Guilhem Mureau
Univ Bordeaux, CNRS, Inria, Bordeaux INP, IMB, UMR 5251, Talence, France
16th May 2024, 4:00pm - 5:00pm (GST)
| Title: | Cryptanalysis of rank-2 module-LIP in Totally Real Number Fields |
| Abstract: | We formally define the Lattice Isomorphism Problem for module lattices (module-LIP) in a number field K. This is a generalization of the problem defined by Ducas, Postlethwaite, Pulles, and van Woerden (Asiacrypt 2022). We also provide the corresponding set of algorithmic and theoretical tools for the future study of this problem in a module setting. Using algerbaic methods, we give an algorithm solving module-LIP for modules of rank 2 in K^2, when K is a totally real number field. For a large class of modules (including O_K^2), and a large class of number fields (including the maximal real subfield of cyclotomic fields) it runs in classical polynomial time in the degree of the field and the residue at 1 of the Dedekind zeta function of the field (under reasonable number theoretic assumptions). |
| Bio: | I started my PhD in September 2023 at Inria / University of Bordeaux (France), after a master degree in pure mathematics. My thesis is about isomorphisms of structured lattices, a subject motivated by the recent use of such concepts in cryptography. More generally, I'm interested in all fields of number theory and their applications in cryptography. |