  Recently, Dor\"oz et al. (2017) proposed a new hard problem, called the
finite field isomorphism problem, and constructed a fully homomorphic
encryption scheme based on this problem. In this paper, we generalize the
problem to the case of Galois rings, resulting in the Galois ring isomorphism
problem. The generalization is achieved by lifting the isomorphism between the
corresponding residue fields. As a result, this generalization allows us to
construct cryptographic primitives over the ring of integers modulo a prime
power, instead of a large prime number.
