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.
Infos pratiques
Prochains exposés
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Dual attacks in code-based (and lattice-based) cryptography
Orateur : Charles Meyer-Hilfiger - Inria Rennes
The hardness of the decoding problem and its generalization, the learning with errors problem, are respectively at the heart of the security of the Post-Quantum code-based scheme HQC and the lattice-based scheme Kyber. Both schemes are to be/now NIST standards. These problems have been actively studied for decades, and the complexity of the state-of-the-art algorithms to solve them is crucially[…]-
Cryptography
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Présentations des nouveaux doctorants Capsule
Orateur : Alisée Lafontaine et Mathias Boucher - INRIA Rennes
2 nouveaux doctorants arrivent dans l'équipe Capsule et présenteront leurs thématiques de recherche. Alisée Lafontaine, encadrée par André Schrottenloher, présentera son stage de M2: "Quantum rebound attacks on double-block length hash functions" Mathias Boucher, encadré par Yixin Shen, parlera des algorithmes quantiques et des réseaux euclidiens. -
Design of fast AES-based Universal Hash Functions and MACs
Orateur : Augustin Bariant - ANSSI
Ultra-fast AES round-based software cryptographic authentication/encryption primitives have recently seen important developments, fuelled by the authenticated encryption competition CAESAR and the prospect of future high-profile applications such as post-5G telecommunication technology security standards. In particular, Universal Hash Functions (UHF) are crucial primitives used as core components[…]-
Cryptography
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Lie algebras and the security of cryptosystems based on classical varieties in disguise
Orateur : Mingjie Chen - KU Leuven
In 2006, de Graaf et al. proposed a strategy based on Lie algebras for finding a linear transformation in the projective linear group that connects two linearly equivalent projective varieties defined over the rational numbers. Their method succeeds for several families of “classical” varieties, such as Veronese varieties, which are known to have large automorphism groups. In this talk, we[…]-
Cryptography
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Some applications of linear programming to Dilithium
Orateur : Paco AZEVEDO OLIVEIRA - Thales & UVSQ
Dilithium is a signature algorithm, considered post-quantum, and recently standardized under the name ML-DSA by NIST. Due to its security and performance, it is recommended in most use cases. During this presentation, I will outline the main ideas behind two studies, conducted in collaboration with Andersson Calle-Vierra, Benoît Cogliati, and Louis Goubin, which provide a better understanding of[…]