public static BigInteger ModOddInverse(BigInteger M, BigInteger X)
{
if (!M.TestBit(0))
{
throw new ArgumentException("must be odd", "M");
}
if (M.SignValue != 1)
{
throw new ArithmeticException("BigInteger: modulus not positive");
}
if (X.SignValue < 0 || X.CompareTo(M) >= 0)
{
X = X.Mod(M);
}
int bits = M.BitLength;
uint[] m = Nat.FromBigInteger(bits, M);
uint[] x = Nat.FromBigInteger(bits, X);
int len = m.Length;
uint[] z = Nat.Create(len);
if (0 == Mod.ModOddInverse(m, x, z))
{
throw new ArithmeticException("BigInteger not invertible");
}
return(Nat.ToBigInteger(len, z));
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(160, x);
if (z[4] == P4 && Nat160.Gte(z, P))
{
Nat160.SubFrom(P, z);
}
return(z);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(192, x);
if (z[5] == P5 && Nat192.Gte(z, P))
{
Nat192.SubFrom(P, z);
}
return(z);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(256, x);
if (z[7] == P7 && Nat256.Gte(z, P))
{
Nat256.SubFrom(P, z);
}
return(z);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] numArray = Nat.FromBigInteger(0x209, x);
if (Nat.Eq(0x11, numArray, P))
{
Nat.Zero(0x11, numArray);
}
return(numArray);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(384, x);
if (z[11] == P11 && Nat.Gte(12, z, P))
{
Nat.SubFrom(12, P, z);
}
return(z);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] array = Nat.FromBigInteger(384, x);
if (array[11] == 4294967295u && Nat.Gte(12, array, SecP384R1Field.P))
{
Nat.SubFrom(12, SecP384R1Field.P, array);
}
return(array);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] array = Nat.FromBigInteger(521, x);
if (Nat.Eq(17, array, P))
{
Nat.Zero(17, array);
}
return(array);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] numArray = Nat.FromBigInteger(0x180, x);
if ((numArray[11] == uint.MaxValue) && Nat.Gte(12, numArray, P))
{
Nat.SubFrom(12, P, numArray);
}
return(numArray);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(521, x);
if (Nat.Eq(17, z, P))
{
Nat.Zero(17, z);
}
return(z);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] array = Nat.FromBigInteger(384, x);
if (array[11] == uint.MaxValue && Nat.Gte(12, array, P))
{
Nat.SubFrom(12, P, array);
}
return(array);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(256, x);
while (Nat256.Gte(z, P))
{
Nat256.SubFrom(P, z);
}
return(z);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(224, x);
if (z[6] == P6 && Nat224.Gte(z, P))
{
Nat224.SubFrom(P, z);
}
return(z);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(128, x);
if (z[3] >= P3 && Nat128.Gte(z, P))
{
Nat128.SubFrom(P, z);
}
return(z);
}
protected virtual BigInteger ModInverse(BigInteger x)
{
int bits = FieldSize;
int len = (bits + 31) >> 5;
uint[] p = Nat.FromBigInteger(bits, q);
uint[] n = Nat.FromBigInteger(bits, x);
uint[] z = Nat.Create(len);
Mod.Invert(p, n, z);
return(Nat.ToBigInteger(len, z));
}
protected virtual BigInteger ModInverse(BigInteger x)
{
int fieldSize = FieldSize;
int len = fieldSize + 31 >> 5;
uint[] p = Nat.FromBigInteger(fieldSize, q);
uint[] array = Nat.FromBigInteger(fieldSize, x);
uint[] z = Nat.Create(len);
Mod.Invert(p, array, z);
return(Nat.ToBigInteger(len, z));
}
protected virtual BigInteger ModInverse(BigInteger x)
{
var bits = this.FieldSize;
var len = (bits + 31) >> 5;
var p = Nat.FromBigInteger(bits, this.Q);
var n = Nat.FromBigInteger(bits, x);
var z = Nat.Create(len);
Mod.Invert(p, n, z);
return(Nat.ToBigInteger(len, z));
}
protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
{
ECCurve c = p.Curve;
int size = FixedPointUtilities.GetCombSize(c);
if (k.BitLength > size)
{
/*
* TODO The comb works best when the scalars are less than the (possibly unknown) order.
* Still, if we want to handle larger scalars, we could allow customization of the comb
* size, or alternatively we could deal with the 'extra' bits either by running the comb
* multiple times as necessary, or by using an alternative multiplier as prelude.
*/
throw new InvalidOperationException("fixed-point comb doesn't support scalars larger than the curve order");
}
FixedPointPreCompInfo info = FixedPointUtilities.Precompute(p);
ECLookupTable lookupTable = info.LookupTable;
int width = info.Width;
int d = (size + width - 1) / width;
ECPoint R = c.Infinity;
int fullComb = d * width;
uint[] K = Nat.FromBigInteger(fullComb, k);
int top = fullComb - 1;
for (int i = 0; i < d; ++i)
{
uint secretIndex = 0;
for (int j = top - i; j >= 0; j -= d)
{
uint secretBit = K[j >> 5] >> (j & 0x1F);
secretIndex ^= secretBit >> 1;
secretIndex <<= 1;
secretIndex ^= secretBit;
}
ECPoint add = lookupTable.Lookup((int)secretIndex);
R = R.TwicePlus(add);
}
return(R.Add(info.Offset));
}
private static int Legendre(BigInteger a, BigInteger b)
{
//int r = 0, bits = b.IntValue;
//for (;;)
//{
// int lowestSetBit = a.GetLowestSetBit();
// a = a.ShiftRight(lowestSetBit);
// r ^= (bits ^ (bits >> 1)) & (lowestSetBit << 1);
// int cmp = a.CompareTo(b);
// if (cmp == 0)
// break;
// if (cmp < 0)
// {
// BigInteger t = a; a = b; b = t;
// int oldBits = bits;
// bits = b.IntValue;
// r ^= oldBits & bits;
// }
// a = a.Subtract(b);
//}
//return BigInteger.One.Equals(b) ? (1 - (r & 2)) : 0;
int bitLength = b.BitLength;
uint[] A = Nat.FromBigInteger(bitLength, a);
uint[] B = Nat.FromBigInteger(bitLength, b);
int r = 0;
int len = B.Length;
for (;;)
{
while (A[0] == 0)
{
Nat.ShiftDownWord(len, A, 0);
}
int shift = Integers.NumberOfTrailingZeros((int)A[0]);
if (shift > 0)
{
Nat.ShiftDownBits(len, A, shift, 0);
int bits = (int)B[0];
r ^= (bits ^ (bits >> 1)) & (shift << 1);
}
int cmp = Nat.Compare(len, A, B);
if (cmp == 0)
{
break;
}
if (cmp < 0)
{
r ^= (int)(A[0] & B[0]);
uint[] t = A; A = B; B = t;
}
while (A[len - 1] == 0)
{
len = len - 1;
}
Nat.Sub(len, A, B, A);
}
return(Nat.IsOne(len, B) ? (1 - (r & 2)) : 0);
}
private static ECPoint ImplShamirsTrickFixedPoint(ECPoint p, BigInteger k, ECPoint q, BigInteger l)
{
ECCurve c = p.Curve;
int combSize = FixedPointUtilities.GetCombSize(c);
if (k.BitLength > combSize || l.BitLength > combSize)
{
/*
* TODO The comb works best when the scalars are less than the (possibly unknown) order.
* Still, if we want to handle larger scalars, we could allow customization of the comb
* size, or alternatively we could deal with the 'extra' bits either by running the comb
* multiple times as necessary, or by using an alternative multiplier as prelude.
*/
throw new InvalidOperationException("fixed-point comb doesn't support scalars larger than the curve order");
}
FixedPointPreCompInfo infoP = FixedPointUtilities.Precompute(p);
FixedPointPreCompInfo infoQ = FixedPointUtilities.Precompute(q);
ECLookupTable lookupTableP = infoP.LookupTable;
ECLookupTable lookupTableQ = infoQ.LookupTable;
int widthP = infoP.Width;
int widthQ = infoQ.Width;
// TODO This shouldn't normally happen, but a better "solution" is desirable anyway
if (widthP != widthQ)
{
FixedPointCombMultiplier m = new FixedPointCombMultiplier();
ECPoint r1 = m.Multiply(p, k);
ECPoint r2 = m.Multiply(q, l);
return(r1.Add(r2));
}
int width = widthP;
int d = (combSize + width - 1) / width;
ECPoint R = c.Infinity;
int fullComb = d * width;
uint[] K = Nat.FromBigInteger(fullComb, k);
uint[] L = Nat.FromBigInteger(fullComb, l);
int top = fullComb - 1;
for (int i = 0; i < d; ++i)
{
uint secretIndexK = 0, secretIndexL = 0;
for (int j = top - i; j >= 0; j -= d)
{
uint secretBitK = K[j >> 5] >> (j & 0x1F);
secretIndexK ^= secretBitK >> 1;
secretIndexK <<= 1;
secretIndexK ^= secretBitK;
uint secretBitL = L[j >> 5] >> (j & 0x1F);
secretIndexL ^= secretBitL >> 1;
secretIndexL <<= 1;
secretIndexL ^= secretBitL;
}
ECPoint addP = lookupTableP.LookupVar((int)secretIndexK);
ECPoint addQ = lookupTableQ.LookupVar((int)secretIndexL);
ECPoint T = addP.Add(addQ);
R = R.TwicePlus(T);
}
return(R.Add(infoP.Offset).Add(infoQ.Offset));
}