Results 11 to 20 of about 4,804,991 (93)

On the distribution of orders of Frobenius action on $\ell$-torsion of abelian surfaces [PDF]

open access: yesPRIKLADNAYa DISKRETNAYa MATEMATIKA, 2020
The computation of the order of Frobenius action on the $\ell$-torsion is a part of Schoof-Elkies-Atkin algorithm for point counting on an elliptic curve $E$ over a finite field $\mathbb{F}_q$.
N. Kolesnikov, S. Novoselov
semanticscholar   +5 more sources

Construction of Secure Random Curves of Genus 2 over Prime Fields

open access: yesInternational Conference on the Theory and Application of Cryptographic Techniques, 2004
International audienceFor counting points of Jacobians of genus 2 curves defined over large prime fields, the best known method is a variant of Schoof's algorithm.
P. Gaudry, É. Schost
semanticscholar   +4 more sources

Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication [PDF]

open access: yesarXiv.org, 2017
Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of explicit ...
Sean Ballentine   +6 more
semanticscholar   +3 more sources

Counting points on abelian surfaces over finite fields with Elkies's method [PDF]

open access: yesarXiv.org, 2022
We generalize Elkies's method, an essential ingredient in the SEA algorithm to count points on elliptic curves over finite fields of large characteristic, to the setting of p.p. abelian surfaces.
J. Kieffer
semanticscholar   +1 more source

Speeding-Up Elliptic Curve Cryptography Algorithm

open access: yesIACR Cryptology ePrint Archive, 2022
In recent decades there has been an increasing interest in Elliptic curve cryptography (ECC) and, especially, the Elliptic Curve Digital Signature Algorithm (ECDSA) in practice.
Diana Maimuţ, A. Matei
semanticscholar   +1 more source

Criterions of Supersinguliarity and Groups of Montgomery and Edwards Curves in Cryptography

open access: yesWSEAS Transactions on Mathematics, 2021
We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves.
R. Skuratovskii, V. Osadchyy
semanticscholar   +1 more source

Elliptic and Edwards Curves Order Counting Method

open access: yes, 2021
We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves.
R. Skuratovskii, V. Osadchyy
semanticscholar   +1 more source

Using zeta functions to factor polynomials over finite fields [PDF]

open access: yesArithmetic Geometry: Computation and Applications, 2017
In 2005, Kayal suggested that Schoof's algorithm for counting points on elliptic curves over finite fields might yield an approach to factor polynomials over finite fields in deterministic polynomial time.
B. Poonen
semanticscholar   +1 more source

Counting points on hyperelliptic curves over finite fields [PDF]

open access: yes, 2000
International audienceWe describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an ...
D.G. Cantor   +21 more
core   +3 more sources

Data Prevention Technique For Securing The Data [PDF]

open access: yes, 2021
The main aim of this paper is to safeguard information through data security and is considered convergence, exploration, infiltration, and footprint. Cloud computing can be a computer-based type of computer that provides numerous PCs and devices looking ...
et. al., Christy A,
core   +1 more source

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