当读取缺少多个RSA参数(DP,DQ,InverseQ,D)的RSA私钥blob时,如何从 提供的参数中计算这些缺失参数?我已经知道可以从提供 的P和Q计算这些,但我不知道如何计算它们。
导入此密钥时,在尝试使用私钥时出错,声称数据不在那里(当然,虽然提供了P和Q)。
我需要能够在多个平台上执行此操作,因此我担心这会让我陷入需要拥有实际代码来计算它们的阵营。
在C#中
答案 0 :(得分:5)
这是C#代码,可以从P,Q和公钥数据构造一整套RSAParameters
。我们假设这个方法的参数是big-endian(和RSAParameters一样)。
private static RSAParameters Create(byte[] p, byte[] q, byte[] exponent, byte[] modulus)
{
var addlParameters = GetFullPrivateParameters(
p: new BigInteger(CopyAndReverse(p)),
q: new BigInteger(CopyAndReverse(q)),
e: new BigInteger(CopyAndReverse(exponent)),
modulus: new BigInteger(CopyAndReverse(modulus)));
return new RSAParameters
{
P = p,
Q = q,
Exponent = exponent,
Modulus = modulus,
D = addlParameters.D,
DP = addlParameters.DP,
DQ = addlParameters.DQ,
InverseQ = addlParameters.InverseQ,
};
}
private static RSAParameters GetFullPrivateParameters(BigInteger p, BigInteger q, BigInteger e, BigInteger modulus)
{
var n = p * q;
var phiOfN = n - p - q + 1; // OR: (p - 1) * (q - 1);
var d = ModInverse(e, phiOfN);
Assert.Equal(1, (d * e) % phiOfN);
var dp = d % (p - 1);
var dq = d % (q - 1);
var qInv = ModInverse(q, p);
//Assert.Equal(1, (qInv * q) % p);
return new RSAParameters
{
D = CopyAndReverse(d.ToByteArray()),
DP = CopyAndReverse(dp.ToByteArray()),
DQ = CopyAndReverse(dq.ToByteArray()),
InverseQ = CopyAndReverse(qInv.ToByteArray()),
};
}
/// <summary>
/// Calculates the modular multiplicative inverse of <paramref name="a"/> modulo <paramref name="m"/>
/// using the extended Euclidean algorithm.
/// </summary>
/// <remarks>
/// This implementation comes from the pseudocode defining the inverse(a, n) function at
/// https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
/// </remarks>
public static BigInteger ModInverse(BigInteger a, BigInteger n)
{
BigInteger t = 0, nt = 1, r = n, nr = a;
if (n < 0)
{
n = -n;
}
if (a < 0)
{
a = n - (-a % n);
}
while (nr != 0)
{
var quot = r / nr;
var tmp = nt; nt = t - quot * nt; t = tmp;
tmp = nr; nr = r - quot * nr; r = tmp;
}
if (r > 1) throw new ArgumentException(nameof(a) + " is not convertible.");
if (t < 0) t = t + n;
return t;
}
private static byte[] CopyAndReverse(byte[] data)
{
byte[] reversed = new byte[data.Length];
Array.Copy(data, 0, reversed, 0, data.Length);
Array.Reverse(reversed);
return reversed;
}