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Improved Divisor Arithmetic on Generic Hyperelliptic Curves

Sebastian Lindner 1 Laurent Imbert 2 Michael J. Jacobson Jr 1 
2 ECO - Exact Computing
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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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https://hal-lirmm.ccsd.cnrs.fr/lirmm-02990000
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Submitted on : Monday, November 15, 2021 - 11:53:14 AM
Last modification on : Monday, November 15, 2021 - 5:30:32 PM
Long-term archiving on: : Wednesday, February 16, 2022 - 8:23:33 PM

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

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