BigInteger exponentiation with negative number

Question

How can I do the same as in this python (using sage) code:

def elGamalDecrypt(c1, c2, p, x):
    return Mod(c2*c1^(-x),p)

with standard Java 7 libraries? All numbers are BigInteger .

I've tried a lot with no avail. In Python it's really simple and FAST.

Answer 1

The BigInteger class in Java 7 has a modPow method, which handles modular exponentiation. So, something like the following should work (although I haven't tested it):

c2.multiply(c1.modPow(x.negate(), p)).mod(p)

The modPow method will only accept a negative exponent -x if c1 and p are coprime. (The name p suggests that p is prime, and if c1 and p aren't coprime, c1 would be divisible by p , and hence the exponentiation would make no sense, so I suspect that this won't be a problem.)

Answer 2

This should do the same since c2 * c1^-x = c2 / (c1 ^ x) :

BigInteger elGamalDecrypt(BigInteger c1, BigInteger c2, BigInteger p, int x) {
    return c2.divide(c1.pow(x)).mod(p);
}