Optimal Computational Secret Sharing

In (t, n)-threshold secret sharing, a secret S is distributed among n participants such that any subset of size t can recover S, while any subset of size t-1 or fewer learns nothing about it. For information-theoretic secret sharing, it is known that the share size must be at least as large as the secret, i.e., |S|. When computational security is employed using cryptographic encryption with a secret key K, previous work has shown that the share size can be reduced to |S|/t+|K|. In this paper, we present a construction achieving a share size of |S|+|K|/t. We further prove that, under reasonable assumptions on the encryption utilized, this share size is optimal.