Description
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 , further relaxing the approximation factor of blocks to .
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 . 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.
Practical infos
Next sessions
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Module Learning With Errors and Structured Extrapolated Dihedral Cosets
Speaker : Jinwei Zheng - Télécom Paris
The Module Learning With Errors (MLWE) problem is the fundamental hardness assumption underlying the key encapsulation and signature schemes ML-KEM and ML-DSA, which have been selected by NIST for post-quantum cryptography standardization. Understanding its quantum hardness is crucial for assessing the security of these standardized schemes. Inspired by the equivalence between LWE and[…]-
Cryptography
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European Cyber Week: atelier cryptographie post-quantique
Dans la continuité des éditions 2021, 2022 et 2024, la DGA — en partenariat avec CREACH LABS et avec le soutien de l'ANSSI, de l'IRISA, de l'IRMAR et du Pôle d'Excellence Cyber — organise la 4e édition de l'atelier consacré à la cryptographie post-quantique dans le cadre de l'European Cyber Week 2026. Attention, il faut s'inscrire (gratuitement) au préalable — s'inscrire à la conférence Les[…] -
Post-quantum day of the cryptography seminar
A scientific day devoted to post-quantum cryptography, held in the wake of the European Cyber Week, with talks more technical than those presented at the ECW.