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Communication Dans Un Congrès Année : 2013

Four-Dimensional GLV via the Weil Restriction

Résumé

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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Dates et versions

hal-00864966 , version 1 (23-09-2013)
hal-00864966 , version 2 (06-11-2013)

Identifiants

Citer

Aurore Guillevic, Sorina Ionica. Four-Dimensional GLV via the Weil Restriction. Advances in Cryptology - ASIACRYPT 2013 - 19th International Conference on the Theory and Application of Cryptology and Information Security, Satya Lokam, Dec 2013, Bengalore, India. pp.79-96, ⟨10.1007/978-3-642-42033-7_5⟩. ⟨hal-00864966v2⟩
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