Cheating Detectable Secret Sharing Scheme Suitable for Implementation

Abstract

A cheating detectable secret sharing scheme is a secret sharing scheme that can detect forged shares in reconstructing a secret. For example, if we store shares in cloud storage, there is a possibility of it being forged. If the administrators of cloud storage are malicious, it is easy for them to forge a share. Therefore, cheating detectable secret sharing schemes have attracted attention, and many efficient schemes have been proposed. However, most existing schemes are not suitable for implementation. The reasons are as follows. First, the computational cost of the schemes is very high. Second, the required finite field for implementation depends on the secret. Finally, the schemes do not support secrets that are bit strings. In this paper, we propose a cheating detectable secret sharing scheme suitable for implementation. However, we assume that cheaters do not know the secret. The basic idea is a bitdecomposing technique. The bit length of the proposed scheme is an optimum. Moreover, the proposed scheme is applicable to any linear secret sharing schemes.