Secret sharing schemes with partial broadcast channels

Truman Welling, Rémi A. Chou, Aylin Yener

Huaxiong Wang, Duncan S. Wong

A secret sharing scheme typically requires secure communications in each of two distribution phases: (1) a dealer distributes shares to participants (share distribution phase); and later (2) the participants in some authorised subset send their share information to a combiner (secret reconstruction phase). While problems on storage required for participants, for example, the size of shares, have been well studied, problems regarding the communication complexity of the two distribution phases seem to have been mostly neglected in the literature so far. In this correspondence, we deal with several communication related problems in the secret reconstruction phase. Firstly, we show that there is a tradeoff between the communication costs and the number of participants involved in the secret reconstruction. We introduce the communication rate as the ratio of the secret size and the total number of communication bits transmitted from the participants to the combiner in the secret reconstruction phase. We derive a lower bound on the communication rate and give constructions that meet the bound. Secondly, we show that the point-to-point secure communication channels for participants to send share information to the combiner can be replaced with partial broadcast channels. We formulate partial broadcast channels as set systems and show that they are equivalent to the well-known combinatorial objects of cover-free family. Surprisingly, we find that the number of partial broadcast channels can be significantly reduced from the number of point-to-point secure channels. Precisely, in its optimal form, the number of channels can be reduced from n to O(log n), where is the number of participants in a secret sharing scheme. We also study the communication rates of partial broadcast channels for the secret reconstruction.

Carles Padró, Germán Sáez

En Zhang, Yongquan Cai

Rational secret sharing was first introduced by Halpern and Teague (STOC, 2004). Since then, a series of works have focused on designing rational secret sharing protocols. However, most existing solutions can share only one secret at one secret sharing process. To share multiple secrets such as m secrets, the dealer must redistribute shares for m times. In addition, previous works assume existence of broadcast channel which is not realistic. Motivated by those problems, this paper proposes a rational multi-secret sharing scheme, which combines the secret sharing scheme with game theory. In the protocol, the problem of sharing multiple secrets is addressed, and there are multiple secrets to be shared during one secret sharing process. Furthermore, this work starts off by constructing a protocol in simultaneous broadcast networks, and then we emulate the broadcast channel over point-to-point networks. Based on a computational assumption, we show that rational players have no incentive to deviate from the protocol and every player can obtain multi-secret fairly.

Carlo Blundo, Alfredo De Santis, Giovanni Di Crescenzo +2 more

Amos Beimel, Aner Ben-Efraim, Carles Padró +1 more