Efficient threshold secret sharing schemes secure against rushing cheaters

In this paper, we consider two very important issues namely detection and identification of k-out-of-n secret sharing schemes against rushing cheaters who are allowed to submit (possibly forged) shares after observing shares of the honest users in the reconstruction phase. Towards this, we present four different schemes. Among these, first we present two k-out-of-n secret sharing schemes, the first one being capable of detecting (k − 1)/3 cheaters such that |V_i| = |S|/∊³ and the second one being capable of detecting n − 1 cheaters such that |V_i| = |S|/∊^k+1, where S denotes the set of all possible secrets, ∊ denotes the successful cheating probability of cheaters and V_i denotes set all possible shares. Next we present two k-out-of-n secret sharing schemes, the first one being capable of identifying (k−1)/3 rushing cheaters with share size |V_i| that satisfies |V_i| = |S|/∊^k. This is the first scheme, whose size of shares does not grow linearly with n but only with k, where n is the number of participants. For the second one, in the setting of public cheater identification, we present an efficient optimal cheater resilient k-out-of-n secret sharing scheme against rushing cheaters having the share size |V_i| = (n−t)^n+2t|S|/∊^n+2t. The proposed scheme achieves flexibility in the sense that the security level (i.e., the cheater(s) success probability) is independent of the secret size. Each of the four proposed schemes has the smallest share size among the existing schemes having the mentioned properties in the respective models.