A Signature Scheme From The Finite Field Isomorphism Problem

In a recent paper the authors and their collaborators proposed a new hard problem, called the finite field isomorphism problem, and they used it to construct a fully homomorphic encryption scheme. In this paper, we investigate how one might build a digital signature scheme from this new problem. Intuitively, the hidden field isomorphism allows us to convert short vectors in the underlying lattice of one field into generic looking vectors in an isomorphic field.