Efficient t-cheater identifiable (k, n) secret-sharing scheme for t ≤⌊((k - 2)/2)⌋

Abstract

In Eurocrypt 2011, Obana proposed a (k, n) secret-sharing scheme that can identify up to ⌊((k - 2)/2)⌋ cheaters. The number of cheaters that this scheme can identify meets its upper bound. When the number of cheaters t satisfies t = ⌊((k - 1)/3)⌋, this scheme is extremely efficient since the size of share |Vi| can be written as |Vi| = |S|/., which almost meets its lower bound, where |S| denotes the size of secret and e denotes the successful cheating probability; when the number of cheaters t is close to . ((k - 2)/2)⌋, the size of share is upper bounded by |Vi| = (n•(t + 1) • 23t - 1|S|)/.σ A new (k, n) secret-sharing scheme capable of identifying ⌊((k - 2)/2)⌋ cheaters is presented in this study. Considering the general case that k shareholders are involved in secret reconstruction, the size of share of the proposed scheme is |Vi| = (2k - 1|S| )/σ, which is independent of the parameters t and n. On the other hand, the size of share in Obana's scheme can be rewritten as |Vi | = (n • (t + 1) • 2k - 1|S|)/σ under the same condition. With respect to the size of share, the proposed scheme is more efficient than previous one when the number of cheaters t is close to ⌊((k - 2)/2)⌋. © 2013 The Institution of Engineering and Technology.