Description
Public key cryptography is based on hard problems, such as the discrete logarithm problem (DLP). In this talk, I focus on the discrete logarithm problem in finite fields:<br/> Given GF(q^k) and a generator g of GF(q^k)*, we say that we solve the DLP in GF(q^k) if, for any arbitrary element h in GF(q^k)*, we are able to recover an integer x such that: g^x = h. When the characteristic is small compared to the extension degree, the best complexity that can be achieved is quasipolynomial in log(q^k). I present here a simplified version of this quasipolynomial algorithm that has several advantages:<br/> 1/ I swear it is simple, or at least I will do my best to make it understandable.<br/> 2/ Together with additional ideas, simplifying the original settings permits to decrease the complexity of relation collection, linear algebra and extension phases, that dominate in practice all discrete logarithms computations. Namely, the complexity is reduced from O(q^7) to O(q^6). 3/ With our simplified settings, the complexity achieved in the general case became similar to the complexity known for Kummer (or twisted Kummer) extensions. Thus it permitted to achieve a discrete log computation in GF_(3^(5*497)), that is not only the highest cardinality reached in characteristic 3, but also not a special extension field as previous target fields were.<br/> This is a joint work with Antoine Joux.
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.