On the hull attacks against Construction A lattices

Jean-François Biasse; Alexandra V. Hostetler; Anuvrat Jaindungarwal

Paper 2026/2325

On the hull attacks against Construction A lattices

Jean-François Biasse, University of South Florida

Alexandra V. Hostetler, University of South Florida

Anuvrat Jaindungarwal, University of South Florida

Abstract

In this paper, we present an algorithm for solving the Lattice Isomorphism Problem between input lattices that are isometric to the Construction A lattice of a certain code C. Our algorithm is a direct extension of a method due to Ducas and Gibbons (PKC 2023). We prove that the run time of our algorithm is $2^{O(n)}$ and that its success probability is $1+o(1)$ over a random choice of C. Crucially, our method works when the hull of C has arbitrary dimension while the method of Ducas and Gibbons is restricted to the case of a trivial hull.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Published elsewhere. Selected Areas in Cryptography 2026
Keywords: Lattice based cryptography Code based cryptography Lattice Isomorphism Problem Code Equivalence Problem Hull attacks
Contact author(s): biasse @ usf edu
avelichehostetler @ usf edu
anuvrat @ usf edu
History: 2026-10-05: approved; 2026-10-03: received; See all versions
Short URL: https://ia.cr/2026/2325
License: CC BY

BibTeX

@misc{cryptoeprint:2026/2325,
      author = {Jean-François Biasse and Alexandra V. Hostetler and Anuvrat Jaindungarwal},
      title = {On the hull attacks against Construction A lattices},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/2325},
      year = {2026},
      url = {https://eprint.iacr.org/2026/2325}
}