Paper 2024/1598 Original: eprint.iacr.org/2024/1598 ↗

On the security of the initial tropical Stickel protocol and its modification based on Linde-de la Puente matrices

Abstract

Recently, a more efficient attack on the initial tropical Stickel protocol has been proposed, different from the previously known Kotov-Ushakov attack, yet equally guaranteed to succeed. Given that the Stickel protocol can be implemented in various ways, such as utilizing platforms beyond the tropical semiring or employing alternative commutative matrix ``classes'' instead of polynomials, we firstly explore the generalizability of this new attack across different implementations of the Stickel protocol. We then conduct a comprehensive security analysis of the Stickel protocol based on Linde-de la Puente (LdlP) matrices. Additionally, we extend the concept of LdlP matrices beyond the tropical semiring, generalizing it to a broader class of semirings and include a discussion of the centralizer of such matrices over the tropical semiring.