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Modular equations for hyperelliptic curves

Mathematics of computation, 2005-01, Vol.74 (249), p.429-454 [Peer Reviewed Journal]

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Title:
Modular equations for hyperelliptic curves
Author: GAUDRY, P ; SCHOST, E
Subjects: Algebra ; Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Coefficients ; Computer Science ; Computer science; control theory; systems ; Coordinate systems ; Cryptography and Security ; Curves ; Exact sciences and technology ; Factorization ; Integers ; Jacobians ; Mathematics ; Number theory ; Polynomials ; Rational functions ; Sciences and techniques of general use ; Theoretical computing
Is Part Of: Mathematics of computation, 2005-01, Vol.74 (249), p.429-454
Description: We define modular equations describing the \ell-torsion subgroups of the Jacobian of a hyperelliptic curve. Over a finite base field, we prove factorization properties that extend the well-known results used in Atkin's improvement of Schoof's genus 1 point counting algorithm.
Publisher: Providence, RI: American Mathematical Society
Language: English
Identifier: ISSN: 0025-5718
EISSN: 1088-6842
DOI: 10.1090/S0025-5718-04-01682-5
CODEN: MCMPAF
Source: Hyper Article en Ligne (HAL) (Open Access)
American Mathematical Society Publications (Open access)

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