Two Optimum Secret Sharing Schemes Revisited

In 2006, Obana et al proposed two optimum secret sharing schemes secure against cheating. They extend the secret s in the Shamir´s scheme to an array of three elements, (s, e₀, e₁), and construct two equations for checking validity. Each item in the equations should be reconstructed using Lagrange´s interpolation. In this paper, we revisit these schemes by introducing a public hash function to construct equations for checking validity. The revisited schemes become more efficient because they only extend the secret to an array of two elements. The new scheme for a single secret saves about 1/3 cost of the original.