Results 31 to 40 of about 10,181 (241)

Computing square-free polarized abelian varieties over finite fields [PDF]

, 2020
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finite field $\mathbb{F}_q$ whose characteristic polynomial (of Frobenius) is square-free and of abelian varieties defined over the prime field $\mathbb{F}_p ...
Marseglia, Stefano
core   +3 more sources

The isogeny conjecture for A-motives [PDF]

Inventiones mathematicae, 2011
ISSN:1432 ...
openaire   +4 more sources

Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves

Journal of Mathematical Cryptology, 2021
Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve E defined over 𝔽p2, if an imaginary quadratic order O can be embedded in End(E) and a ...
Xiao Guanju, Luo Lixia, Deng Yingpu
doaj   +1 more source

Vectorized and Parallel Computation of Large Smooth-Degree Isogenies using Precedence-Constrained Scheduling

Transactions on Cryptographic Hardware and Embedded Systems, 2023
Strategies and their evaluations play important roles in speeding up the computation of large smooth-degree isogenies. The concept of optimal strategies for such computation was introduced by De Feo et al., and virtually all implementations of isogeny ...
Kittiphon Phalakarn, Vorapong Suppakitpaisarn, Francisco Rodríguez-Henríquez, M. Anwar Hasan   +3 more
doaj   +1 more source

Abelian varieties isogenous to a power of an elliptic curve over a Galois extension [PDF]

, 2018
Given an elliptic curve $E/k$ and a Galois extension $k'/k$, we construct an exact functor from torsion-free modules over the endomorphism ring ${\rm End}(E_{k'})$ with a semilinear ${\rm Gal}(k'/k)$ action to abelian varieties over $k$ that are $k ...
Vogt, Isabel
core   +3 more sources

Isogeny in superstable groups [PDF]

Archive for Mathematical Logic, 2014
We study and develop a notion of isogeny for superstable groups. We prove several fundamental properties of the notion and then use it to formulate and prove uniqueness results. Connections to existing model theoretic notions are explained.
openaire   +3 more sources

Hash functions from superspecial genus-2 curves using Richelot isogenies

Journal of Mathematical Cryptology, 2020
In 2018 Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field 𝔽p2.
Castryck Wouter, Decru Thomas, Smith Benjamin   +2 more
doaj   +1 more source

Multiplicative isogeny estimates [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1998
AbstractThe theory of isogeny estimates for Abelian varieties provides ‘additive bounds’ of the form ‘d is at most B’ for the degrees d of certain isogenies. We investigate whether these can be improved to ‘multiplicative bounds’ of the form ‘d divides B’.
openaire   +3 more sources

The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type

Forum of Mathematics, Sigma, 2021
In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of ${\text {GL}_2}$-type. The proof combines Faltings’ method with Serre’s modularity conjecture, isogeny estimates and results from Arakelov ...
Rafael von Känel
doaj   +1 more source

On the cyclicity of the rational points group of abelian varieties over finite fields

, 2018
We propose a simple criterion to know if an abelian variety $A$ defined over a finite field $\mathbb{F}_q$ is cyclic, i.e., it has a cyclic group of rational points; this criterion is based on the endomorphism ring End$_{\mathbb{F}_q}(A)$.
Giangreco-Maidana, Alejandro J.
core   +2 more sources