A coding theorem for cheating-detectable (2, 2)-threshold blockwise secret sharing schemes

Authors:
Mitsugu Iwamoto;Hirosuke Yamamoto;Hiroki Koga
Affiliations:
Graduate School of Information Systems, University of Electro-Communications, Chofu-shi, Tokyo, Japan;Graduate School of Frontier Sciences, University of Tokyo, Kashiwa-shi, Chiba, Japan;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba-shi, Ibaraki, Japan
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Year:
2009

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Abstract

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.