Tompa and Woll considered a problem of cheaters in (k; n) threshold secret sharing schemes. We rst derive a tight lower bound on the size of shares jV i j for this problem: jV i j (jSj 1)= + 1, where V i denotes the set of shares of participant P i , S denotes the set of secrets, and denotes the cheating probability. We next present an optimum scheme which meets the equality of our bound by usi...

It is shown that in some cases it is possible to reconstruct a block design D uniquely from incomplete knowledge of a minimal defining set for D. This surprising result has implications for the use of minimal defining sets in secret sharing schemes. AMS classifications: Primary: 94A62, Secondary: 05B05.

Audio and optical cryptography schemes in [1] are secret sharing schemes that protect audio and visual secrets by using sounds and images, respectively. However, 2-out-of-n schemes in [1] are constructed by log 2 n independent 2-out-of-2 schemes, meaning so that a 2-out-of-n scheme needs log 2 n different cover sounds or images. More cover sounds (images) will be more difficult for the huma...

A secret sharing scheme allows to share a secret among several participants such that only certain groups of them can recover it. Veri able 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...

Although the usual goal of sharing analysis is to detect which pairs of variables share, the standard choice for sharing analysis is a domain that characterizes set-sharing. In this paper, we question, apparently for the first time, whether this domain is over-complex for pair-sharing analysis. We show that the answer is yes. By defining an equivalence relation over the set-sharing domain we ob...

In this paper, we show that there exists a t-cheater identi able (k; n) threshold secret sharing scheme such as follows for cheating probability " > 0. If k 3t+ 1, then 1. Just k participants are enough to identify who are cheaters. 2. jV i j is independent of n. That is, jV i j = jSj(1=") (t+2) , where S denotes the set of secrets and V i denotes the set of shares of a participant P i , respec...

Recent results of Cascudo, Cramer, and Xing on the construction of arithmetic secret sharing schemes are improved by using some new bounds on the torsion limits of algebraic function fields. Furthermore, new bounds on the torsion limits of certain towers of function fields are given.

We show how it is possible for two parties to cooperate in generating the parameters for an RSA encryption system in such a w a y that neither individually has the ability to decrypt enciphered data. In order to decrypt data the two parties instead follow the cooperative procedure described.

Padró and Sáez [PS] introduced the concept of a k-partite access structure for secret sharing and gave a complete characterization of ideal bipartite structures. We derive a necessary condition for ideal tripartite structures, which we conjecture is necessary for all k.