问题描述

我有一个 java.security.interfaces.RSAPrivateKey 和对应的 java.security.interfaces.RSAPublicKey 包含(仅)模数、私有指数和公共指数.

I have a java.security.interfaces.RSAPrivateKey and the corresponding java.security.interfaces.RSAPublicKey containing (only) modulus, private exponent and public exponent.

如果我对 RSA 的理解正确，应该可以恢复 java.security.interfaces.RSAPrivateCrtKey 的数字(用于 CRT 密钥).

If I understand RSA right, it should be possible to recover the numbers for java.security.interfaces.RSAPrivateCrtKey (for CRT keys).

如果是这样，我该怎么做?(我假设已经有一些实现了).

If so, how do I do it? (I assume there is some implementation already).

推荐答案

这个是可以的，而且有比较快的算法找参数.下面是一些说明该算法的 Java 代码.

It is possible to do this, and there is a relatively fast algorithm to find the parameters. Here is some Java code that illustrates the algorithm.

/**
 * 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);

}

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