A Multi-Secret Sharing Scheme Based on the Stern-Brocot Tree

Abstract

In 2004, Yang et al. proposed an efficient multi-secret sharing scheme based on two-variable one-way function and Shamirpsilas secret sharing, which needs to reconstruct a (t-1) or (p-1)th degree Lagrange interpolation polynomial. This paper proposes a more efficient multi-secret sharing scheme based on Yang et al.'s scheme and the Stern-Brocot tree, which needs to reconstruct a (t-1) or (p/2-1)th degree Lagrange interpolation polynomial. Thus, the computing time and the storage cost of this scheme is less than that of Yang et al.'s scheme.