Cheating detectable secret sharing schemes supporting an arbitrary finite field

Abstract

In this paper, we present k-out-of-n threshold secret sharing scheme which can detect share forgery by at most k-1 cheaters. Though, efficient schemes with such a property are presented so far, some schemes cannot be applied when a secret is an element of and some schemes require a secret to be an element of a multiplicative group. The schemes proposed in the paper possess such a merit that a secret can be an element of arbitrary finite field. Let |S| and ε be the size of secret and successful cheating probability of cheaters, respectively. Then the sizes of share |Vi| of two proposed schemes respectively satisfy |Vi| = (2· |S|)/ε |Vi| = (4· |S|)/ε) and which are only 2 and 3 bits longer than the existing lower bound. © 2014 Springer International Publishing.