Consideration for multi-threshold multi-secret sharing schemes

In this paper, we propose the new (t_i, n) threshold multi secret sharing scheme. In our scheme, each user keeps only one share and the secret vectors K_i = {k_i,₁,..., k_i,_mi} are shared according to independent (t_i, n) threshold access structures (i = l,..., h). Here note that a (t_i, n) threshold multi-secret sharing scheme has been proposed by Shi et al. [1]. Unfortunately, however, there is a serious attack on Shi´s scheme that can reconstruct all elements of K_i with only t₁ shares. In this paper, we shall give the solution to this problem by using one-way functions. Furthermore, Shi´s scheme has a drawback such that the dimension of the secret vector K_i cannot exceed t_i. On the other hand, our scheme has no such a restriction. Finally, we demonstrate that our scheme is more efficient than Shi´s scheme by showing that our scheme is more efficient than the three naive improvements on the protocol of Shi et al.