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

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.

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