In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure from an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop...

Inthispaper,wepropose twosecureverifiablemulti-secret sharingschemes thatarebasedonnon-homogeneous linearrecursionsandelliptic curvesoverZN .Suchschemeshavesimpleconstructionandverificationphases.Moreover thesehavevarious techniques for the reconstruction phase. The security of the proposed schemes is based on the security of the ECRSA cryptosystem and the intractability of the ECDLP. 2007 Else...

We present a stronger notion of veriiable secret sharing and exhibit a protocol implementing it. We show that our new notion is preferable to the old ones whenever veriiable secret sharing is used as a tool within larger protocols, rather than being a goal in itself.

The generalized secret sharing scheme is a method used to divide secret into a set of participants such that only the qualified subsets of participants can reconstruct the secret. In this paper, we first propose a new generalized secret sharing scheme with cheater detection. The security of the scheme is based on discrete logarithm problem. Based on this scheme, we present a group-oriented gene...

Proactive Secret Sharing (PSS) scheme is a method to periodically renew n secret shares in a (k, n) threshold-based Secret Sharing Scheme (SSS) without modifying the secret, or reconstructing the secret to reproduce new shares. Traditionally, PSS schemes are developed for the Shamir’s SSS which is a single SSS. Bai (2006) developed a multiple-secret sharing scheme using matrix projection. This ...

We prove that for every n and 1 < t < n any t-out-of-n threshold secret sharing scheme for one-bit secrets requires share size log(t + 1). Our bound is tight when t = n− 1 and n is a prime power. In 1990 Kilian and Nisan proved the incomparable bound log(n − t + 2). Taken together, the two bounds imply that the share size of Shamir’s secret sharing scheme (Comm. ACM ’79) is optimal up to an add...

In a ) , ( n t secret sharing scheme (SS), a dealer divides a secret into n shares in such a way that (a) the secret can be recovered successfully with t or more than t shares, and (b) the secret cannot be recovered with fewer than t shares. In a weighted secret sharing scheme (WSS), each share of a shareholder has a positive weight. The secret can be recovered if the overall weight of shares i...

‎In a (t,n)-threshold secret sharing scheme‎, ‎a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together‎, ‎but no group of fewer than t participants can do‎. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao‎, ‎and the intractability of the elliptic curve discrete logar...

This paper describes an efficient (k, n) threshold digital signature scheme. In the scheme, k out of n signers cooperate to issue a signature without using trusted center. No secret communication is required among signers across the network. As a base scheme, Pedersen's verifiable secret sharing (VSS) is applied to generate shared secret keys in such a way that no secret communication is requir...

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-...