//функция вычисления квадратоного корня по модулю простого числа q public BInteger ModSqrt(BInteger a, BInteger q) { BInteger b = new BInteger(); do { b.genRandomBits(255, new Random()); } while (Legendre(b, q) == 1); BInteger s = 0; BInteger t = q - 1; while ((t & 1) != 1) { s++; t = t >> 1; } BInteger InvA = a.modInverse(q); BInteger c = b.modPow(t, q); BInteger r = a.modPow(((t + 1) / 2), q); BInteger d = new BInteger(); for (int i = 1; i < s; i++) { BInteger temp = 2; temp = temp.modPow((s - i - 1), q); d = (r.modPow(2, q) * InvA).modPow(temp, q); if (d == (q - 1)) r = (r * c) % q; c = c.modPow(2, q); } return r; }
//подписываем сообщение public string SingGen(byte[] h, BInteger d) { BInteger alpha = new BInteger(h); BInteger e = alpha % n; if (e == 0) e = 1; BInteger k = new BInteger(); ECPoint C = new ECPoint(); BInteger r = new BInteger(); BInteger s = new BInteger(); 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; }
public static void SqrtTest(int rounds) { Random rand = new Random(); for (int count = 0; count < rounds; count++) { // generate data of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 1024); Console.Write("Round = " + count); BInteger a = new BInteger(); a.genRandomBits(t1, rand); BInteger b = a.sqrt(); BInteger c = (b + 1) * (b + 1); // check that b is the largest integer such that b*b <= a if (c <= a) { Console.WriteLine("\nError at round " + count); Console.WriteLine(a + "\n"); return; } Console.WriteLine(" <PASSED>."); } }
//Генерируем секретный ключ заданной длины public BInteger GenPrivateKey(int BitSize) { BInteger d = new BInteger(); do { d.genRandomBits(BitSize, new Random()); } while ((d < 0) || (d > n)); return d; }
public BInteger genCoPrime(int bits, Random rand) { bool done = false; BInteger result = new BInteger(); while (!done) { result.genRandomBits(bits, rand); //Console.WriteLine(result.ToString(16)); // gcd test BInteger g = result.gcd(this); if (g.dataLength == 1 && g.data[0] == 1) done = true; } return result; }
public static BInteger genPseudoPrime(int bits, int confidence, Random rand) { BInteger result = new BInteger(); bool done = false; while (!done) { result.genRandomBits(bits, rand); result.data[0] |= 0x01; // make it odd // prime test done = result.isProbablePrime(confidence); } return result; }
public bool SolovayStrassenTest(int confidence) { BInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; int bits = thisVal.bitCount(); BInteger a = new BInteger(); BInteger p_sub1 = thisVal - 1; BInteger p_sub1_shift = p_sub1 >> 1; Random rand = new Random(); for (int round = 0; round < confidence; round++) { bool done = false; while (!done) // generate a < n { int testBits = 0; // make sure "a" has at least 2 bits while (testBits < 2) testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0 if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1)) done = true; } // check whether a factor exists (fix for version 1.03) BInteger gcdTest = a.gcd(thisVal); if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1) return false; // calculate a^((p-1)/2) mod p BInteger expResult = a.modPow(p_sub1_shift, thisVal); if (expResult == p_sub1) expResult = -1; // calculate Jacobi symbol BInteger jacob = Jacobi(a, thisVal); //Console.WriteLine("a = " + a.ToString(10) + " b = " + thisVal.ToString(10)); //Console.WriteLine("expResult = " + expResult.ToString(10) + " Jacob = " + jacob.ToString(10)); // if they are different then it is not prime if (expResult != jacob) return false; } return true; }
public bool RabinMillerTest(int confidence) { BInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; // calculate values of s and t BInteger p_sub1 = thisVal - (new BInteger(1)); int s = 0; for (int index = 0; index < p_sub1.dataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((p_sub1.data[index] & mask) != 0) { index = p_sub1.dataLength; // to break the outer loop break; } mask <<= 1; s++; } } BInteger t = p_sub1 >> s; int bits = thisVal.bitCount(); BInteger a = new BInteger(); Random rand = new Random(); for (int round = 0; round < confidence; round++) { bool done = false; while (!done) // generate a < n { int testBits = 0; // make sure "a" has at least 2 bits while (testBits < 2) testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0 if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1)) done = true; } // check whether a factor exists (fix for version 1.03) BInteger gcdTest = a.gcd(thisVal); if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1) return false; BInteger b = a.modPow(t, thisVal); bool result = false; if (b.dataLength == 1 && b.data[0] == 1) // a^t mod p = 1 result = true; for (int j = 0; result == false && j < s; j++) { if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1 { result = true; break; } b = (b * b) % thisVal; } if (result == false) return false; } return true; }
public bool FermatLittleTest(int confidence) { BInteger thisVal; if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative thisVal = -this; else thisVal = this; if (thisVal.dataLength == 1) { // test small numbers if (thisVal.data[0] == 0 || thisVal.data[0] == 1) return false; else if (thisVal.data[0] == 2 || thisVal.data[0] == 3) return true; } if ((thisVal.data[0] & 0x1) == 0) // even numbers return false; int bits = thisVal.bitCount(); BInteger a = new BInteger(); BInteger p_sub1 = thisVal - (new BInteger(1)); Random rand = new Random(); for (int round = 0; round < confidence; round++) { bool done = false; while (!done) // generate a < n { int testBits = 0; // make sure "a" has at least 2 bits while (testBits < 2) testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0 if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1)) done = true; } // check whether a factor exists (fix for version 1.03) BInteger gcdTest = a.gcd(thisVal); if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1) return false; // calculate a^(p-1) mod p BInteger expResult = a.modPow(p_sub1, thisVal); int resultLen = expResult.dataLength; // is NOT prime is a^(p-1) mod p != 1 if (resultLen > 1 || (resultLen == 1 && expResult.data[0] != 1)) { //Console.WriteLine("a = " + a.ToString()); return false; } } return true; }