如何从RSAPrivateKey获取RSAPrivateCrtKey？
我有一个java.security.interfaces.RSAPrivateKey和相应的java.security.interfaces.RSAPublicKey包含（仅）模数，私有指数和公共指数。
如果我理解RSA正确，则应该可以恢复java.security.interfaces.RSAPrivateCrtKey（对于CRT键）的数字。
如果是这样，我该怎么办？ （我假设已经有一些实现）。
可以这样做，并且有一个相对快速的算法来查找参数。 这是一些说明算法的Java代码。
/** * 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) > 0) { 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); }