java.math.BigInteger，pow方法仅接受int

Question

I'm doing a DSA Signature Verification and Validation assignment, I need to perform a calculation which is like this: v = (((g)^u1(y)^u2) mod p) mod q , where g, u1, y, u2, p and q are all BigInteger objects, I got stuck with g^u1 and y^u2 , I want to use the pow method to do the calculation, but this method only accepts int parameter, so I'm not able to calculate g^u1 like this:

g.pow(u1);

It's resonable that this method only accepts int parameter, because in this case, g is a 1024 bit prime, and u1 here equals 666075361584433975742185154706661067887879287196 , the result of g^u1 will become extremely large. My question is, how should I perform the calculation of v = (((g)^u1(y)^u2) mod p) mod q .

Answer 1

Indeed g^u1 becomes very large. However, you can take advantage of the fact that

a * b  mod  n

can be computed as

(a mod n  *  b mod n)  mod  n

Here, a = g ^ u1 and b = y ^ u2 , and these computations can be done efficiently using modPow . ((g)^u1(y)^u2) mod p will be:

g.modPow(u1,p).multiply(y.modPow(u2,p)).mod(p)

Answer 2

You are going to do mod p anyway - so why don't you use BigInteger.modPow()

Note that

g^u1 * y^u2 mod p == (g^u1 modp * y^u2 mod p) mod p