.COORD_JACOBIAN:
case ECCurve.COORD_LAMBDA_PROJECTIVE:
return new ECFieldElement[] { one };
case ECCurve.COORD_JACOBIAN_CHUDNOVSKY:
return new ECFieldElement[] { one, one, one };
case ECCurve.COORD_JACOBIAN_MODIFIED:
return new ECFieldElement[] { one, curve.A };
default:
throw new ArgumentException("unknown coordinate system");
}
}
/// <summary>
/// Hashes a seed t into a point T on the curve. Returns null if t is unsuitable.
/// </summary>
/// <param name="curve">The elliptic curve in Weierstrass form</param>
/// <param name="t">The seed</param>
/// <returns>A random point T uniquely determined by seed t, otherwise null</returns>
public static ECPoint?HashToWeierstrassCurve(ECCurve curve, byte[] t)
{
ECFieldElement x, ax, x3, y, y2;
BigInteger P = curve.Field.Characteristic;
SHA256? sha256 = SHA256.Create();
BigInteger hash = new BigInteger(sha256.ComputeHash(t));
// Check that the hash is within valid range
if (hash.CompareTo(BigInteger.One) < 0 || hash.CompareTo(P) >= 0)
{
return(null);
}
// A valid point (x,y) must satisfy: y^2 = x^3 + Ax + B mod P
// Convert hash from BigInt to FieldElement x modulo P
x = curve.FromBigInteger(hash); // x
ax = x.Multiply(curve.A); // Ax
x3 = x.Square().Multiply(x); // x^3 = x^2 * x
y2 = x3.Add(ax).Add(curve.B); // y^2 = x^3 + Ax + B
y = y2.Sqrt(); // y = sqrt(x^3 + Ax + B)
// y == null if square root mod P does not exist
if (y == null)
{
return(null);
}
ECPoint T = curve.CreatePoint(x.ToBigInteger(), y.ToBigInteger());
// Use the built-in point validator, which also checks for membership
// in weak subgroups
if (!T.IsValid())
{
return(null);
}
return(T);
}
private void ImplSqrtTest(ECCurve c)
{
if (ECAlgorithms.IsFpCurve(c))
{
BigInteger p = c.Field.Characteristic;
BigInteger pMinusOne = p.Subtract(BigInteger.One);
BigInteger legendreExponent = p.ShiftRight(1);
int count = 0;
while (count < 10)
{
BigInteger nonSquare = BigIntegers.CreateRandomInRange(BigInteger.Two, pMinusOne, secRand);
if (!nonSquare.ModPow(legendreExponent, p).Equals(BigInteger.One))
{
ECFieldElement root = c.FromBigInteger(nonSquare).Sqrt();
Assert.IsNull(root);
++count;
}
}
}
}
private void ImplSqrtTest(ECCurve c)
{
if (ECAlgorithms.IsFpCurve(c))
{
BigInteger p = c.Field.Characteristic;
BigInteger pMinusOne = p.Subtract(BigInteger.One);
BigInteger legendreExponent = p.ShiftRight(1);
int count = 0;
while (count < 10)
{
BigInteger nonSquare = BigIntegers.CreateRandomInRange(BigInteger.Two, pMinusOne, secRand);
if (!nonSquare.ModPow(legendreExponent, p).Equals(BigInteger.One))
{
ECFieldElement root = c.FromBigInteger(nonSquare).Sqrt();
Assert.IsNull(root);
++count;
}
}
}
else if (ECAlgorithms.IsF2mCurve(c))
{
int m = c.FieldSize;
BigInteger x = new BigInteger(m, secRand);
ECFieldElement fe = c.FromBigInteger(x);
for (int i = 0; i < 100; ++i)
{
ECFieldElement sq = fe.Square();
ECFieldElement check = sq.Sqrt();
Assert.AreEqual(fe, check);
fe = sq;
}
}
}
public override ECPoint Add(ECPoint b)
{
if (base.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
ECCurve curve = this.Curve;
int coordinateSystem = curve.CoordinateSystem;
ECFieldElement rawXCoord = base.RawXCoord;
ECFieldElement rawXCoord2 = b.RawXCoord;
int num = coordinateSystem;
switch (num)
{
case 0:
{
ECFieldElement rawYCoord = base.RawYCoord;
ECFieldElement rawYCoord2 = b.RawYCoord;
ECFieldElement eCFieldElement = rawXCoord.Add(rawXCoord2);
ECFieldElement eCFieldElement2 = rawYCoord.Add(rawYCoord2);
if (!eCFieldElement.IsZero)
{
ECFieldElement eCFieldElement3 = eCFieldElement2.Divide(eCFieldElement);
ECFieldElement eCFieldElement4 = eCFieldElement3.Square().Add(eCFieldElement3).Add(eCFieldElement).Add(curve.A);
ECFieldElement y = eCFieldElement3.Multiply(rawXCoord.Add(eCFieldElement4)).Add(eCFieldElement4).Add(rawYCoord);
return(new F2mPoint(curve, eCFieldElement4, y, base.IsCompressed));
}
if (eCFieldElement2.IsZero)
{
return(this.Twice());
}
return(curve.Infinity);
}
case 1:
{
ECFieldElement rawYCoord3 = base.RawYCoord;
ECFieldElement eCFieldElement5 = base.RawZCoords[0];
ECFieldElement rawYCoord4 = b.RawYCoord;
ECFieldElement eCFieldElement6 = b.RawZCoords[0];
bool isOne = eCFieldElement5.IsOne;
ECFieldElement eCFieldElement7 = rawYCoord4;
ECFieldElement eCFieldElement8 = rawXCoord2;
if (!isOne)
{
eCFieldElement7 = eCFieldElement7.Multiply(eCFieldElement5);
eCFieldElement8 = eCFieldElement8.Multiply(eCFieldElement5);
}
bool isOne2 = eCFieldElement6.IsOne;
ECFieldElement eCFieldElement9 = rawYCoord3;
ECFieldElement eCFieldElement10 = rawXCoord;
if (!isOne2)
{
eCFieldElement9 = eCFieldElement9.Multiply(eCFieldElement6);
eCFieldElement10 = eCFieldElement10.Multiply(eCFieldElement6);
}
ECFieldElement eCFieldElement11 = eCFieldElement7.Add(eCFieldElement9);
ECFieldElement eCFieldElement12 = eCFieldElement8.Add(eCFieldElement10);
if (!eCFieldElement12.IsZero)
{
ECFieldElement eCFieldElement13 = eCFieldElement12.Square();
ECFieldElement eCFieldElement14 = eCFieldElement13.Multiply(eCFieldElement12);
ECFieldElement b2 = isOne ? eCFieldElement6 : (isOne2 ? eCFieldElement5 : eCFieldElement5.Multiply(eCFieldElement6));
ECFieldElement eCFieldElement15 = eCFieldElement11.Add(eCFieldElement12);
ECFieldElement eCFieldElement16 = eCFieldElement15.MultiplyPlusProduct(eCFieldElement11, eCFieldElement13, curve.A).Multiply(b2).Add(eCFieldElement14);
ECFieldElement x = eCFieldElement12.Multiply(eCFieldElement16);
ECFieldElement b3 = isOne2 ? eCFieldElement13 : eCFieldElement13.Multiply(eCFieldElement6);
ECFieldElement y2 = eCFieldElement11.MultiplyPlusProduct(rawXCoord, eCFieldElement12, rawYCoord3).MultiplyPlusProduct(b3, eCFieldElement15, eCFieldElement16);
ECFieldElement eCFieldElement17 = eCFieldElement14.Multiply(b2);
return(new F2mPoint(curve, x, y2, new ECFieldElement[]
{
eCFieldElement17
}, base.IsCompressed));
}
if (eCFieldElement11.IsZero)
{
return(this.Twice());
}
return(curve.Infinity);
}
default:
if (num != 6)
{
throw new InvalidOperationException("unsupported coordinate system");
}
if (rawXCoord.IsZero)
{
if (rawXCoord2.IsZero)
{
return(curve.Infinity);
}
return(b.Add(this));
}
else
{
ECFieldElement rawYCoord5 = base.RawYCoord;
ECFieldElement eCFieldElement18 = base.RawZCoords[0];
ECFieldElement rawYCoord6 = b.RawYCoord;
ECFieldElement eCFieldElement19 = b.RawZCoords[0];
bool isOne3 = eCFieldElement18.IsOne;
ECFieldElement eCFieldElement20 = rawXCoord2;
ECFieldElement eCFieldElement21 = rawYCoord6;
if (!isOne3)
{
eCFieldElement20 = eCFieldElement20.Multiply(eCFieldElement18);
eCFieldElement21 = eCFieldElement21.Multiply(eCFieldElement18);
}
bool isOne4 = eCFieldElement19.IsOne;
ECFieldElement eCFieldElement22 = rawXCoord;
ECFieldElement eCFieldElement23 = rawYCoord5;
if (!isOne4)
{
eCFieldElement22 = eCFieldElement22.Multiply(eCFieldElement19);
eCFieldElement23 = eCFieldElement23.Multiply(eCFieldElement19);
}
ECFieldElement eCFieldElement24 = eCFieldElement23.Add(eCFieldElement21);
ECFieldElement eCFieldElement25 = eCFieldElement22.Add(eCFieldElement20);
if (!eCFieldElement25.IsZero)
{
ECFieldElement eCFieldElement27;
ECFieldElement y3;
ECFieldElement eCFieldElement29;
if (rawXCoord2.IsZero)
{
ECPoint eCPoint = this.Normalize();
rawXCoord = eCPoint.RawXCoord;
ECFieldElement yCoord = eCPoint.YCoord;
ECFieldElement b4 = rawYCoord6;
ECFieldElement eCFieldElement26 = yCoord.Add(b4).Divide(rawXCoord);
eCFieldElement27 = eCFieldElement26.Square().Add(eCFieldElement26).Add(rawXCoord).Add(curve.A);
if (eCFieldElement27.IsZero)
{
return(new F2mPoint(curve, eCFieldElement27, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement28 = eCFieldElement26.Multiply(rawXCoord.Add(eCFieldElement27)).Add(eCFieldElement27).Add(yCoord);
y3 = eCFieldElement28.Divide(eCFieldElement27).Add(eCFieldElement27);
eCFieldElement29 = curve.FromBigInteger(BigInteger.One);
}
else
{
eCFieldElement25 = eCFieldElement25.Square();
ECFieldElement eCFieldElement30 = eCFieldElement24.Multiply(eCFieldElement22);
ECFieldElement eCFieldElement31 = eCFieldElement24.Multiply(eCFieldElement20);
eCFieldElement27 = eCFieldElement30.Multiply(eCFieldElement31);
if (eCFieldElement27.IsZero)
{
return(new F2mPoint(curve, eCFieldElement27, curve.B.Sqrt(), base.IsCompressed));
}
ECFieldElement eCFieldElement32 = eCFieldElement24.Multiply(eCFieldElement25);
if (!isOne4)
{
eCFieldElement32 = eCFieldElement32.Multiply(eCFieldElement19);
}
y3 = eCFieldElement31.Add(eCFieldElement25).SquarePlusProduct(eCFieldElement32, rawYCoord5.Add(eCFieldElement18));
eCFieldElement29 = eCFieldElement32;
if (!isOne3)
{
eCFieldElement29 = eCFieldElement29.Multiply(eCFieldElement18);
}
}
return(new F2mPoint(curve, eCFieldElement27, y3, new ECFieldElement[]
{
eCFieldElement29
}, base.IsCompressed));
}
if (eCFieldElement24.IsZero)
{
return(this.Twice());
}
return(curve.Infinity);
}
break;
}
}