  As society becomes more reliant on computers, cryptographic security becomes
increasingly important. Current encryption schemes include the ElGamal
signature scheme, which depends on the complexity of the discrete logarithm
problem. It is thought that the functions that such schemes use have inverses
that are computationally intractable. In relation to this, we are interested in
counting the solutions to a generalization of the discrete logarithm problem
modulo a prime power. This is achieved by interpolating to p-adic functions,
and using Hensel's lemma, or other methods in the case of singular lifting, and
the Chinese Remainder Theorem.
