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 ...

Secret-sharing schemes are an important tool in cryptography that is used in the construction of many secure protocols. However, the shares’ size in the best known secret-sharing schemes realizing general access structures is exponential in the number of parties in the access structure, making them impractical. On the other hand, the best lower bound known for sharing of an `-bit secret with re...

In his paper [9], Stadler develops techniques for improving the security of existing secret sharing protocols by allowing to check whether the secret shares given out by the dealer are valid. In particular, the secret sharing is executed over abelian groups. In this paper we develop similar methods over non-abelian groups.

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 [...

We present a new protocol for the verifiable redistribution of secrets from (m,n) to (m,n) access structures for threshold sharing schemes. Our protocol enables the addition or removal of shareholders and also guards against mobile adversaries that cause permanent damage. We observe that existing protocols either cannot be readily extended to allow redistribution between different access struct...

We present a new protocol for verifiably redistributing secrets from an (m,n) threshold sharing scheme to an (m′, n′) scheme. Our protocol guards against dynamic adversaries. We observe that existing protocols either cannot be readily extended to allow redistribution between different threshold schemes, or have vulnerabilities that allow faulty old shareholders to distribute invalid shares to n...

This paper studies the methods for changing thresholds in the absence of secure channels after the setup of threshold secret sharing schemes. First, we construct a perfect (t, n) threshold scheme that is threshold changeable to t ′ > t , which is optimal with respect to the share size. This improves the scheme of Wang and Wong by relaxing the requirement from q ≥ n + v to q > n with the secret-...