通过使用Java安全模数,公共和私人指数还原RSA私钥
问题描述:
我试图找到Java(本地或BouncyCastle提供程序)实现在PKCS#1中使用给定的参数生成RSA私钥{e,n,d }。通过使用Java安全模数,公共和私人指数还原RSA私钥
丹Boneh有paper描述了这样做的算法。该解决方案在PyCrypto(Python)中可用,以及由Mounir IDRASSI发布的独立utility,用于在SFM格式(n,e,d)和CRT格式(p,q,dp,dq,u)之间转换RSA密钥)以及其他方式。但是,我无法找到任何准备用于Java的东西。
更新:我发现在https://github.com/martinpaljak/RSAKeyConverter/blob/master/src/opensc/RSAKeyConverter.java
答
这样的实现我在this答案,我将重现这里提供了一些代码:
/**
* 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) > 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);
}
我实施了为好,直接在Java中不看任何其他代码,只是论文而已,但可能借用一些算法。但是,它在另一台计算机上。所以我认为你想转换为CRT,因为它不完全清楚你在做什么。 –