On a Fast (K, n)-Threshold Secret Sharing Scheme

概要

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In Shamirs (k,n)-threshold secret sharing scheme (threshold scheme) [1], a heavy computational cost is required to make n shares and recover the secret from k shares. As a solution to this problem, several fast threshold schemes have been proposed. However, there is no fast ideal (k,n)-threshold scheme, where k and n are arbitrary. This paper proposes a new fast (k,n)-threshold scheme which uses just EXCLUSIVE-OR (XOR) operations to make n shares and recover the secret from k shares. We prove that every combination of k or more participants can recover the secret, but every group of less than k participants cannot obtain any information about the secret in the proposed scheme. Moreover, the proposed scheme is an ideal secret sharing scheme similar to Shamirs scheme, in which every bitsize of shares equals that of the secret. We also evaluate the efficiency of the scheme, and show that our scheme realizes operations that are much faster than Shamirs.
（社）電子情報通信学会の論文
2008-09-01