On hermitian decomposition lattices and the module-LIP problem in rank 2

Thomas Espitau; Heorhii Pliatsok

Paper 2024/1148

On hermitian decomposition lattices and the module-LIP problem in rank 2

Thomas Espitau, PQShield, France

Heorhii Pliatsok, IRISA, Rennes

Abstract

In this short note, we introduce a specific class of rank two lattices over CM fields endowed with additional symmetries, which are involved in the decomposition of algebraic integers in Hermitian squares. As an application, we show an elementary reduction from the module-LIP problem in rank 2 over a CM or totally real number field to the finding of a square basis in such lattices.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Keywords: Hermitian forms modules lattices LIP
Contact author(s): thomas @ espitau com
History: 2024-07-19: approved; 2024-07-15: received; See all versions
Short URL: https://ia.cr/2024/1148
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1148,
      author = {Thomas Espitau and Heorhii Pliatsok},
      title = {On hermitian decomposition lattices and the module-{LIP} problem in rank 2},
      howpublished = {Cryptology ePrint Archive, Paper 2024/1148},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/1148}},
      url = {https://eprint.iacr.org/2024/1148}
}