Verifiable secret sharing

About: Verifiable secret sharing is a research topic. Over the lifetime, 4241 publications have been published within this topic receiving 99569 citations.

An explication of secret sharing schemes

Abstract: This paper is an explication of secret sharing schemes, emphasizing combinatorial construction methods. The main problem we consider is the construction of perfect secret sharing schemes, for specified access structures, with the maximum possible information rate. In this paper, we present numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean circuit construction of Benaloh and Leichter (for general access structures), the vector space construction of Brickell, and the Simmons geometric construction. We discuss the connections between ideal schemes (i.e., those with information rate equal to one) and matroids. We also mention the entropy bounds of Capocelli et al. Then we give a very general construciton, called the decomposition construction, and numerous applications of it. In particular, we study schemes for access structures based on graphs and the many interesting bounds that can be proved; and we determine the exact value of the optimal information rate for all access structures on at most four participants.

Secure Multiparty Computation and Secret Sharing

Abstract: In a data-driven society, individuals and companies encounter numerous situations where private information is an important resource. How can parties handle confidential data if they do not trust everyone involved? This text is the first to present a comprehensive treatment of unconditionally secure techniques for multiparty computation (MPC) and secret sharing. In a secure MPC, each party possesses some private data, while secret sharing provides a way for one party to spread information on a secret such that all parties together hold full information, yet no single party has all the information. The authors present basic feasibility results from the last 30 years, generalizations to arbitrary access structures using linear secret sharing, some recent techniques for efficiency improvements, and a general treatment of the theory of secret sharing, focusing on asymptotic results with interesting applications related to MPC.

A verifiable random function with short proofs and keys

Abstract: We give a simple and efficient construction of a verifiable random function (VRF) on bilinear groups. Our construction is direct. In contrast to prior VRF constructions [14,15], it avoids using an inefficient Goldreich-Levin transformation, thereby saving several factors in security. Our proofs of security are based on a decisional bilinear Diffie-Hellman inversion assumption, which seems reasonable given current state of knowledge. For small message spaces, our VRF's proofs and keys have constant size. By utilizing a collision-resistant hash function, our VRF can also be used with arbitrary message spaces. We show that our scheme can be instantiated with an elliptic group of very reasonable size. Furthermore, it can be made distributed and proactive.

Civitas: Toward a Secure Voting System

Abstract: Civitas is the first electronic voting system that is coercion-resistant, universally and voter verifiable, and suitable for remote voting. This paper describes the design and implementation of Civitas. Assurance is established in the design through security proofs, and in the implementation through information-flow security analysis. Experimental results give a quantitative evaluation of the tradeoffs between time, cost, and security.