Galois ring isomorphism problem
This work addresses the need for more flexible cryptographic schemes in applied cryptography, though it is incremental as it builds directly on prior work.
The paper tackles the problem of generalizing the finite field isomorphism problem to Galois rings, enabling the construction of cryptographic primitives over integers modulo a prime power rather than a large prime.
Recently, Doröz 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.