One important result in secret sharing is the Brickell-Davenport Theorem: every ideal perfect secret sharing scheme defines a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory definition of ideal secret sharing scheme for the general case, in which non-perfect schemes are considered as well. Without providing another...

A perfect secret sharing scheme allows a secret K to be shared among a set of participants in such a way that only qualified subsets of participants can recover the secret, and unqualified subsets of participants obtain no information regarding the secret. In this paper, we propose a construction of perfect secret sharing schemes with uniform, generalized access structures of rank 3. Compared w...

Traditional Secret Sharing (SS) schemes reconstruct secret exactly the same as the original one but involve complex computation. Visual Secret Sharing (VSS) schemes decode the secret without computation, but each share is m times as big as the original and the quality of the reconstructed secret image is reduced. Probabilistic visual secret sharing (Prob.VSS) schemes for a binary image use only...

In the paper we propose general framework for Automatic Secret Generation and Sharing (ASGS) that should be independent of underlying secret sharing scheme. ASGS allows to prevent the dealer from knowing the secret or even to eliminate him at all. Two situations are discussed. First concerns simultaneous generation and sharing of the random, prior nonexistent secret. Such a secret remains unkno...

We consider secret sharing schemes in which the dealer is able (after a preprocessing stage) to activate a particular access structure out of a given set and/or to allow the participants to reconstruct diierent secrets (in diierent time instants) by sending them the same broadcast message. In this paper we establish a formal setting to study secret sharing schemes of this kind. The security of ...

Given a graph G, a perfect secret sharing scheme based on G is a method to distribute a secret data among the vertices of G, the participants, so that a subset of participants can recover the secret if they contain an edge of G, otherwise they can obtain no information regarding the key. The average information rate is the ratio of the size of the secret and the average size of the share a part...

Abstmct-Given a set of parties {l,. , n ) , an access structure is a monotone collection of subsets of the parties. For a certain domain of secrets, a secret-sharing scheme for an access structure is a method for a dealer to distribute shares to the parties. These shares enable subsets in the access structure to reconstruct the secret, while subsets not in the access structure get no informatio...

This paper investigates the security of Proactive Secret Sharing Schemes. We start with revision of the mobile adversary model of Herzberg’s et al. imposing less restriction to the adversary. We first investigate the approach of using commitment to 0 in the renewal phase in order to renew the player’s shares. In the considered model some well known computationally secure protocols (which use th...

Secret sharing schemes divide a secret among multiple participants so that only authorized subsets of parties can reconstruct it. We show that SETUP (Secretly Embedded Trapdoor with Universal Protection) attack can be embedded in secret sharing schemes that employ enough randomness to give the attacker an overwhelming advantage to access the secret. In case of ideal schemes, a coalition of a fe...

Many mathematical structures have been used to model Secret Sharing Schemes. This paper firstly presents a secret sharing schemes based on starter-adder sets of generalized Kirkman squares. Finally, we prove that the scheme is perfect.