Construction of a k-complete addition law on abelian surfaces with rational theta constants

Christophe Arene 1 Romain Cosset 2, *
* Corresponding author
2 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : In this paper we explain how to construct F_q-complete addition laws on the Jacobian of an hyperelliptic curve of genus 2. This is usefull for robustness and is needed for some applications (like for instance on embedded devices).
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Christophe Arene, Romain Cosset. Construction of a k-complete addition law on abelian surfaces with rational theta constants. AGCT 2011, 2011, Marseille, France. AMS, Contemporary Mathematics, 574, Arithmetic, Geometry, Cryptography and Coding Theory. 〈10.1090/conm/574〉. 〈hal-00645652〉

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