c# - How to calculate RSA's additional private key parameters from P and Q? -

when reading rsa private key blob, lacks several rsa parameters (dp, dq, inverseq, d), how can calculate these missing parameters are supplied? i've read it's possible calculate these p , q are supplied, don't know how calculate them.

when importing key, errors when trying use private key claiming data isn't there (of course p , q supplied though).

i need able on multiple platforms, i'm afraid puts me in camp of needing own actual code calculate them.

in c#

here c# code can construct full set of rsaparameters p, q, , public key data. assume parameters method big-endian (as rsaparameters).

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 modular multiplicative inverse of <paramref name="a"/> modulo <paramref name="m"/> /// using extended euclidean algorithm. /// </summary> /// <remarks> /// implementation comes pseudocode defining inverse(a, n) function @ /// 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)     {         = 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) + " 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; }