A Simple (v, t, n)-Fairness Secret Sharing Scheme with One Shadow for Each Participant

Abstract

Secret sharing scheme is an important method to share secrets among all participants. Though there are many secret sharing schemes proposed, however, most of the schemes are unfair. For a fair secret sharing scheme, even if there are participants are dishonest, the probability to recover the shared secret is still equal for all participants without releasing their shadows simultaneously. In this article, we propose a simple (v, t, n)-fairness secret sharing scheme. The (v, t, n)-fairness secret sharing scheme is a (t, n) secret sharing scheme with the feature that if there are v, v < t/2, share holders being dishonest, all other share holders still have equal probability to obtain the secret without releasing their shadows simultaneously. The merit of the proposed scheme is that each participant holds only one shadow such that it is convenient and practical for all users, and the computational complexity is quite low for cheater detection or identification.