Article history: Received 15 December 2009 Received in revised form 14 April 2010 Accepted 17 April 2010

Threshold secret sharing schemes do not prevent any malicious behavior of the dealer or shareholders and so we need verifiable secret sharing, to detect and identify the cheaters, to achieve fair reconstruction of a secret. The problem of verifiable secret sharing is to verify the shares distributed by the dealer. A novel approach for verifiable secret sharing is presented in this paper where b...

Cellular automata have been used for design of cryptosystems. Recently some secret sharing schemes based on linear memory cellular automata have been introduced which are used for both text and image. In this paper, we illustrate that these secret sharing schemes are vulnerable to dishonest participants’ collusion. We propose a cheating model for the secret sharing schemes based on linear memor...

Threshold schemes are ideally suited to situations where a group of mutually suspicious individuals with conflicting interests must cooperate. The schemes allow a user to divide portions of a secret among a participants group. Any t or more participants from a participants group of n members can cooperate to regain the original secret while (t-1) or fewer participants cannot reveal anything abo...

A black-box secret sharing scheme for the threshold access structure Tt,n is one which works over any finite Abelian group G. Briefly, such a scheme differs from an ordinary linear secret sharing scheme (over, say, a given finite field) in that distribution matrix and reconstruction vectors are defined over Z and are designed independently of the group G from which the secret and the shares are...

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.

A clutter or antichain on a set defines a hypergraph. Matroid ports are a special class of clutters, and this paper deals with the diameter of matroid ports, that is, the diameter of the corresponding hypergraphs. Specifically, we prove that the diameter of every matroid port is at most 2. The main interest of our result is its application to secret sharing. Brickell and Davenport proved in 198...

The commonly used technique for cheating detection requires that extra information be given to each participant. However, in a secret sharing scheme when the size of shares increases the security of the system degrades. In this paper we study the cheating problem in Shamir's scheme (in the sense of Tompa and Woll 1] attack) and present alternative solutions to this problem. First we consider ch...

The complexity of a secret sharing scheme is defined as the ratio between the maximum length of the shares and the length of the secret. The optimization of this parameter for general access structures is an important and very difficult open problem in secret sharing. We explore in this paper the connections of this open problem with matroids and polymatroids. Matroid ports were introduced by L...

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...