Results 71 to 80 of about 10,757 (241)

Computing isogenies between abelian varieties [PDF]

Compositio Mathematica, 2012
AbstractWe describe an efficient algorithm for the computation of separable isogenies between abelian varieties represented in the coordinate system given by algebraic theta functions. Let A be an abelian variety of dimension g defined over a field of odd characteristic. Our algorithm comprises two principal steps. First, given a theta null point for A
Lubicz, David, Robert, Damien
openaire   +5 more sources

Isogenies on Kummer Surfaces

Mathematics of Computation
We first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient ( N , N ) (N,N) -isogenies, for any odd  N N , both on the general Kummer surface and on the Fast model.
Corte-Real Santos, M, Flynn, EV
openaire   +2 more sources

A Compact and Scalable Hardware/Software Co-design of SIKE

Transactions on Cryptographic Hardware and Embedded Systems, 2020
We present efficient and compact hardware/software co-design implementations of the Supersingular Isogeny Key Encapsulation (SIKE) protocol on field-programmable gate arrays (FPGAs).
Pedro Maat C. Massolino, Patrick Longa, Joost Renes, Lejla Batina   +3 more
doaj   +1 more source

Isogeny classes of abelian varieties over function fields

, 2005
We study isogeny classes of abelian varieties over a function field in one variable over the field of complex numbers.Comment: 22 ...
Zarhin, Yuri G.
core   +7 more sources

A note on local formulae for the parity of Selmer ranks

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3112-3132, October 2025.
Abstract In this note, we provide evidence for a certain ‘twisted’ version of the parity conjecture for Jacobians, introduced in prior work of Dokchitser, Green, Konstantinou and the author. To do this, we use arithmetic duality theorems for abelian varieties to study the determinant of certain endomorphisms acting on p∞$p^\infty$‐Selmer groups.
Adam Morgan
wiley   +1 more source

Constructing Permutation Rational Functions from Isogenies [PDF]

SIAM Journal on Discrete Mathematics, 2018
A permutation rational function $f\in \mathbb{F}_q(x)$ is a rational function that induces a bijection on $\mathbb{F}_q$, that is, for all $y\in\mathbb{F}_q$ there exists exactly one $x\in\mathbb{F}_q$ such that $f(x)=y$. Permutation rational functions are intimately related to exceptional rational functions, and more generally exceptional covers of ...
Bisson, Gaetan, Tibouchi, Mehdi
openaire   +2 more sources

Towards Isogeny-Based Password-Authenticated Key Establishment

Journal of Mathematical Cryptology, 2020
Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure.
Taraskin Oleg, Soukharev Vladimir, Jao David, LeGrow Jason T.   +3 more
doaj   +1 more source

On fixed‐point‐free involutions in actions of finite exceptional groups of Lie type

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract Let G$G$ be a nontrivial transitive permutation group on a finite set Ω$\Omega$. By a classical theorem of Jordan, G$G$ contains a derangement, which is an element with no fixed points on Ω$\Omega$. Given a prime divisor r$r$ of |Ω|$|\Omega |$, we say that G$G$ is r$r$‐elusive if it does not contain a derangement of order r$r$. In a paper from
Timothy C. Burness, Mikko Korhonen
wiley   +1 more source

On the supersingular GPST attack

Journal of Mathematical Cryptology, 2021
The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange.
Basso Andrea, Pazuki Fabien
doaj   +1 more source

Uniformizing the Stacks of Abelian Sheaves

, 2004
Elliptic sheaves (which are related to Drinfeld modules) were introduced by Drinfeld and further studied by Laumon--Rapoport--Stuhler and others. They can be viewed as function field analogues of elliptic curves and hence are objects "of dimension 1 ...
A. Blum, A. Genestier, A. Grothendieck, A. Grothendieck, A. Grothendieck, C. S. Seshadri, D. Eisenbud, D. Knutson, G. Anderson, G. Faltings, G. Laumon, G. Laumon, G. Laumon, I. Y. Potemine, J.-F. Boutot, L. Lafforgue, L. Lafforgue, M. Harris, M. Rapoport, M. Raynaud, M. Rosen, N. Katz, P. Deligne, P. Deligne, R. Hartshorne, S. Bosch, Th. Hausberger, U. Stuhler, V. G. Drinfeld, V. G. Drinfeld, V. G. Drinfeld, V. G. Drinfeld, V. G. Drinfeld, V. Čerednik, Y. I. Manin, Y. Taguchi   +35 more
core   +5 more sources