Results 71 to 80 of about 4,641 (196)

Renormalization, Isogenies, and Rational Symmetries of Differential Equations

Advances in Mathematical Physics, 2010
We give an example of infinite-order rational transformation that leaves a linear differential equation covariant. This example can be seen as a nontrivial but still simple illustration of an exact representation of the renormalization group.
A. Bostan, S. Boukraa, S. Hassani, J.-M. Maillard, J.-A. Weil, N. Zenine, N. Abarenkova   +6 more
doaj   +1 more source

CAPYBARA and TSUBAKI: Verifiable Random Functions from Group Actions and Isogenies

IACR Cryptology ePrint Archive
In this work, we introduce two post-quantum Verifiable Random Function (VRF) constructions based on abelian group actions and isogeny group actions with a twist. The former relies on the standard group action Decisional Diffie-Hellman (GA-DDH) assumption.
Yi-Fu Lai
semanticscholar   +1 more source

Traces of Hecke operators on Drinfeld modular forms for GL2(Fq[T])$\operatorname{GL}_2(\mathbb {F}_q[T])$

Mathematika, Volume 72, Issue 2, April 2026.
Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley   +1 more source

On the Parallelization of Square-Root Vélu’s Formulas

Mathematical and Computational Applications
A primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies.
Jorge Chávez-Saab, Odalis Ortega, Amalia Pizarro-Madariaga   +2 more
doaj   +1 more source

Genus Two Isogeny Cryptography [PDF]

, 2019
We study \((\ell ,\ell )\)-isogeny graphs of principally polarised supersingular abelian surfaces (PPSSAS). The \((\ell ,\ell )\)-isogeny graph has cycles of small length that can be used to break the collision resistance assumption of the genus two isogeny hash function suggested by Takashima.
Flynn, E, Ti, Y
openaire   +3 more sources

Ordinary primes for GL2$\operatorname{GL}_2$‐type abelian varieties and weight 2 modular forms

Mathematika, Volume 72, Issue 2, April 2026.
Abstract Let A$A$ be a g$g$‐dimensional abelian variety defined over a number field F$F$. It is conjectured that the set of ordinary primes of A$A$ over F$F$ has positive density, and this is known to be true when g=1,2$g=1, 2$, or for certain abelian varieties with extra endomorphisms.
Tian Wang, Pengcheng Zhang
wiley   +1 more source

Cyclic isogenies of elliptic curves over fixed quadratic fields [PDF]

, 2022
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cyclic isogenies of elliptic curves over $\mathbb{Q}$. Although more than 40 years have passed, the determination of cyclic isogenies of elliptic curves over a
Najman, Filip, Banwait, Barinder S., Padurariu, Oana   +2 more
core   +1 more source

Graph potentials and topological quantum field theories

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay   +2 more
wiley   +1 more source

Digital Signature in Class Group of Isogenies Elliptic Curves

Безопасность информационных технологий, 2010
Digital signature protocol based on Schnorr protocol is proposed. Protection against quantum attacks is achieved by using isogenies computation problem.
J. V. Gel, A. G. Rostovtsev
doaj  

Efficient computation of (2n,2n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2^n,2^n)$$\end{document}-isogenies

Designs, Codes and Cryptography
Elliptic curves are abelian varieties of dimension one; the two-dimensional analogues are abelian surfaces. In this work we present an algorithm to compute (2n,2n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage ...
S. Kunzweiler
semanticscholar   +1 more source