From Statistical Zero Knowledge to Secret Sharing

Secret Sharing and Statistical Zero Knowledge

We show a general connection between various types of statistical zero-knowledge (SZK) proof systems and (unconditionally secure) secret sharing schemes. Viewed through the SZK lens, we obtain several new results on secret-sharing: • Characterizations: We obtain an almost-characterization of access structures for which there are secret-sharing schemes with an efficient sharing algorithm (but no...

Non-Interactive and Information-Theoretic Secure Publicly Verifiable Secret Sharing

A publicly verifiable secret sharing scheme is more applicable than a verifiable secret sharing because of the property that the validity of the shares distributed by the dealer can be verified by any party. In this paper, we construct a non-interactive and informationtheoretic publicly verifiable secret sharing by a computationally binding and unconditionally hiding commitment scheme and zero-...

A Verifiable Secret Sharing Scheme with Statistical zero-knowledge

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...

Secret Sharing and Perfect Zero Knowledge

Privacy Preserving Distributed K-Means Clustering in Malicious Model Using Verifiable Secret Sharing Scheme

In this article, the authors propose an approach for privacy preserving distributed clustering that assumes malicious model. In the literature, there do exist, numerous approaches that assume a semi honest model. However, such an assumption is, at best, reasonable in experimentations; rarely true in real world. Hence, it is essential to investigate approaches for privacy preservation using a ma...