Seminario: "Invariants and Group Actions: An Algebraic Attack Framework for Isomorphism Problems" - Giuseppe D'Alconzo

UMI Crittografia e Codici: On line Seminars

Invariants and Group Actions: An Algebraic Attack Framework for Isomorphism Problems

Giuseppe D'Alconzo (Telsy S.p.A.)

Abstract: Many hard problems underlying code and lattice-based signature schemes can be cast as isomorphism problems: given two objects, determine whether a hidden group element maps one to the other. In this talk, we present a general framework for attacking such problems using tools from invariant theory and algebraic geometry. The central idea is to study the action of the relevant group on the object space and construct invariant functions that are unchanged by the "easy" part of the hidden transformation, isolating the "hard" part as a root of an explicit system of polynomial equations. We illustrate this framework using the Linear Code Equivalence (LCE) problem, where the hidden transformation is a monomial matrix decomposable into a diagonal part and a permutation part. Using Plücker coordinates and invariant rational functions on the Grassmannian, we construct algebraically independent invariants under diagonal scaling, yielding polynomial equations with the hidden permutation as a root. We discuss how this construction generalizes beyond LCE to other isomorphism problems, and outline the current limitations and open questions in turning such invariant-theoretic constructions into practical cryptanalytic tools.

  
https://us06web.zoom.us/j/4015041788?pwd=bkVtWVhEWDhNMyswQXA3enYycy9hQT09
Meeting ID: 401 504 1788
Passcode: 21ccmz