//сложение точки P c собой же public static ECPoint Double(ECPoint p) { ECPoint p2 = new ECPoint(); p2.a = p.a; p2.b = p.b; p2.FieldChar = p.FieldChar; BigInteger dy = 3 * p.x * p.x + p.a; BigInteger dx = 2 * p.y; if (dx < 0) dx += p.FieldChar; if (dy < 0) dy += p.FieldChar; BigInteger m = (dy * modInverse(dx, p.FieldChar)) % p.FieldChar; p2.x = (m * m - p.x - p.x) % p.FieldChar; p2.y = (m * (p.x - p2.x) - p.y) % p.FieldChar; if (p2.x < 0) p2.x += p.FieldChar; if (p2.y < 0) p2.y += p.FieldChar; return p2; }
//сложение двух точек P1 и P2 public static ECPoint operator +(ECPoint leftPoint, ECPoint rightPoint) { ECPoint resultPoint = new ECPoint(); resultPoint.a = leftPoint.a; resultPoint.b = leftPoint.b; resultPoint.FieldChar = leftPoint.FieldChar; BigInteger dy = rightPoint.y - leftPoint.y; BigInteger dx = rightPoint.x - leftPoint.x; if (dx < 0) dx += leftPoint.FieldChar; if (dy < 0) dy += leftPoint.FieldChar; BigInteger m = (dy * modInverse(dx, leftPoint.FieldChar)) % leftPoint.FieldChar; if (m < 0) m += leftPoint.FieldChar; resultPoint.x = (m * m - leftPoint.x - rightPoint.x) % leftPoint.FieldChar; resultPoint.y = (m * (leftPoint.x - resultPoint.x) - leftPoint.y) % leftPoint.FieldChar; if (resultPoint.x < 0) resultPoint.x += leftPoint.FieldChar; if (resultPoint.y < 0) resultPoint.y += leftPoint.FieldChar; return resultPoint; }
//сложение двух точек P1 и P2 public static ECPoint operator +(ECPoint p1, ECPoint p2) { ECPoint p3 = new ECPoint(); p3.a = p1.a; p3.b = p1.b; p3.FieldChar = p1.FieldChar; BigInteger dy = p2.y - p1.y; BigInteger dx = p2.x - p1.x; if (dx < 0) dx += p1.FieldChar; if (dy < 0) dy += p1.FieldChar; BigInteger m = (dy * dx.modInverse(p1.FieldChar)) % p1.FieldChar; if (m < 0) m += p1.FieldChar; p3.x = (m * m - p1.x - p2.x) % p1.FieldChar; p3.y = (m * (p1.x - p3.x) - p1.y) % p1.FieldChar; if (p3.x < 0) p3.x += p1.FieldChar; if (p3.y < 0) p3.y += p1.FieldChar; return p3; }
public ECPoint(ECPoint p) { x = p.x; y = p.y; a = p.a; b = p.b; FieldChar = p.FieldChar; }
//Восстанавливаем координату y из координаты x и бита четности y private ECPoint GDecompression() { byte y = xG[0]; byte[] x=new byte[xG.Length-1]; Array.Copy(xG, 1, x, 0, xG.Length - 1); BigInteger Xcord = new BigInteger(x); BigInteger temp = (Xcord * Xcord * Xcord + a * Xcord + b) % p; BigInteger beta = ModSqrt(temp, p); BigInteger Ycord = new BigInteger(); if ((beta % 2) == (y % 2)) Ycord = beta; else Ycord = p - beta; ECPoint G = new ECPoint(); G.a = a; G.b = b; G.FieldChar = p; G.x = Xcord; G.y = Ycord; this.G = G; return G; }
//проверяем подпись public bool SingVer(byte[] H, string sing, ECPoint Q) { string Rvector = sing.Substring(0, n.bitCount() / 4); string Svector = sing.Substring(n.bitCount() / 4, n.bitCount() / 4); BigInteger r = new BigInteger(Rvector, 16); BigInteger s = new BigInteger(Svector, 16); if ((r < 1) || (r > (n - 1)) || (s < 1) || (s > (n - 1))) return false; BigInteger alpha = new BigInteger(H); BigInteger e = alpha % n; if (e == 0) e = 1; BigInteger v = e.modInverse(n); BigInteger z1 = (s * v) % n; BigInteger z2 = n + ((-(r * v)) % n); this.G = GDecompression(); ECPoint A = ECPoint.multiply(z1, G); ECPoint B = ECPoint.multiply(z2, Q); ECPoint C = A + B; BigInteger R = C.x % n; if (R == r) return true; else return false; }
//подписываем сообщение public string SingGen(byte[] h, BigInteger d) { BigInteger alpha = new BigInteger(h); BigInteger e = alpha % n; if (e == 0) e = 1; BigInteger k = new BigInteger(); ECPoint C=new ECPoint(); BigInteger r=new BigInteger(); BigInteger s = new BigInteger(); do { do { k.genRandomBits(n.bitCount(), new Random()); } while ((k < 0) || (k > n)); C = ECPoint.multiply(k, G); r = C.x % n; s = ((r * d) + (k * e)) % n; } while ((r == 0)||(s==0)); string Rvector = padding(r.ToHexString(),n.bitCount()/4); string Svector = padding(s.ToHexString(), n.bitCount() / 4); return Rvector + Svector; }
//умножение точки на число x, по сути своей представляет x сложений точки самой с собой public static ECPoint Multiply(BigInteger x, ECPoint p) { ECPoint temp = p; x = x - 1; while (x != 0) { if ((x % 2) != 0) { if ((temp.x == p.x) || (temp.y == p.y)) temp = Double(temp); else temp = temp + p; x = x - 1; } x = x / 2; p = Double(p); } return temp; }
public override string Encrypt(string text) { p = new BigInteger("6277101735386680763835789423207666416083908700390324961279", 10); a = new BigInteger("-3", 10); b = new BigInteger("64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1", 16); xG = FromHexStringToByte("03188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012"); n = new BigInteger("ffffffffffffffffffffffff99def836146bc9b1b4d22831", 16); BigInteger d = GenPrivateKey(192); Q = GenPublicKey(d); GOST hash = new GOST(256); byte[] H = hash.GetHash(Encoding.Default.GetBytes(text)); signature = GenerateSignature(H, d); return signature; }