An isogeny-based quantum-resistant secret sharing scheme

Abstract

In a secret sharing scheme, a secret is distributed among several participants in such a way that only any authorized subset of participants is able to recover the secret. So far, the security of many secret sharing schemes has been based on the hardness of some mathematical problems, such as discrete logarithm and factorization. These problems can be solved in polynomial time using Shor?s algorithm for a quantum computer. In this paper, we propose an efficient multi-secret sharing scheme based on the hardness of computing isogenies between supersingular elliptic curves. The proposed scheme is based on De Feo and Jao key exchange protocol. We prove that our scheme is secure under computational assumptions in which there is no known efficient quantum algorithm.