Results 11 to 20 of about 284,852 (62)

Schoof's algorithm and isogeny cycles

, 1994
The heart of Schoof's algorithm for computing the cardinality m of an elliptic curve over a finite field is the computation of m modulo small primes l. Elkies and Atkin have designed practical improvements to the basic algorithm, that make use of “good” primes l. We show how to use powers of good primes in an efficient way.
Jean-Marc Couveignes, François Morain
openalex   +5 more sources

Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm [PDF]

Proceedings of the 2006 international symposium on Symbolic and algebraic computation, 2006
The Schoof-Elkies-Atkin algorithm is the only known method for counting the number of points of an elliptic curve defined over a finite field of large characteristic. Several practical and asymptotical improvements for the phase called eigenvalue computation are proposed.
Gaudry, Pierrick, Morain, François
openaire   +5 more sources

Computing the eigenvalue in the schoof-elkies-atkin algorithm using abelian lifts [PDF]

Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007
The Schoof-Elkies-Atkin algorithm is the best known method for counting the number of points of an elliptic curve defined over a finite field of large characteristic. We use Abelian properties of division polynomials to design a fast theoretical and practical algorithm for nding the eigenvalue.
Éric Schost, P. Mihailescu, François Morain   +2 more
openaire   +1 more source

Remarks on the Schoof-Elkies-Atkin algorithm [PDF]

Mathematics of Computation, 1998
Schoof’s algorithm computes the number m m of points on an elliptic curve E E defined over a finite field F q {\Bbb F}_q . Schoof determines m m modulo small primes ℓ \ell using the characteristic equation of ...
openaire   +2 more sources

Efficient Implementation of Schoof’s Algorithm [PDF]

, 1998
Schoof's algorithm is used to find a secure elliptic curve for cryptosystems, as it can compute the number of rational points on a randomly selected elliptic curve defined over a finite field. By realizing efficient combination of several improvements, such as Atkin-Elkies's method, the isogeny cycles method, and trial search by match-and-sort ...
Masayuki Noro, Jun Kogure, Kazuhiro Yokoyama, Tetsuya Izu   +3 more
openaire   +2 more sources

Efficient Implementation of Schoof’s Algorithm in Case of Characteristic 2 [PDF]

, 2000
In order to choose a secure elliptic curve for Elliptic Curve Cryptosystems, it is necessary to count the order of a randomly selected elliptic curve. Schoof’s algorithm and its variants by Elkies and Atkin are known as efficient methods to count the orders of elliptic curves.
Kazuhiro Yokoyama, Jun Kogure, Tetsuya Izu   +2 more
openaire   +2 more sources

Subglacial landscape formation and sediment discharge: relating basal conditions to bedform dimensions and properties at Rutford Ice Stream, West Antarctica

Boreas, EarlyView.
Basal conditions that facilitate fast ice flow are still poorly understood and their parameterization in ice‐flow models results in high uncertainties in ice‐flow and consequent sea‐level rise projections. Direct observations of basal conditions beneath modern ice streams are limited due to the inaccessibility of the bed.
Rebecca Schlegel, Lucas K. Zoet, Adam D. Booth, Andrew M. Smith, Roger A. Clark, Alex M. Brisbourne   +5 more
wiley   +1 more source

Selecting Observationally Constrained Global Climate Model Ensembles Using Autoencoders and Transfer Learning

Journal of Geophysical Research: Machine Learning and Computation, Volume 2, Issue 1, March 2025.
Abstract Climate modes of variability are recurring patterns that influence climate phenomena across spatial scales. Accurately representing these modes in Global Climate Models (GCMs) is crucial for assessing model performance and reducing uncertainty in future climate projections.
Chibuike Chiedozie Ibebuchi, Oluwaferanmi Akinyemi, Itohan‐Osa Abu   +2 more
wiley   +1 more source

SERS‐Based Assessment of DNA Methylation for the Evaluation of Measurable Residual Disease in Acute Promyelocytic Leukaemia

Journal of Cellular and Molecular Medicine, Volume 29, Issue 5, March 2025.
ABSTRACT Acute promyelocytic leukaemia (APL) is a type of acute myeloid leukaemia characterised by the reciprocal translocation t(15;17), which offers a unique possibility for measurable residual disease (MRD) monitoring by PCR amplification of the PML‐RARA transcripts.
Anamaria Bancos, Stefania D. Iancu, Vlad Moisoiu, Alexandra Ghiaur, Adrian Bogdan Tigu, Cristina Buran, Georgiana Ion, Camelia Stancioaica, Bogdan Ionescu, Mihaela Dragomir, Codruta F. Buldus, Diana Cenariu, Madalina Nistor, David Kegyes, Diana Gulei, Nicolae Leopold, Daniel Coriu, Ciprian Tomuleasa   +17 more
wiley   +1 more source

$L$-Functions of Elliptic Curves Modulo Integers [PDF]

arXiv, 2021
In 1985, Schoof devised an algorithm to compute zeta functions of elliptic curves over finite fields by directly computing the numerators of these rational functions modulo sufficiently many primes (see \cite{schoof_1985}). If $E/K$ is an elliptic curve with nonconstant $j$-invariant defined over a function field $K$ of characteristic $p \geq 5$, we ...
arxiv