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Abstract

An inconsistency in shares is detected with a small volume of communications traffic. n inconsistency detecting devices generate random numbers s_i and make the random numbers s_i public. The n inconsistency detecting devices generate a common random number s which is the sum total of the random numbers s₀, . . . , s_n−1. The n inconsistency detecting devices calculate shares [c]_i. The n inconsistency detecting devices generate shares [r]_i, each of which would become a random number r by reconstruction. The n inconsistency detecting devices calculate shares [d]_i, each of which would become a judgment value d by reconstruction. One inconsistency detecting device receives shares [d]₁, . . . , [d]_n−1 from n−1 inconsistency detecting devices. The one inconsistency detecting device restores n−k shares [d]′_k, . . . , [d]′_n−1 from k shares [d]₀, . . . , [d]_k−1. The one inconsistency detecting device judges, for j=k, . . . , n−1, whether or not a share [d]_j and a share [d]′_j coincide with each other.

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