Algorithms and arithmetic operators for computing the $\eta_T$ pairing in characteristic three
Résumé
Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the $\eta_T$ pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes cube root extraction over $\mathbb{F}_{3^m}$. We propose a hardware accelerator based on a unified arithmetic operator able to perform the operations required by a given algorithm. We describe the implementation of a compact coprocessor for the field $\mathbb{F}_{3^{97}}$ given by $\mathbb{F}_3[x]/(x^{97}+x^{12}+2)$, which compares favorably with other solutions described in the open literature.
Fichier principal
pairing_appendix.pdf (70.01 Ko)
Télécharger le fichier
bbdost_final.pdf (359.09 Ko)
Télécharger le fichier
Origine | Fichiers éditeurs autorisés sur une archive ouverte |
---|
Origine | Fichiers éditeurs autorisés sur une archive ouverte |
---|
Loading...