Results 91 to 100 of about 10,757 (241)

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, Paulo Ricardo Reis, Diogo Pereira   +2 more
doaj   +1 more source

Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem [PDF]

, 2017
Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multiplication.
Jetchev, Dimitar, Wesolowski, Benjamin
core   +1 more source

Parabolic subgroups in characteristics 2 and 3

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract This text brings to an end the classification of non‐reduced parabolic subgroups in positive characteristic, especially 2 and 3: they are all obtained as intersections of parabolics having maximal reduced part. We prove this result and deduce a few geometric consequences on rational projective homogeneous varieties.
Matilde Maccan
wiley   +1 more source

Optimized SeaSign for Enhanced Efficiency

IEEE Access
This paper optimized SeaSign – an isogeny-based digital signature algorithm that combines the class group actions of CSIDH with the notion of Fiat-Shamir with abort.
Suhri Kim
doaj   +1 more source

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, LeGrow Jason, Leonardi Christopher, Ruiz-Lopez Luis   +3 more
doaj   +1 more source

Strong subgroup recurrence and the Nevo–Stuck–Zimmer theorem

Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.
Abstract Let Γ$\Gamma$ be a countable group and Sub(Γ)$\mathrm{Sub}(\Gamma)$ its Chabauty space, namely, the compact Γ$\Gamma$‐space consisting of all subgroups of Γ$\Gamma$. We call a subgroup Δ∈Sub(Γ)$\Delta \in \mathrm{Sub}(\Gamma)$ a boomerang subgroup if for every γ∈Γ$\gamma \in \Gamma$, γniΔγ−ni→Δ$\gamma ^{n_i} \Delta \gamma ^{-n_i} \rightarrow ...
Yair Glasner, Waltraud Lederle
wiley   +1 more source

POKEx: Performance Analysis of POKÉ-Key Exchange and SIDH-Variants

IEEE Access
In this paper, we present a comparative performance analysis of the POKÉ-based key exchange and SIDH variants. SIDH gained attention for its small key size and efficient performance, and has been selected as an alternate candidate in NIST PQC ...
Hyeonhak Kim, Suhri Kim
doaj   +1 more source

Explicit classification of isogeny graphs of rational elliptic curves [PDF]

, 2022
Alexander J. Barrios
openalex   +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

Mod p points on shimura varieties of parahoric level

Forum of Mathematics, Pi
We 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