Consideration for multi-threshold multi-secret sharing schemes
Atsushi Waseda, Masakazu Soshi · International Symposium on Information Theory and its Applications · 2012
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 t 1 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.