Four-Dimensional GLV via the Weil Restriction

Aurore Guillevic 1, 2 Sorina Ionica 1
1 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : The Gallant-Lambert-Vanstone (GLV) algorithm uses efficiently computable endomorphisms to accelerate the computation of scalar multiplication of points on an abelian variety. Freeman and Satoh proposed for cryptographic use two families of genus 2 curves defined over Fp which have the property that the corresponding Jacobians are (2,2)-isogenous over an extension field to a product of elliptic curves de fined over Fp2. We exploit the relationship between the endomorphism rings of isogenous abelian varieties to exhibit efficiently computable endomorphisms on both the genus 2 Jacobian and the elliptic curve. This leads to a four-dimensional GLV method on Freeman and Satoh's Jacobians and on two new families of elliptic curves de fined over Fp2.
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Communication dans un congrès
Kazue Sako and Palash Sarkar. Asiacrypt - 19th Annual International Conference on the Theory and Application of Cryptology and Information Security, Dec 2013, Bengalore, India. Springer, 2013
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Aurore Guillevic, Sorina Ionica. Four-Dimensional GLV via the Weil Restriction. Kazue Sako and Palash Sarkar. Asiacrypt - 19th Annual International Conference on the Theory and Application of Cryptology and Information Security, Dec 2013, Bengalore, India. Springer, 2013. 〈hal-00864966v2〉

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