Sashimi: Cutting up CSI-FiSh Secret Keys to Produce an Actively Secure Distributed Signing Protocol

Abstract

We present the first actively secure variant of a distributed signature scheme based on isogenies. The protocol produces signatures from the recent CSI-FiSh signature scheme. Our scheme works for any access structure, as we use a replicated secret sharing scheme to define the underlying secret sharing; as such it is only practical when the number of maximally unqualified sets is relatively small. This, however, includes the important case of full threshold, and (n, t)-threshold schemes when n is small.