The complexity and randomness of linear multi-secret sharing schemes with non-threshold structures

Abstract

In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multisecret sharing scheme is measured by means of the complexity σ and the randomness τ . Informally, the complexity σ is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness τ is the ratio between the amount of information distributed to the set of users U = {1, · · · , n} and the minimum of information corresponding to every key.In this paper, we discuss σ and τ of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make σ and τ to be the minimum, respectively. That is, they are optimal.

Efficient multisecret sharing scheme using new proposed computational security model

“…The desirable aim is to reduce the size of shares. There are papers that assessed and proposed some methods to reduce share size in MSS schemes, but to the best of our knowledge, the shortest share size among MSS schemes is greater than the size of a secret. In the proposed model the size of each share is equal to the size of a secret.…”