NDLI: Trisection for genus 2 curves in odd characteristic

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Trisection for genus 2 curves in odd characteristic

Content Provider	Springer Nature Link
Author	Riquelme, Edgardo
Copyright Year	2016
Abstract	We provide trisection (division by 3) algorithms for Jacobians of genus 2 curves over finite fields $$\mathbb {F}_q$$ of odd characteristic which rely on the factorization of a polynomial whose roots correspond (bijectively) to the set of trisections of the given divisor. We also construct a polynomial whose roots allow us to calculate the 3-torsion divisors. We show the relation between the rank of the 3-torsion subgroup and the factorization of this 3-torsion polynomial, and describe the factorization of the trisection polynomials in terms of the Galois structure of the 3-torsion subgroup. We also generalize these ideas for $$\ell \in \{5,7\}$$ .
Ending Page	397
Page Count	25
Starting Page	373
File Format	PDF
ISSN	09381279
e-ISSN	14320622
Journal	Applicable Algebra in Engineering, Communication and Computing
Issue Number	5
Volume Number	27
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-01-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hyperelliptic curves Finite field Special curves and curves of low genus Computer Hardware Trisection Genus 2 Artificial Intelligence (incl. Robotics) Jacobian Jacobians, Prym varieties Theory of Computation Symbolic and Algebraic Manipulation Curves over finite and local fields
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory

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