Ideal Perfect Multilevel Threshold Secret Sharing Scheme

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.