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 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.