(k, n) Secret Sharing Scheme against Two Types of Cheaters
In a (k, n) secret sharing scheme, k or more qualified shareholders can reconstruct the secret, but less than k of them are unable to get any information about the secret. The secret sharing schemes with cheating detection were designed to solve a problem that some vicious participants (cheaters) release forged shares in secret reconstruction. We divide the cheaters into inside cheaters and outside cheaters based on their different identities. The inside cheaters are qualified shareholders who aim to cheat other honest shareholders, the outside cheaters are disqualified shareholders who do not receive shares from dealer, they try to filch information of valid shares in secret reconstruction. In conventional cheating detection schemes, both the two type of cheaters can be detected. However, it cannot stop the information of valid shares from being revealed to the outside cheaters. Once the outside cheaters gather enough shares, they can reconstruct the secret exclusively. In this paper, we propose a (k, n) secret sharing scheme based on Shamir's scheme. The secret reconstruction in our scheme consists of two phases. In Phase 1, the outside cheaters can be detected, and no information of shares is revealed in this phase, in Phase 2, all participants can work together to detect the cheating of inside cheaters. In addition, our scheme is not base on any computational assumptions, it is unconditionally secure.