In a (k,n) Shamir's threshold scheme, if one or more of the n shares are fake, then the secret may not be reconstructed correctly by some sets of k shares. Supposing that at most t of the n shares are fake, Rees et al. (1999) described two algorithms to determine consistent sets of shares so that the secret can be reconstructed correctly from k shares in any of these consistent sets. In their algorithms, no honest participant can be absent and at least n-t shares should be pooled during the secret reconstruction phase. In this paper, we propose a modified algorithm for this problem so that the number of participants taking part in the secret reconstruction can be reduced to k+2t and the shares need to be pooled can be reduced to, in the best case, k+t, and less than or equal to k+2t in the others. Its efficiency is also investigated.
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