Improving Anonymity in Shared Key Primitives Based on Perfect Hash Families

We propose a new scheme for sharing symmetric key operations among a set of participants according to a (t,n) threshold access structure. We focus on anonymity properties of this scheme and show that this scheme provides improved values of anonymity measures than the existing ones. In particular, the scheme can provide optimal and equitable participant anonymity when it is based on balanced perfect hash families.

💡 Research Summary

The paper addresses the problem of anonymity in symmetric‑key sharing schemes that are built on a (t, n) threshold access structure. In such schemes a set of n participants is organized so that any t of them can jointly recover at least one secret key, while any smaller set learns nothing. The authors focus on quantifying anonymity both at the group level (which t‑subset actually performed the operation) and at the individual level (whether a particular participant was involved).

Zaverucha and Stinson (2010) introduced a set of anonymity measures: µ = 1 – max Pr