**A Verifiable Secret Sharing Scheme with Statistical zero-knowledge**

*Chunming Tang and Zhuojun Liu and Mingsheng Wang*

**Abstract: ** 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\neq 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 protocol in which the prover proves that a
pair (x,y) is generated by a polynomial f(x), i.e., y=f(x)(mod m), where m is a prime.
Based on above four protocols, we put forward a verifiable
(t,n)-secret sharing scheme, which can avoid all known the
dealer's cheats.
In particular, all above protocols are statistical zero-knowledge.

**Category / Keywords: **cryptographic protocols / secret sharing, verifiable secret sharing, statistical zero-knowledge

**Date: **received 10 Oct 2003

**Contact author: **ctang at mmrc iss ac cn

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**Version: **20031013:194551 (All versions of this report)

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