internal bool RabinMillerTest( int certainty, Random random) { Debug.Assert(certainty > 0); Debug.Assert(BitLength > 2); Debug.Assert(TestBit(0)); // let n = 1 + d . 2^s BigInteger n = this; BigInteger nMinusOne = n.Subtract(One); int s = nMinusOne.GetLowestSetBit(); BigInteger r = nMinusOne.ShiftRight(s); Debug.Assert(s >= 1); do { // TODO Make a method for random BigIntegers in range 0 < x < n) // - Method can be optimized by only replacing examined bits at each trial BigInteger a; do { a = new BigInteger(n.BitLength, random); } while (a.CompareTo(One) <= 0 || a.CompareTo(nMinusOne) >= 0); BigInteger y = a.ModPow(r, n); if (!y.Equals(One)) { int j = 0; while (!y.Equals(nMinusOne)) { if (++j == s) return false; y = y.ModPow(Two, n); if (y.Equals(One)) return false; } } certainty -= 2; // composites pass for only 1/4 possible 'a' } while (certainty > 0); return true; }
public byte[] ToBytes(byte[] nonce, byte[] serverNonce, byte[] newNonce, byte[] encryptedAnswer) { this.newNonce = newNonce; AESKeyData key = AES.GenerateKeyDataFromNonces(serverNonce, newNonce); byte[] plaintextAnswer = AES.DecryptAES(key, encryptedAnswer); // logger.debug("plaintext answer: {0}", BitConverter.ToString(plaintextAnswer)); int g; BigInteger dhPrime; BigInteger ga; using (MemoryStream dhInnerData = new MemoryStream(plaintextAnswer)) { using (BinaryReader dhInnerDataReader = new BinaryReader(dhInnerData)) { byte[] hashsum = dhInnerDataReader.ReadBytes(20); uint code = dhInnerDataReader.ReadUInt32(); if (code != 0xb5890dba) { throw new InvalidOperationException($"invalid dh_inner_data code: {code}"); } // logger.debug("valid code"); byte[] nonceFromServer1 = dhInnerDataReader.ReadBytes(16); if (!nonceFromServer1.SequenceEqual(nonce)) { throw new InvalidOperationException("invalid nonce in encrypted answer"); } // logger.debug("valid nonce"); byte[] serverNonceFromServer1 = dhInnerDataReader.ReadBytes(16); if (!serverNonceFromServer1.SequenceEqual(serverNonce)) { throw new InvalidOperationException("invalid server nonce in encrypted answer"); } // logger.debug("valid server nonce"); g = dhInnerDataReader.ReadInt32(); dhPrime = new BigInteger(1, Serializers.Bytes.read(dhInnerDataReader)); ga = new BigInteger(1, Serializers.Bytes.read(dhInnerDataReader)); int serverTime = dhInnerDataReader.ReadInt32(); timeOffset = serverTime - (int)(Convert.ToInt64((DateTime.UtcNow - new DateTime(1970, 1, 1)).TotalMilliseconds) / 1000); // logger.debug("g: {0}, dhprime: {1}, ga: {2}", g, dhPrime, ga); } } BigInteger b = new BigInteger(2048, new Random()); BigInteger gb = BigInteger.ValueOf(g).ModPow(b, dhPrime); _gab = ga.ModPow(b, dhPrime); // logger.debug("gab: {0}", gab); // prepare client dh inner data byte[] clientDHInnerDataBytes; using (MemoryStream clientDhInnerData = new MemoryStream()) { using (BinaryWriter clientDhInnerDataWriter = new BinaryWriter(clientDhInnerData)) { clientDhInnerDataWriter.Write(0x6643b654); // client_dh_inner_data clientDhInnerDataWriter.Write(nonce); clientDhInnerDataWriter.Write(serverNonce); clientDhInnerDataWriter.Write((long)0); // TODO: retry_id Serializers.Bytes.write(clientDhInnerDataWriter, gb.ToByteArrayUnsigned()); using (MemoryStream clientDhInnerDataWithHash = new MemoryStream()) { using (BinaryWriter clientDhInnerDataWithHashWriter = new BinaryWriter(clientDhInnerDataWithHash)) { using (SHA1 sha1 = new SHA1Managed()) { clientDhInnerDataWithHashWriter.Write(sha1.ComputeHash(clientDhInnerData.GetBuffer(), 0, (int)clientDhInnerData.Position)); clientDhInnerDataWithHashWriter.Write(clientDhInnerData.GetBuffer(), 0, (int)clientDhInnerData.Position); clientDHInnerDataBytes = clientDhInnerDataWithHash.ToArray(); } } } } } // logger.debug("client dh inner data papared len {0}: {1}", clientDHInnerDataBytes.Length, BitConverter.ToString(clientDHInnerDataBytes).Replace("-", "")); // encryption byte[] clientDhInnerDataEncryptedBytes = AES.EncryptAES(key, clientDHInnerDataBytes); // logger.debug("inner data encrypted {0}: {1}", clientDhInnerDataEncryptedBytes.Length, BitConverter.ToString(clientDhInnerDataEncryptedBytes).Replace("-", "")); // prepare set_client_dh_params byte[] setclientDhParamsBytes; using (MemoryStream setClientDhParams = new MemoryStream()) { using (BinaryWriter setClientDhParamsWriter = new BinaryWriter(setClientDhParams)) { setClientDhParamsWriter.Write(0xf5045f1f); setClientDhParamsWriter.Write(nonce); setClientDhParamsWriter.Write(serverNonce); Serializers.Bytes.write(setClientDhParamsWriter, clientDhInnerDataEncryptedBytes); setclientDhParamsBytes = setClientDhParams.ToArray(); } } // logger.debug("set client dh params prepared: {0}", BitConverter.ToString(setclientDhParamsBytes)); return setclientDhParamsBytes; }