Ideal Perfect Multilevel Threshold Secret Sharing Scheme

Abstract

Shamir proposed the first (t, n) threshold secret sharing scheme. Shamir's scheme is ideal and perfect. In this paper, we propose two modifications of Shamir's secret sharing scheme. In our first modification, each shareholder keeps both x-coordinate and y-coordinate of a polynomial as private share. In our second modification, dealer uses polynomial with degree larger than the threshold value t to generate shares for a (t, n) threshold scheme. We show that these two modified schemes are ideal and perfect. Using these two modifications, we design a multilevel threshold secret sharing schemes (MTSS). We prove that the proposed scheme is secure.