Restore RSA private key by modulus, public and pri

Question

I'm trying to find Java (native or BouncyCastle provider) implementation for generating a RSA private key in PKCS#1 using given params {e,n,d}.

There is paper by Dan Boneh that describes an algorithm for doing so. The solution is available in PyCrypto (Python), as well as there is a standalone utility posted by Mounir IDRASSI that converts RSA keys between the SFM format (n,e,d) and CRT format (p,q,dp,dq,u), and the other way around. However I was not able to find anything ready to use for Java.

Update: I found such implementation at https://github.com/martinpaljak/RSAKeyConverter/blob/master/src/opensc/RSAKeyConverter.java

Answer 1

I provided some code in this answer which I will reproduce here:

/**
 * Find a factor of n by following the algorithm outlined in Handbook of Applied Cryptography, section
 * 8.2.2(i). See http://cacr.uwaterloo.ca/hac/about/chap8.pdf.
 *
 */

private static BigInteger findFactor(BigInteger e, BigInteger d, BigInteger n) {
    BigInteger edMinus1 = e.multiply(d).subtract(BigInteger.ONE);
    int s = edMinus1.getLowestSetBit();
    BigInteger t = edMinus1.shiftRight(s);

    for (int aInt = 2; true; aInt++) {
        BigInteger aPow = BigInteger.valueOf(aInt).modPow(t, n);
        for (int i = 1; i <= s; i++) {
            if (aPow.equals(BigInteger.ONE)) {
                break;
            }
            if (aPow.equals(n.subtract(BigInteger.ONE))) {
                break;
            }
            BigInteger aPowSquared = aPow.multiply(aPow).mod(n);
            if (aPowSquared.equals(BigInteger.ONE)) {
                return aPow.subtract(BigInteger.ONE).gcd(n);
            }
            aPow = aPowSquared;
        }
    }

}

public static RSAPrivateCrtKey createCrtKey(RSAPublicKey rsaPub, RSAPrivateKey rsaPriv) throws NoSuchAlgorithmException, InvalidKeySpecException {

    BigInteger e = rsaPub.getPublicExponent();
    BigInteger d = rsaPriv.getPrivateExponent();
    BigInteger n = rsaPub.getModulus();
    BigInteger p = findFactor(e, d, n);
    BigInteger q = n.divide(p);
    if (p.compareTo(q) > 1) {
        BigInteger t = p;
        p = q;
        q = t;
    }
    BigInteger exp1 = d.mod(p.subtract(BigInteger.ONE));
    BigInteger exp2 = d.mod(q.subtract(BigInteger.ONE));
    BigInteger coeff = q.modInverse(p);
    RSAPrivateCrtKeySpec keySpec = new RSAPrivateCrtKeySpec(n, e, d, p, q, exp1, exp2, coeff);
    KeyFactory kf = KeyFactory.getInstance("RSA");
    return (RSAPrivateCrtKey) kf.generatePrivate(keySpec);

}