Ideal social secret sharing using Birkhoff interpolation method

The concept of social secret sharing was introduced in 2010 by Nojoumian et al. In Nojoumian et al.’s scheme (called SSS), the number of shares allocated to each party depends on the player’s reputation and the way he interacts with other parties. In other words, weights of the players are periodically adjusted such that cooperative participants receive more shares compared to non-cooperative parties. As our contribution, we propose an ideal social secret sharing (Ideal-SSS) in which the size of each player’s share is equal to the size of the secret. This property will be achieved using hierarchical threshold secret sharing. We show that the proposed scheme is secure in a passive adversary model. Compared to SSS, our proposed scheme is more efficient in terms of the share size, communication complexity and computational complexity of the “sharing” protocol. However, the “social tuning” and “reconstruction” protocols of SSS are computationally more efficient than those of the proposed scheme. Depending on the number of execution of social tuning protocol, this might be a reasonable compromise because the reconstruction protocol is executed only once throughout the secret’s lifetime. Copyright c ⃝ 2010 John Wiley & Sons, Ltd.