Asynchronous Rational Secret Sharing Scheme

Threshold Secret sharing scheme is an important way to protect a secret, which is vastly used in keymanagement, secure multi-party computation and so on. But the original threshold scheme proposedby Shamir did not pay much attention to the verification of share which may be replaced by a fakeshare, and this lowers the robustness of the scheme. Afterwards, verifiable secret sharing schemesproposed by many researchers have focused on this property and reached both high efficiency andsecurity. While in the real world, agents are more likely to be rational individuals who are neithergood nor bad, but follow their best interests. Halpern proposed a new kind of scheme based on gametheory, i.e. rational secret sharing, a new field of research on secret sharing, in that even if agents donot believe in each other, they can still reconstruct the secret cooperatively,. Although researcherssolved some of the problems in rational secret sharing, there are still some reality-related problems tobe solved such as application in asynchronous channel, mix agents model, cheat proof and fixed roundreconstruct, etc.Because the popular communication networks in reality are more of asynchronous, we take theasynchronous channel with a few assumptions as our communication environment. By analyzing theexisting secret sharing schemes, we sum up several ideas of constructing a new scheme, specificallyhow to share a secret in asynchronous channel with rational individuals. Our works are list asfollowing:(1) We put forward a possible exploit of the existing asynchronous rational secret sharing, and thenpropose a new scheme based on limited punishment strategy and a new kind of secret sequence whichhas solved this problem as well as the non-creditable threat in most existing scheme. Moreover, wepoint out three key issues of none-fixed round rational secret sharing: the construction of rounds, howto choose the end-game signal and the sequential actions in asynchronous channel.(2) By hiding the knowledge of threshold, we construct a one-round asynchronous rational secretsharing scheme.(3) We propose a hybrid rational secret sharing scheme with both malicious and honest agents andcompare with other similar scheme. The scheme can reach both security and high efficiency.Besides, we get three conclusions about rational secret sharing: employing a list which contains thereal secret and releasing the position of the real by the relationship of these secrets can reach a bettersecurity; that all shareholders start next round only after they all receive all shares can avoid thepotential vulnerability caused by asynchronous channel; fixed-round rational secret sharing schemecan be achieved by hiding the threshold or add honest shareholders in the scheme.