public FastECPoint Multiply(FastInteger b)
{
if (b.Sign == -1)
{
throw new FormatException("The multiplicator cannot be negative");
}
//b = b % Secp256k1.N;
FastInteger exp = (b * 3) ^ b;
FastECPoint result = FastECPoint.Infinity;
FastECPoint affine = this.Normalize();
FastECPoint negative = affine.Negate();
int high = exp.BitsCount;
FastInteger bit = FastInteger.One << high;
for (int i = high; --i >= 0; bit >>= 1)
{
result = result.Twice();
if (!(exp & bit).IsZero)
{
result = result.Add(!(b & bit).IsZero ? negative : affine);
}
}
result = result.Normalize();
return(result);
}
public FastInteger ModPow(FastInteger power, FastInteger prime, Func <FastInteger, FastInteger> modPFunction)
{
FastInteger a = this;
if (power.IsNegative)
{
a = a.ModInverse(prime);
power = -power;
}
int highestBitPosition = power.Digits * 31 - 1;
while (highestBitPosition >= 0 && !power.GetBitAt(highestBitPosition))
{
highestBitPosition--;
}
FastInteger result = highestBitPosition < 0 ? One : a;
for (int i = highestBitPosition; --i >= 0;)
{
result = modPFunction(result.Square());
if (power.GetBitAt(i))
{
result = modPFunction(result * a);
}
}
var diff = result - prime;
return(diff.IsNegative ? result : diff);
}
private static void remodP(ref FastInteger x)
{
while (x >= Secp256k1.FP)
{
x -= Secp256k1.FP;
}
while (x < 0)
{
x += Secp256k1.FP;
}
}
private static FastInteger modP(FastInteger x)
{
while (true)
{
var high = x >> 256;
if (high.IsZero)
{
return(x);
}
x = (x & LowMask) + high * 0x1000003D1;
}
}
public FastInteger ShanksSqrt(FastInteger p, Func <FastInteger, FastInteger> modPFunction)
{
if (this.ModPow((p - 1) >> 1, p, modPFunction) == (p - 1))
{
return(-1);
} //No Sqrt Exists
if ((p.LowestByte & 3) == 3)
{
var result = this.ModPow((p + 1) >> 2, p, modPFunction);
return(result);
}
throw new NotImplementedException("Not a special prime modulo.");
}
/// <summary>
/// return this / n modulo p.
/// </summary>
/// <param name="n"></param>
/// <param name="p"></param>
/// <returns></returns>
public FastInteger DivideModulo(FastInteger n, FastInteger p)
{
if (n.IsZero)
{
return(n);
}
if (p.IsZero)
{
return(p);
}
FastInteger a = this; //x * a + u1 * b = n
FastInteger c = 0; //y * c + u2 * d = p
FastInteger x = n;
while (p.IsEven)
{
p >>= 1;
}
FastInteger y = p;
while (x.IsEven)
{
x >>= 1;
a = a.IsEven ? a >> 1 : (a + p) >> 1;
}
while (!x.IsZero)
{
while (x.IsEven)
{
x >>= 1;
a = a.IsEven ? a >> 1 : (a + p) >> 1;
}
FastInteger diff = x - y;
if (diff.IsNegative)
{
y = x;
x = -diff;
FastInteger temp = a; a = c; c = temp;
}
else
{
x = diff;
}
a -= c;
if (a.IsNegative)
{
a += p;
}
}
return(c);
}
public static byte[] ToByteArrayUnsigned(this FastInteger i, bool bigEndian)
{
byte[] bytes = i.ToByteArray();
int length = bytes.Length;
while (length > 1 && ((bytes[length - 1] == 0 && bytes[length - 2] < 128) || (bytes[length - 1] == 255 && bytes[length - 2] >= 128)))
{
length--;
}
Array.Resize(ref bytes, length);
if (bigEndian)
{
Array.Reverse(bytes, 0, bytes.Length);
}
return(bytes);
}
public static FastInteger operator +(FastInteger number1, FastInteger number2)
{
int digits1 = number1.Digits;
int digits2 = number2.Digits;
if (digits1 < digits2)
{
int temp1 = digits1; digits1 = digits2; digits2 = temp1;
FastInteger temp2 = number1; number1 = number2; number2 = temp2;
}
if (number2.IsZero)
{
return(number1);
}
int bitcount = 1 + Math.Max(number1.BitsCount, number2.BitsCount);
int[] result = new int[(bitcount + 30) / 31];
int carry = 0;
for (int i = 0; i < digits2; i++)
{
carry += (number1.bits[i] & LowMask) + (number2.bits[i] & LowMask);
result[i] = carry & LowMask;
carry = (carry >> 31) & 1;
}
for (int i = digits2; i < digits1; i++)
{
carry += (number1.bits[i] & LowMask) + number2.Extender;
result[i] = carry & LowMask;
carry = (carry >> 31) & 1;
}
carry += (number1.IsNegative ? -1 : 0) + (number2.IsNegative ? -1 : 0);
if (carry == -1)
{
result[digits1 - 1] |= -1 << 31;
}
if (digits1 < result.Length)
{
result[digits1] = carry;
}
return(new FastInteger(result));
}
public static FastInteger operator ^(FastInteger x, FastInteger y)
{
if (x.Digits < y.Digits)
{
FastInteger temp = x; x = y; y = temp;
}
if (y.IsZero)
{
return(x);
}
int[] result = new int[x.Digits];
for (int i = y.Digits; --i >= 0;)
{
result[i] = (x.bits[i] ^ y.bits[i]) & LowMask;
}
for (int i = y.Digits; i < x.Digits; i++)
{
result[i] = (x.bits[i] ^ y.Extender) & LowMask;
}
result[result.Length - 1] |= (x.Extender ^ y.Extender) << 31;
return(new FastInteger(result));
}
public FastECPoint(byte[] bytes, bool isCompressed)
{
this._x = bytes.Take(256 / 8).ToFastIntegerUnsigned(false);
if (isCompressed)
{
var x2 = modP(this.X.Square());
var x3 = modP(x2 * this.X);
this._y = (x3 + 7).ShanksSqrt(Secp256k1.FP, modP);
byte lowerY = this._y.LowestByte;
if (lowerY != bytes[256 / 8])
{
this._y = Secp256k1.FP - this._y;
lowerY = this._y.LowestByte;
if (lowerY != bytes[256 / 8])
{
throw new InvalidOperationException("Compressed bytes verification byte failed.");
}
}
}
else
{
this._y = bytes.Skip(256 / 8).Take(256 / 8).ToFastIntegerUnsigned(false);
}
}
public override string ToString()
{
FastInteger x = this;
bool negative = x.IsNegative;
if (negative)
{
x = -x;
}
StringBuilder sb = new StringBuilder();
int[] bits = new int[x.bits.Length];
x.bits.CopyTo(bits, 0);
do
{
long mod = 0;
for (int i = bits.Length; --i >= 0;)
{
mod = (mod << 31) + bits[i];
bits[i] = (int)Math.DivRem(mod, 10L, out mod);
}
sb.Append((char)('0' + mod));
} while (bits.Any(b => b != 0));
if (negative)
{
sb.Append('-');
}
for (int i = 0, j = sb.Length - 1; i < j; i++, j--)
{
char c = sb[i];
sb[i] = sb[j];
sb[j] = c;
}
return(sb.ToString());
}
public FastInteger ModInverse(FastInteger p)
{
return(One.DivideModulo(this, p));
}
public static FastInteger ToFastInteger(this ulong[] bits)
{
FastInteger result = new FastInteger(bits.SelectMany(l => BitConverter.GetBytes(l)).Concat(Enumerable.Repeat((byte)0, 1)).ToArray());
return(result);
}
public FastECPoint(FastInteger x, FastInteger y, bool isInfinity)
{
_x = x;
_y = y;
_isInfinity = isInfinity;
}
public static FastInteger Abs(FastInteger number)
{
return(number.IsNegative ? -number : number);
}
public static bool UnitTest()
{
Random random = new Random(1001);
for (int i = 10000; --i >= 0;)
{
byte[] bytes1 = new byte[31 + random.Next(2)];
byte[] bytes2 = new byte[31 + random.Next(2)];
random.NextBytes(bytes1);
random.NextBytes(bytes2);
BigInteger n1 = new BigInteger(bytes1);
BigInteger n2 = new BigInteger(bytes2);
FastInteger f1 = new FastInteger(bytes1);
FastInteger f2 = new FastInteger(bytes2);
if (n1.ToString() != f1.ToString())
{
System.Diagnostics.Debugger.Break();
}
if (n2.ToString() != f2.ToString())
{
System.Diagnostics.Debugger.Break();
}
BigInteger a1 = n1 + n2;
FastInteger a2 = f1 + f2;
if (a1.ToString() != a2.ToString())
{
var by1 = a1.ToByteArray();
var by2 = a2.ToByteArray();
System.Diagnostics.Debugger.Break();
}
BigInteger s1 = n1 - n2;
FastInteger s2 = f1 - f2;
if (s1.ToString() != s2.ToString())
{
var by1 = s1.ToByteArray();
var by2 = s2.ToByteArray();
System.Diagnostics.Debugger.Break();
}
BigInteger m1 = n1 * n2;
FastInteger m2 = f1 * f2;
if (m1.ToString() != m2.ToString())
{
System.Diagnostics.Debugger.Break();
}
int shrvalue = random.Next(256) + 1;
BigInteger sh1 = n1 >> shrvalue;
FastInteger sh2 = f1 >> shrvalue;
if (sh1.ToString() != sh2.ToString())
{
System.Diagnostics.Debugger.Break();
}
if ((-f1).ToString() != (-n1).ToString() || (-f2).ToString() != (-n2).ToString())
{
System.Diagnostics.Debugger.Break();
}
int shlvalue = random.Next(256) + 1;
BigInteger shl1 = n1 << shlvalue;
FastInteger shl2 = f1 << shlvalue;
if (shl1.ToString() != shl2.ToString())
{
System.Diagnostics.Debugger.Break();
}
BigInteger and1 = n1 & n2;
FastInteger and2 = f1 & f2;
if (and1.ToString() != and2.ToString())
{
System.Diagnostics.Debugger.Break();
}
BigInteger xor1 = n1 ^ n2;
FastInteger xor2 = f1 ^ f2;
if (xor1.ToString() != xor2.ToString())
{
System.Diagnostics.Debugger.Break();
}
}
return(true);
}
public static FastInteger Square(this FastInteger x)
{
return(x * x);
}
public FastECPoint(FastInteger x, FastInteger y)
{
_x = x;
_y = y;
}
public FastECPoint(FastInteger x, FastInteger y, FastInteger z, bool isInfinity) : this(x, y, isInfinity)
{
_z = z;
}
public static string FastIntegerToHex(FastInteger value)
{
return(BytesToHex(value.ToByteArrayUnsigned(true)));
}
public static string ToHex(this FastInteger b)
{
return(Hex.FastIntegerToHex(b));
}