An Efficient V-Fairness (t, n) Threshold Secret Sharing Scheme

Abstract

Lee and Laih proposed a v-fairness (t, n) secret sharing scheme such that the participants can recover a secret without providing their shadows simultaneously. Besides, the honest participants can obtain the secret even if there are v cheaters among the t participants in their scheme, where v<t/2. However, in Lee and Laih's scheme, each participant must keep three shadows to reconstruct only one secret. In this paper, we propose an efficient v-fairness (t, n) multi-secret sharing scheme, which reduces the number of secret shadows kept by each member and increases the messages that can be concealed in the system. Consequently, our scheme allows each member just keeps two shadows. Besides, we only take a slight computation cost to accomplish the purpose of sharing multiple secrets. Thus, our scheme is more efficient and generic than the previous related papers.

Fair secret reconstruction in (t, n) secret sharing

“…In their scheme, the dealer divides the secret into multiple subsecrets with different threshold values and generates shares for each sub-secret. There are some recent papers (Lee, 2011;Yang et al, 2011) to improve Laih et al's scheme. One main problem of the V-fairness (t, n) secret reconstruction scheme is that the number of cheaters in this model is limited to be less than t/2.…”

A Fair (t, n)-Threshold Secret Sharing Scheme with Efficient Cheater Identifying

“…Laih and Lee [2] proposed a vfair (t, n)-threshold secret sharing scheme, in which all participants do not have to show their secret shares simultaneously to recover the secret with the same probability, even if there are v(< t/2) dishonest participants. [3] and [5] further improved Laih scheme [2]. In 2003, Tian [6] utilized the consistency of secret shares to detect attackers, and constructed a fair (t, n)-threshold scheme with the help of the schemes of Tompa and Woll [7].…”