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Journal Articles ACM Communications in Computer Algebra Year : 2020

Improved Divisor Arithmetic on Generic Hyperelliptic Curves

Laurent Imbert

Abstract

The divisor class group of a hyperelliptic curve defined over a finite field is a finite abelian group at the center of a number of important open questions in algebraic geometry, number theory and cryptography. Many of these problems lend themselves to numerical investigation, and as emphasized by Sutherland [14, 13], fast arithmetic in the divisor class group is crucial for their efficiency. Besides, implementations of these fundamental operations are at the core of the algebraic geometry packages of widely-used computer algebra systems such as Magma and Sage.
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Dates and versions

lirmm-02990000 , version 1 (15-11-2021)

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Sebastian Lindner, Laurent Imbert, Michael J. Jacobson Jr. Improved Divisor Arithmetic on Generic Hyperelliptic Curves. ACM Communications in Computer Algebra, 2020, 54 (3), pp.95-99. ⟨10.1145/3457341.3457345⟩. ⟨lirmm-02990000⟩
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