Simple and Asymptotically Optimal t-Cheater Identifiable Secret Sharing Scheme

In this paper, we consider the problem of k-out-of-n secret sharing scheme, capable of identifying t cheaters. We design a very simple k-out-of-n secret sharing scheme, which can identify up to t cheaters, with probability at least 1 − ε, where 0 < ε < 1/2, provided t < k/2. This is the maximum number of cheaters, which can be identified by any k-out-of-n secret sharing scheme, capable of identifying t cheaters. In our scheme, the set of all possible i share Vi satisfies the condition that |Vi| = |S|/ε, where S denotes the set of all possible secrets. Moreover, our scheme requires polynomial computation. In EUROCRYPT 2011, Satoshi Obana presented two SSCI schemes, which can identify up to t < k/2 cheaters. However, the schemes require |Vi| ≈ (n·(t+1)·2 3t−1·|S|) ε and |Vi| ≈ ((n·t·2 )·|S|) ε2 respectively. Moreover, both the schemes are computationally inefficient, as they require to perform exponential computation in general. So comparing our scheme with the schemes of Obana, we find that not only our scheme is computationally efficient, but in our scheme the share size is significantly smaller than that of Obana. Thus our scheme solves one of the open problems left by Obana, urging to design efficient SSCI scheme with t < k/2. In CRYPT