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;
}
