Efficient t-cheater identifiable (k, n) secret-sharing scheme for t #x02A7D; [((k - 2)/2)]

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|/e, 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) * 2 |S|)/e. 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| = (2 |S| )/e, 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) * 2 |S|)/e 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).