Aperiodic logarithmic signatures

TL;DR

This paper introduces a novel method for constructing aperiodic logarithmic signatures that lack periodic blocks, enhancing cryptographic security by avoiding structures exploited in previous attacks.

Contribution

It presents a new construction approach for logarithmic signatures based on group factorizations, avoiding amalgamated transversals and periodic blocks.

Findings

Constructed logarithmic signatures without periodic blocks

Enhanced cryptographic security against specific attacks

Based on advanced group factorization theory

Abstract

In this paper we propose a method to construct logarithmic signatures which are not amalgamated transversal and further do not even have a periodic block. The latter property was crucial for the successful attack on the system MST3 by Blackburn et al. [1]. The idea for our construction is based on the theory in Szab\'o's book about group factorizations [12].