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.