Results 11 to 20 of about 4,794,474 (74)
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication [PDF]
arXiv.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
Schoofův algoritmus pro Weierstrassovy křivky
, 2023 Schoof's algorithm is the starting point for the most efficient methods for determining the number of rational points on an elliptic curve defined over a finite field. The goal of this thesis is to introduce the subject of elliptic curves, with the emphasis on Weierstrass curves over a finite field, to describe Schoof's algorithm and its time ...
Zvoníček, Václav
openaire +2 more sources
Counting points on abelian surfaces over finite fields with Elkies's method [PDF]
arXiv.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
IACR 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
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 +3 more sources
Criterions of Supersinguliarity and Groups of Montgomery and Edwards Curves in Cryptography
WSEAS 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
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 +2 more
openaire +1 more source
Elliptic and Edwards Curves Order Counting Method
, 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]
Arithmetic 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]
, 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