Description
In constructive Galois theory, there are two main questions: the direct problem and the inverse problem. For the inverse problem the question is whether it is possible to find a polynomial such that the Galois group of that polynomial is a given finite group. In this talk, we will focus on the direct problem. Given a polynomial f we explain how to compute the Galois group of this polynomial. The presented algorithms are implemented in KASH and work up to degree 23 for polynomials over number fields and function fields (in one variable).<br/> In a second part of the talk, we report on a database containing number fields up to degree 15. The database is complete in the sense that for each transitive group up to degree 15 there is at least one polynomial in the database which has this given Galois group.
Next sessions
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Dual attacks in code-based (and lattice-based) cryptography
Speaker : 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
Speaker : 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
Speaker : 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
Speaker : 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
Speaker : 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[…]