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.
Category / Keywords: implementation / $\eta_T$ pairing, finite field arithmetic, elliptic curve, hardware accelerator, FPGA Date: received 1 Nov 2007, last revised 9 Sep 2008 Contact author: beuchat at risk tsukuba ac jp Available format(s): PDF | BibTeX Citation Version: 20080910:013639 (All versions of this report) Short URL: ia.cr/2007/417 Discussion forum: Show discussion | Start new discussion