Results 1 to 10 of about 124 (95)
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
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Binary quadratic forms, elliptic curves and Schoof's algorithm [PDF]
, 2015 In this thesis, I show that the representation of prime integers by reduced binary quadratic forms of given discriminant can be obtained in polynomial complexity using Schoof's algorithm for counting the number of points of elliptic curves over finite fields.
Federico Pintore
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Universal elliptic Gau�� sums for Atkin primes in Schoof's algorithm [PDF]
, 2017 This work builds on earlier results. We define universal elliptic Gau sums for Atkin primes in Schoof's algorithm for counting points on elliptic curves. Subsequently, we show these quantities admit an efficiently computable representation in terms of the $j$-invariant and two other modular functions.
Christian J. Berghoff
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Elliptic Gau�� sums and Schoof's algorithm [PDF]
, 2016 16 pages, revised ...
Christian J. Berghoff
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Speeding-Up Elliptic Curve Cryptography Algorithms
Mathematics, 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, Alexandru Cristian Matei
doaj +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
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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 ...
Tetsuya Izu +3 more
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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
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On the distribution of orders of Frobenius action on $\ell$-torsion of abelian surfaces [PDF]
, 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 $\mathbb{F}_q$.
Kolesnikov, Nikita, Novoselov, Semyon
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