/// <summary>
/// 人为素数的密钥生成方法 如果参数不能通过素性检测则抛出异常
/// </summary>
/// <param name="p"></param>
/// <param name="q"></param>
/// <returns></returns>
public static BigInteger[] GenKey(ulong p, ulong q)
{
PrimeGen pgen = new PrimeGen();
if (!pgen.RabinMiller(p, 100))
{
throw new NotPrimeNumberException(p.ToString());
}
if (!pgen.RabinMiller(q, 100))
{
throw new NotPrimeNumberException(q.ToString());
}
BigInteger N = p * q;
BigInteger r = (p - 1) * (q - 1);
BigInteger e = pgen.Gen();
e %= r;
while (RSA_Math.SteinGCD(e, r) != 1)
{
e = pgen.Gen();
e %= r;
}
BigInteger d = RSA_Math.ExEuclid(e, r);
return(new BigInteger[] { N, e, d });
}
/// <summary>
/// RSA密钥生成方法 除密钥外还返回了大素数p和q
/// </summary>
/// <returns>[n e d p q]</returns>
public static BigInteger[] GenKeyAdd()
{
PrimeGen pgen = new PrimeGen();
BigInteger p = pgen.Gen();
BigInteger q = pgen.Gen();
BigInteger N = p * q;
BigInteger r = (p - 1) * (q - 1);
BigInteger e = pgen.Gen();
e %= r;
while (RSA_Math.SteinGCD(e, r) != 1)
{
e = pgen.Gen();
e %= r;
}
BigInteger d = RSA_Math.ExEuclid(e, r);
return(new BigInteger[] { N, e, d, p, q });
}
/// <summary>
/// Rabin-Miller素性检测
/// </summary>
/// <param name="biN">被检数</param>
/// <param name="iK">测试轮数 默认50</param>
/// <returns>true：biN为素数，false：biN不是素数</returns>
public bool RabinMiller(BigInteger biN, int iK = 50)
{
if ((biN & 1) == 0)
{
return(false);
}
BigInteger s = 0, i = 1;
BigInteger t = biN - 1;
while ((t & 1) == 0)
{
t >>= 1;
++s;
}
while (iK-- != 0)
{
RNGCryptoServiceProvider csp = new RNGCryptoServiceProvider();
byte[] baCsp = new byte[8];
csp.GetNonZeroBytes(baCsp);
BigInteger b = BitConverter.ToUInt64(baCsp, 0) % (biN - 2) + 2;
BigInteger y = RSA_Math.RepeatMod(b, t, biN);
if (y == 1)
{
return(true);
}
while (y != biN - 1)
{
if (i == s)
{
return(false);
}
y = RSA_Math.RepeatMod(y, 2, biN);
++i;
}
}
return(true);
}
/// <summary>
/// RSA解密基本方法
/// </summary>
/// <param name="biCipher"></param>
/// <param name="d"></param>
/// <param name="N"></param>
/// <returns></returns>
public static BigInteger Decrypt(BigInteger biCipher, BigInteger d, BigInteger N)
{
return(RSA_Math.RepeatMod(biCipher, d, N));
}
/// <summary>
/// RSA加密基本方法
/// </summary>
/// <param name="biPlain"></param>
/// <param name="e"></param>
/// <param name="N"></param>
/// <returns></returns>
public static BigInteger Encrypt(BigInteger biPlain, BigInteger e, BigInteger N)
{
return(RSA_Math.RepeatMod(biPlain, e, N));
}
