Results 1 to 10 of about 4,819,653 (62)
Schoof's algorithm and isogeny cycles
International Workshop on Ant Colony Optimization and Swarm Intelligence, 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.
François Morain, Jean-Marc Couveignes
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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 ...
L. Dewaghe
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Efficient Implementation of Schoof’s Algorithm in Case of Characteristic 2 [PDF]
International Conference on Theory and Practice of Public Key Cryptography, 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 +2 more
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Efficient Implementation of Schoof’s Algorithm [PDF]
International Conference on the Theory and Application of Cryptology and Information Security, 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 +3 more
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Universal elliptic Gau�� sums for Atkin primes in Schoof's algorithm
, 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
, 2016 16 pages, revised ...
Christian J. Berghoff
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Binary quadratic forms, elliptic curves and Schoof's algorithm
, 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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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
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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
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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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