How to find m in c = m^e (mod n) if c, e, n are known

Question

Suppose I have known java BigIntegers c, e, and n, is there a way to quickly calculate the BigInteger m, where:

c = m^e (mod n)

Answer 1

Well, sort of... Suppose that you have determined the number "d" such that

d*e=1  (mod phi(n))

Where phi(n) is the size of the set of relatively prime numbers relative to n. For example, if n=pq where p and q are prime, then phi(n)=(p-1)*(q-1).

Then

m=c^d (mod n)

In the case where you don't already know "d", then I think it is going to be pretty difficult for you to invert that function in general. Good luck.