...
I could swear that
^n means raising to the power of n. But, it turns out that it doesn't. It actually means
index from end operator. As for the missing parts, I didn't know them. I was only following the ruby scripts from learnmeabitcoin. Thanks for the time it took you to correct me.
I would say it is
Logical exclusive OR operator ^.
I did make the changes, but still get false result. For k=100 I should be getting:
Test it step by step:
Is ECdouble giving the correct result for G, 2G, O?
Is ECaddition doing it as well: G+G, G+(-G), G+2G, 2G+3G, 3G+4G?
Finally is ECMultiplication correct for small numbers (1-10), for big numbers (n-1), for numbers >=n ?
Your inverse function is still wrong. You could give up and use the simpler (but slower) version:
public static BigInteger inverse(BigInteger a, BigInteger m)
{
return BigInteger.ModPow(a, m - 2, m);
}
Looking at your struggle is just painful. Here is working code.
using System;
using System.Numerics;
public class Program
{
static BigInteger p = BigInteger.Parse("115792089237316195423570985008687907853269984665640564039457584007908834671663");
static BigInteger n = BigInteger.Parse("115792089237316195423570985008687907852837564279074904382605163141518161494337");
static BigInteger[] zero = {0,0};
static BigInteger[] g = {
BigInteger.Parse("55066263022277343669578718895168534326250603453777594175500187360389116729240"),
BigInteger.Parse("32670510020758816978083085130507043184471273380659243275938904335757337482424")
};
public static void Main()
{
BigInteger[] g0 = {0,0}, g2 = ECdouble(g), g4 = ECdouble(g2);
BigInteger[] z = ECMultiplication(7, g);
//z = ECaddition(z, g);
//z = ECaddition(z, g2);
//z = ECaddition(z, g4);
Console.WriteLine(z[0].ToString());
Console.WriteLine(z[1].ToString());
Console.WriteLine(IsOnCurve(z));
Console.WriteLine(IsOnCurve(zero));
}
public static BigInteger inverse(BigInteger a, BigInteger m) { return BigInteger.ModPow(a, m-2, m); }
public static BigInteger[] ECdouble(BigInteger[] point)
{
if (point[1] == 0) return zero;
BigInteger slope = (3 * BigInteger.ModPow(point[0], 2, p) * inverse((2 * point[1]), p)) % p;
BigInteger x = (BigInteger.ModPow(slope, 2, p) - (2 * point[0])) % p;
BigInteger y = (slope * (point[0] - x) - point[1]) % p;
if (x < 0) x += p;
if (y < 0) y += p;
BigInteger[] coord = { x, y };
return coord;
}
public static BigInteger[] ECaddition(BigInteger[] point1, BigInteger[] point2)
{
if (point1[1] == 0) return point2;
if (point2[1] == 0) return point1;
if (point1[0] == point2[0]) {
if (point1[1] == point2[1]) return ECdouble(point1);
return zero;
}
BigInteger slope = ((point2[1] - point1[1]) * inverse(point2[0] - point1[0], p)) % p;
BigInteger x = (BigInteger.ModPow(slope, 2, p) - point1[0] - point2[0]) % p;
BigInteger y = ((slope * (point1[0] - x)) - point1[1]) % p;
if (x < 0) x += p;
if (y < 0) y += p;
BigInteger[] coord = { x, y };
return coord;
}
public static BigInteger[] ECMultiplication(BigInteger k, BigInteger[] Gpoint)
{
BigInteger[] powerOfTwo = Gpoint;
BigInteger[] result = zero;
k %= n; if (k < 0) k += n;
while (k > 0) {
if ((k&1) == 1) result = ECaddition(result, powerOfTwo);
k >>= 1;
powerOfTwo = ECdouble(powerOfTwo);
}
return result;
}
public static bool IsOnCurve(BigInteger[] point)
{
BigInteger x = point[0] % p; if (x<0) x += p;
BigInteger y = point[1] % p; if (y<0) y += p;
return BigInteger.ModPow(y, 2, p) == (BigInteger.ModPow(x, 3, p) + 7) % p;
}
}
Seems like it should be "a<0" as per the Ruby example.
