Results 81 to 90 of about 3,064 (192)
A subexponential-time, polynomial quantum space algorithm for inverting the CM group action
Journal of Mathematical Cryptology, 2020 We present a quantum algorithm which computes group action inverses of the complex multiplication group action on isogenous ordinary elliptic curves, using subexponential time, but only polynomial quantum space.
Jao David +3 more
doaj +1 more source
A Comparison of Security and its Performance for Key Agreements in Post-Quantum Cryptography
IEEE Access, 2020 Nowadays, we are surrounded by devices collecting and transmitting private information. Currently, the two main mathematical problems that guarantee security on the Internet are the Integer Factorization Problem and the Discrete Logarithm Problem ...
Fabio Borges +2 more
doaj +1 more source
A note on the cohomology of moduli spaces of local shtukas
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3709-3729, December 2025.Abstract We study localized versions of spectral action of Fargues–Scholze, using methods from higher algebra. As our main motivation and application, we deduce a formula for the cohomology of moduli spaces of local shtukas under certain genericity assumptions, and discuss its relation with the Kottwitz conjecture.
David Hansen, Christian Johansson
wiley +1 more source
Comprehensive Analysis and Implementation of Isogeny-Based Hash Functions
IEEE AccessThis paper analyzes the security and performance of the isogeny-based hash functions. The isogeny-based hash function was first proposed by Charles, Goren, and Lauter, and is referred to as the CGL hash function.
Donghoe Heo +4 more
doaj +1 more source
Algebraic Geometry, 2016 We prove by means of the study of the infinitesimal variation of Hodge structure and a generalization of the classical Babbage-Enriques-Petri theorem that the Jacobian variety of a generic element of a $k$ codimensional subvariety of $\mathcal M_g$ is not isogenous to a distinct Jacobian if $g>3k+4$.
Marcucci, Valeria +2 more
openaire +7 more sources
Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph [PDF]
, 2022 We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular.
Enric Florit, Benjamin Smith
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Mod p points on shimura varieties of parahoric level
Forum of Mathematics, PiWe study the $\overline {\mathbb {F}}_{p}$ -points of the Kisin–Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point,
Pol van Hoften
doaj +1 more source
Isogeny graphs and Isogeny Volcanoes
, 2020 \textit{Isogeny graphs} are a type of graphs, where the vertices represent elliptic curves and the edges represent isogenies. I will examine some of the structures of these graphs in this thesis. It turns out that the majority of the components of such a graph will be \textit{volcanoes}, see \cref{defn:pvolcano}.
openaire +1 more source
On Ribet’s isogeny for $J_0(65)$
Proceedings of the American Mathematical Society, 2018 Let $J^{65}$ be the Jacobian of the Shimura curve attached to the indefinite quaternion algebra over $\mathbb{Q}$ of discriminant $65$. We study the isogenies $J_0(65)\rightarrow J^{65}$ defined over $\mathbb{Q}$, whose existence was proved by Ribet.
Klosin, K., Papikian, M.
openaire +4 more sources
Infinite Families Of Isogeny-Torsion Graphs
, 2022 Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined over $\mathbb{Q}$. The isogeny graph associated to $\mathcal{E}$ is a graph which has a vertex for each element of $\mathcal{E}$ and an edge for each $\mathbb{Q}$-isogeny of ...
Chiloyan, Garen
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