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ANTS
2010
Springer
13 years 11 months ago
2010
Springer
Abstract. We answer a question asked by Hajdu and Tengely: The only arithmetic progression in coprime integers of the form (a2 , b2 , c2 , d5 ) is (1, 1, 1, 1). For the proof, we ...
ANTS
2010
Springer
13 years 11 months ago
2010
Springer
![Visualizing Elements of Sha[3] in Genus 2 Jacobians](https://www.sciweavers.org/files/imagecache/thumbnail/default/content.jpg "Visualizing Elements of Sha[3] in Genus 2 Jacobians")
Abstract. Mazur proved that any element ξ of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in...
ANTS
2010
Springer
13 years 10 months ago
2010
Springer
In this paper, we present a new approach based on theta functions to compute Weil and Tate pairings. A benefit of our method, which does not rely on the classical Miller's alg...
ANTS
2010
Springer
13 years 11 months ago
2010
Springer
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between ellip...
CEC
2010
IEEE
13 years 4 months ago
2010
IEEE
The operation of drilling rigs is highly expensive. It is therefore important to be able to identify and analyse variables affecting rig operations. We investigate the use of Genet...