Efficient t-cheater identifiable (k, n) secret-sharing scheme for t ⩽ [((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 |V_i| can be written as |V_i| = |S|/ε, which almost meets its lower bound, where |S| denotes the size of secret and ε 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 |V_i| = (n·(t + 1) · 2^3t-1|S|)/ε. 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 |V_i| = (2^{k - 1}|S| )/ε, 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 |V_i| = (n · (t + 1) · 2^{k - 1}|S|)/ε 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)].