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A secret sharing scheme allows to share a secret among several participants such that only certain groups of them can recover it. Veriiable secret sharing has been proposed to achieve security against cheating participants. Its rst realization had the special property that everybody, not only the participants, can verify that the shares are correctly distributed. We will call such schemes publi...

In this paper we study the amount of secret information that must be given to participants in any secret sharing scheme that is secure against coalitions of dishonest participants in the model of Tompa and Woll 20]. We show that any (k; n) threshold secret sharing algorithm in which any coalition of less than k participants has probability of successful cheating less than some > 0 it must give ...

We introduce the notion of Linear Integer Secret-Sharing (LISS) schemes, and show constructions of such schemes for any access structure. We show that any LISS scheme can be used to build a secure distributed protocol for exponentiation in any group. This implies, for instance, distributed RSA protocols for arbitrary access structures and with arbitrary public exponents.

Secret sharing schemes protect secrets by distributing them over diierent locations (share holders). In particular, in k out of n threshold schemes, security is assured if throughout the entire lifetime of the secret the adversary is restricted to compromise less than k of the n locations. For long-lived and sensitive secrets this protection may be insuucient. We propose an eecient proactive se...

Sharing among program variables is vital information when analyzing logic programs. This information is often expressed either as sets or as pairs of program variables that (may) share. That is, either as set-sharing or as pair-sharing. It has been recently argued that (a) set-sharing is interesting not as an observable property in itself, but as an encoding for accurate pair-sharing, and that ...

We suggest a general method of the construction of secret-sharing schemes based on orthogonal systems of partial (in particular, everywhere determined) k-ary operations which generalizes some known methods of the construction of such schemes by a nite elds and point the orthogonal systems of k-ary operations respecting to these known schemes. The di erent transformations of orthogonal systems o...

We point out some mistakes in Lemma 5.1 and Proposition 5.2 in our paper. Since we are supposing that a ≤ b, the first and the second statements of Lemma 5.1 are not symmetric. The second one must be corrected to: 2. y r = max{0, (t − aN 1)/b} and x r = (t − by r)/a. Besides, the proof of Lemma 5.1 can be more easily understood by beginning it with the proof of the third statement. Due to this ...

An Audio Secret Sharing (ASS) scheme is a special type of secret sharing scheme [3], which the shares of embedded messages use music as cover sound. Desmedt et al. firstly introduced the (2, 2) ASS scheme with one cover sound and also the generalized (2, n) ASS scheme with log2n different cover sounds. No only will more cover sounds overburden the human hearing system but also may become diff...

In the paper we discuss how to share the secrets, that are graphs. So, far secret sharing schemes were designed to work with numbers. As the first step, we propose conditions for “graph to number” conversion methods. Hence, the existing schemes can be used, without weakening their properties. Next, we show how graph properties can be used to extend capabilities of secret sharing schemes. This l...