Description
The main focus of this PhD thesis lies on the computational problem Learning With Errors (LWE). It is a core building block of lattice-based cryptography, which itself is among the most promising candidates to replace current cryptographic protocols once large-scale quantum computers may be available. The contributions of the present work are separated into two different parts. First, we study the hardness of structured variants of LWE. To this end, we show that under suitable parameter choices the Module Learning With Errors (M-LWE) problem doesn't become significantly easier to solve even if the underlying secret is replaced by a binary vector. Furthermore, we provide a classical hardness reduction for M-LWE, which further strengthens our confidence in its suitability for cryptography. Additionally, we define a new hardness assumption, the Middle-Product Computational Learning With Rounding (MP-CLWR) problem, which inherits the advantages of two existing LWE variants. Finally, we study problems related to the partial Vandermonde matrix. This is a recent source of hardness assumptions for lattice-based cryptography and its rigorous study is important to gain trust in it. In the second part of this manuscript, we show that the new hardness assumptions we introduced before serve for the construction of efficient public-key encryption. On the one hand, we design a new encryption scheme, whose security is provably based on the MP-CLWR problem. On the other hand, we modify an existing encryption scheme, called PASS Encrypt, to provide it with a security proof based on two explicitly stated partial Vandermonde problems.<br/> lien: https://youtu.be/Bu_PWWb63iU
Next sessions
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Adelic reduction of module lattices
Speaker : Henry Bambury - DGA-MI et Inria Rennes
We give a strict generalisation of the LLL algorithm over number fields, based on the reduction theory of $GL(n)$ over the adele ring of a number field. Our algorithm is free of heuristics, with rigorous bounds on output quality and complexity. -- based on joint work with Seungki Kim, Changmin Lee and Phong Nguyen ---
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.