ENGE, Andreas; MILAN, Jérôme

doi:10.1007/978-3-319-12060-7_3

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ENGE, Andreas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

MILAN, Jérôme
KoDe Software

Langue

Communication dans un congrès

Ce document a été publié dans

Security, Privacy, and Applied Cryptography Engineering, 2014-10-18, Pune. vol. 8804, p. 28-46

Springer

Résumé en anglais

This study reports on an implementation of cryptographic pairings in a general purpose computer algebra system. For security levels equivalent to the different AES flavours, we exhibit suitable curves in parametric families and show that optimal ate and twisted ate pairings exist and can be efficiently evaluated. We provide a correct description of Miller's algorithm for signed binary expansions such as the NAF and extend a recent variant due to Boxall et al. to addition-subtraction chains. We analyse and compare several algorithms proposed in the literature for the final exponentiation. Finally, we give recommendations on which curve and pairing to choose at each security level.< Réduire

Mots clés en anglais

pairings

implementation

elliptic curve cryptology

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194645

DOI

http://dx.doi.org/10.1007/978-3-319-12060-7_3

Projet Européen

Algorithmic Number Theory in Computer Science

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251