CryptoDB
Cryptanalysis of rank-2 module-LIP in totally real number fields
| Authors: |
|
|---|---|
| Download: | |
| Conference: | EUROCRYPT 2024 |
| 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), taking into account the arithmetic and algebraic specificity of module lattices from their representation using pseudo-bases. We also provide the corresponding set of algorithmic and theoretical tools for the future study of this problem in a module setting. Our main contribution is an algorithm solving module-LIP for modules of rank 2 in K^2, when K is a totally real number field. Our algorithm exploits the connection between this problem, relative norm equations and the decomposition of algebraic integers as sums of two squares. For a large class of modules, including O_K^2, it runs in classical polynomial time (under reasonable number theoretic assumptions). We provide a proof-of-concept code running over the maximal real subfield of cyclotomic fields. |
BibTeX
@inproceedings{eurocrypt-2024-33939,
title={Cryptanalysis of rank-2 module-LIP in totally real number fields},
publisher={Springer-Verlag},
author={Guilhem Mureau and Alice Pellet-Mary and Georges Pliatsok and Alexandre Wallet},
year=2024
}