Description
Code-based cryptography has a long history, almost as long as the history of public-key encryption (PKE). While we can construct almost all primitives from codes such as PKE, signature, group signature etc, it is a long standing open problem to construct an identity-based encryption from codes. We solve this problem by relying on codes with rank metric. The concept of identity-based encryption (IBE), introduced by Shamir in 1984, allows the use of users’ identifier information such as email as public key for encryption. There are two problems that makes the design of IBE extremely hard: the requirement that the public key can be an arbitrary string and the possibility to extract decryption keys from the public keys. In fact, it took nearly twenty years for the problem of designing an efficient method to implement an IBE to be solved. The known methods of designing IBE are based on different tools: from elliptic curve pairings by Sakai, Ohgishi and Kasahara and by Boneh and Franklin in 2000 and 2001 respectively; from the quadratic residue problem by Cocks in 2001; and finally from the Learning-with-Error problem by Gentry, Peikert, and Vaikuntanathan in 2008.<br/> Among all candidates for post-quantum cryptography, there only exist thus lattice-based IBE. In this paper, we propose a new method, based on the hardness of learning problems with rank metric, to design the first code-based IBE scheme. In order to overcome the two above problems in designing an IBE scheme, we first construct a rank-based PKE, called RankPKE, where the public key space is dense and thus can be obtained from a hash of any identity. We then extract a decryption key from any public key by constructing an trapdoor function which relies on RankSign - a signature scheme from PQCrypto 2014.<br/> In order to prove the security of our schemes, we introduced a new problem for rank metric: the Rank Support Learning problem (RSL). A high technical contribution of the paper is devoted to study in details the hardness of the RSL problem.
Prochains exposés
-
Cyclotomic Cosets: Hidden Subgroup and Quantum Sieving Algorithm for Prime-Power Moduli
Orateur : Mathias Boucher - Université de Rennes
The Dihedral Coset Problem (DCP), also known as the hidden shift problem, plays a fundamental role in post-quantum public-key cryptography, since the Learning-With-Error problem reduces to DCP. The “Simon meets Kuperberg” quantum algorithm by Bonnetain and Naya-Plasencia solves the DCP in quasi-polynomial time when the modulus is a power of two. We provide a generalization of this algorithm for[…] -
Adelic reduction of module lattices
Orateur : 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
-
-
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. The talks will take place at Amphi E in building 02A. To register for lunch, please do so before oct 30th using this link. -
Chiffrement homomorphe à l'aide des groupes après Nuida
Orateur : Pierre Guillot - Ravel Technologies/Université de strasbourg
Nuida et d'autres ont montré comment on peut obtenir un protocole de chiffrement pleinement homomorphe si l'on sait chiffrer les éléments d'un groupe G convenable, tout en sachant faire l'opération de G "en homomorphe". Les exemples étaient jusqu'à présent limités au chiffrement d'un bit à la fois, avec beaucoup d'opérations à effectuer pour "simuler" les portes logiques usuelles. Je vais[…]-
Cryptography
-
-
TBD
Orateur : Dung Bui - Northwestern University
-
Nouveaux doctorants
Exposés courts des nouveaux doctorants (Elouan, Quentin, Eliot)