Efficient Regular Scalar Multiplication on the Jacobian of Hyperelliptic Curve over Prime Field Based on Divisor Splitting

Christophe Negre 1 Thomas Plantard 2
1 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : We consider in this paper scalar multiplication algorithms over a hyperelliptic curve which are immune against simple power analysis and timing attack. To reach this goal we adapt the regular modular exponentiation based on multiplicative splitting presented in JCEN 2017 to scalar multiplication over a hyperelliptic curve. For hyperelliptic curves of genus g = 2 and 3, we provide an algorithm to split the base divisor as a sum of two divisors with smaller degree. Then we obtain an algorithm with a regular sequence of doubling always followed by an addition with a low degree divisor. We also provide efficient formulas to add such low degree divisors with a divisor of degree g. A complexity analysis and implementation results show that the proposed approach is better than the classical Double-and-add-always approach for scalar multiplication.
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Pré-publication, Document de travail
2018
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Soumis le : mardi 31 juillet 2018 - 15:30:21
Dernière modification le : mardi 11 septembre 2018 - 01:12:27

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Christophe Negre, Thomas Plantard. Efficient Regular Scalar Multiplication on the Jacobian of Hyperelliptic Curve over Prime Field Based on Divisor Splitting. 2018. 〈hal-01852041〉

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