In this paper, we first propose a protocol in which the prover can show that a = b holds for two committed integers a and b; also, we present a protocol in which the prover can prove that a 6= 0 holds for committed integer a; then, we construct a protocol to prove that the degree of a polynomial f(x) equals to t− 1 exactly, which has been as an open problem(see[21]); finally, we provide a proto...

In secret sharing scheme, the master secret and all the private shares (which are distributed by the dealer to the shareholders) are the two secrets which are to be maintained confidentially. In all the secret sharing schemes proposed till date, private shares are reused to reconstruct the master secret. But we proposed a new way of Proactive Secret Sharing Scheme in which, instead of renewing ...

This paper presents a non-interactive verifiable secret sharing scheme (VSS) tolerating a dishonest majority based on data predistributed by a trusted authority. As an application of this VSS scheme we present very efficient unconditionally secure multiparty protocols based on pre-distributed data which generalize two-party computations based on linear pre-distributed bit commitments. The main ...

We present new cryptographic protocols for multi-authority secret ballot elections that guarantee privacy, robustness, and universal verifiability. Application of some novel techniques, in particular the construction of witness hiding/indistinguishable protocols from Cramer, Damg̊ard and Schoenmakers, and the verifiable secret sharing scheme of Pedersen, reduce the work required by the voter or ...

In this paper, we present a very important primitive called Information Checking Protocol (ICP) which plays an important role in constructing statistical Verifiable Secret Sharing (VSS) and Weak Secret Sharing (WSS) protocols. Informally, ICP is a tool for authenticating messages in the presence of computationally unbounded corrupted parties. Here we extend the basic bare-bone definition of ICP...

We introduce and formally define polynomial commitment schemes, and provide two efficient constructions. A polynomial commitment scheme allows a committer to commit to a polynomial with a short string that can be used by a verifier to confirm claimed evaluations of the committed polynomial. Although the homomorphic commitment schemes in the literature can be used to achieve this goal, the sizes...

Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Computer Science and Technology, Anhui University, Hefei, 230039, China Department of Computer Science and Information Engineering, Asia University, Taichung, 413, Taiwan Department of Computer Science and Electrical Engineering, University of Missouri—Kansas City, Kansas City, Missouri 64110-2499,...

In the standard general-adversary model for multi-party protocols, a global adversary structure is given, and every party must trust in this particular structure. We introduce a more general model, the asymmetric-trust model, wherein every party is allowed to trust in a different, personally customized adversary structure. We have two main contributions. First, we present non-trivial lower and ...

The round complexity of interactive protocols is one of their most important complexity measures. In this work we prove that existing lower bounds for the round complexity of VSS can be circumvented by introducing a negligible probability of error in the reconstruction phase. Previous results show matching lower and upper bounds of three rounds for VSS, with n = 3t + 1, where the reconstruction...

Verifiable secret sharing schemes (VSS) are secret sharing schemes (SSS) dealing with possible cheating by participants. In this paper we use the VSS proposed by Cramer, Damgard and Maurer [6, 7, 5]. They introduced a purely linear algebraic method to transform monotone span program (MSP) based secret sharing schemes into VSS. In fact, the monotone span program model of Karchmer and Wigderson [...