Paper 2024/601
Improved Provable Reduction of NTRU and Hypercubic Lattices
Abstract
Lattice-based cryptography typically uses lattices with special properties to improve efficiency. We show how blockwise reduction can exploit lattices with special geometric properties, effectively reducing the required blocksize to solve the shortest vector problem to half of the lattice's rank, and in the case of the hypercubic lattice $\mathbb{Z}^n$, further relaxing the approximation factor of blocks to $\sqrt{2}$. We study both provable algorithms and the heuristic well-known primal attack, in the case where the lattice has a first minimum that is almost as short as that of the hypercubic lattice $\mathbb{Z}^n$. Remarkably, these near-hypercubic lattices cover Falcon and most concrete instances of the NTRU cryptosystem: this is the first provable result showing that breaking NTRU lattices can be reduced to finding shortest lattice vectors in halved dimension, thereby providing a positive response to a conjecture of Gama, Howgrave-Graham and Nguyen at Eurocrypt 2006.
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Published elsewhere. Minor revision. PQCrypto 2024
- Keywords
- LatticesCryptanalysisNTRULIP
- Contact author(s)
-
henry bambury @ m4x org
phong nguyen @ inria fr - History
- 2024-04-22: approved
- 2024-04-18: received
- See all versions
- Short URL
- https://ia.cr/2024/601
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/601,
author = {Henry Bambury and Phong Q. Nguyen},
title = {Improved Provable Reduction of NTRU and Hypercubic Lattices},
howpublished = {Cryptology ePrint Archive, Paper 2024/601},
year = {2024},
note = {\url{https://eprint.iacr.org/2024/601}},
url = {https://eprint.iacr.org/2024/601}
}
