Updating the Parameters of a Threshold Scheme by Minimal Broadcast

Abstract

Abstract-Threshold schemes allow secret data to be protected among a set of participants in such a way that only a prespecified threshold of participants can reconstruct the secret from private information (shares) distributed to them on a system setup using secure channels. We consider the general problem of designing unconditionally secure threshold schemes whose defining parameters (the threshold and the number of participants) can later be changed by using only public channel broadcast messages. In this paper, we are interested in the efficiency of such threshold schemes, and seek to minimize storage costs (size of shares) as well as optimize performance in low-bandwidth environments by minimizing the size of necessary broadcast messages. We prove a number of lower bounds on the smallest size of broadcast message necessary to make general changes to the parameters of a threshold scheme in which each participant already holds shares of minimal size. We establish the tightness of these bounds by demonstrating optimal schemes.

A lattice-based changeable threshold multi-secret sharing scheme and its application to threshold cryptography

“…The rst of such a scheme was introduced by Blakley and Shamir, independently, in 1979 [5,6]. Since then, some new features have been added to the secret sharing schemes such as veri ability of the shares [7,8], resistance of the scheme in the presence of a number of cheaters [9,10], and dynamic change of the threshold and/or the number of participants [11,12].…”

A Multi-stage Secret Sharing Scheme Using All-or-Nothing Transform Approach

“…Later, various features like verifiability of the shares [3], resistance against the presence of a number of cheaters [4], dynamic change of the threshold and the number of participants [5] were added to the threshold secret sharing scheme.…”

Dynamic access policies for unconditionally secure secret sharing schemes

“…The problem of making more general changes to an access policy in Model 6 Type C environments has been considered in [1]. Let U be a family of access structures.…”

“…In [1] this problem was investigated more closely for the case of threshold schemes that require just one change. Bounds were proven for the minimal amount of broadcast information that needs to be used for threshold schemes with minimal secret storage that are changeable to U for the entire range of possible sets U (where the only restriction was that U defined a family of threshold access structures).…”

“…Open Problem 2: Can the results of [1] for bounding the broadcast size for enabling one change to threshold schemes be extended to multiple changes for arbitrary access policies?…”