Arithmétique et topologie des noeuds modulaires

Autor: Simon, Christopher-Lloyd

Publikováno v: Algebraic Topology [math.AT]. Université de Lille, 2022. English. ⟨NNT : ⟩
Algebraic Topology [math.AT]. Université de Lille, 2022. English. ⟨NNT : 2022ULILB012⟩

In this work, dedicated to the modular group PSL(2;Z), we investigate several arithmetical and topological structures underlying its set of conjugacy classes, such as equivalence relations and bilinear pairings.The modular group PSL(2;Z) acts on the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::94028441621c4bb662e7219df6f4ce39
https://theses.hal.science/tel-03945655

Algorithmic of curves in the context of bilinear and post-quantum cryptography

Autor: Simon Masson

Publikováno v: Cryptography and Security [cs.CR]. Université de Lorraine, 2020. English. ⟨NNT : 2020LORR0151⟩
HAL

This thesis studies the algorithmic of several cryptographic applications related to elliptic curves and isogenies of elliptic curves. On the one hand, we study the tradeoff between efficiency and security in pairing-based cryptography at the 128-bit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::6751efadd87a9f27ab9fe73455045267
https://theses.hal.science/tel-03052499/file/ThesisSimonMasson7.pdf

Sur les minima des formes hamiltoniennes binaires définies positives

Autor: Chenevier, Gaëtan, Paulin, Frédéric

Let $A$ be a definite quaternion algebra over $\mathbb Q$, with discriminant $D_A$, and $O$ a maximal order of $A$. We show that the minimum of the positive definite hamiltonian binary forms over $O$ with discrimiminant $-1$ is $\sqrt{D_A}$. When the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=arXiv_dedup_::473499d1c0ee2554672c1a443332f0c8
https://hal.archives-ouvertes.fr/hal-02124311