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NATO science for peace and security series. D, Information and communication security

Secret Sharing and Error Correcting

Svetla Nikova⋆, Ventzislav Nikov

Published Jan 1, 2009• 1 citation
Publisher

Abstract

The goal of this paper is to present a survey on certain recent developments in the theory of unconditional Multi Party Computation (MPC) and Secret Sharing Schemes (SSS) related to Error Correcting Codes.
DOI
10.3233/978-1-60750-002-5-28

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It is known that a secret sharing scheme (SSS) with perfect cheating detection cannot be realized because such a SSS requires infinite share rates. However, this impossibility comes from the fact that block coding is not used and any decoding error is not allowed in the SSS. Hence, in this paper, we consider a SSS constructed by block coding with an arbitrarily small decoding error probability. It is shown that the perfect cheating detection with finite rates is possible for the 2-out-of-2 SSS in a certain asymptotic sense. Furthermore, the supremum of the achievable exponent in the maximum success probability of impersonation attack turns out to be the mutual information between the two shares.