Paper 2009/207

Unconditionally Secure Social Secret Sharing Scheme

Mehrdad Nojoumian, Douglas R. Stinson, and Morgan Grainger

Abstract

We introduce the notion of a Social Secret Sharing Scheme, in which shares are allocated based on a player's reliability and the way he interacts with other participants. During the share refresh phase, weights of participants are adjusted in a way that participants who cooperate will end up with more shares than those who defect. On the other hand, corrupted players will be disenrolled immediately for the computation safety. Our motivation is that, in real world applications, components of a secure multiparty computation framework may have different levels of importance as well as credibility. Therefore, a robust construction should balance these two factors respectively, that is adjusting the responsibility based on the reliability. The proposed construction has a variety of desirable properties. It is an unconditionally verifiable scheme in the sense that it can detect malicious participants without relying on any computational assumptions. The scheme proactively renews shares at each cycle without changing the secret, and allows trusted participants to gain more authority in the scheme, i.e., a dynamic access structure. The other prominent property of the scheme is that, it gradually reduces the influence of irresponsible players due to the self-reinforcement property of social interactions among players.