A New (t, n)-Threshold Multi-secret Sharing Scheme

Abstract

In a (t, n)-threshold multi-secret sharing scheme, at least t or more participants in n participants can reconstruct p(p ≥ 1) secrets simultaneously through pooling their secret shadows. Pang et al. proposed a multi-secret sharing scheme using an (n + p – 1)th degree Lagrange interpolation polynomial. In their scheme, the degree of the polynomial is dynamic; with the increase in the number of the shared secrets p, the Lagrange interpolation operation becomes more and more complex, at the same time, computing time and storage requirement are large. Motivated by these concerns, we propose an alternative (t, n)-threshold multi-secret sharing scheme based on Shamir’s secret sharing scheme, which uses a fixed nth degree Lagrange interpolation polynomial and has the same power as Pang et al.’s scheme. Furthermore, our scheme needs less computing time and less storage requirement than Pang et al.’s scheme.