### Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers

Jean-Luc Beuchat, Jérémie Detrey, Nicolas Estibals, Eiji Okamoto, and Francisco Rodríguez-Henríquez

##### Abstract

This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware implementation of Miller's loop based on a pipelined Karatsuba-Ofman multiplier. Thanks to a careful selection of algorithms for computing the tower field arithmetic associated to the Tate pairing, we manage to keep the pipeline busy. We also describe the strategies we considered to design our parallel multiplier. They are included in a VHDL code generator allowing for the exploration of a wide range of operators. Then, we outline the architecture of a coprocessor for the Tate pairing over $\mathbb{F}_{3^m}$. However, a final exponentiation is still needed to obtain a unique value, which is desirable in most of the cryptographic protocols. We supplement our pairing accelerator with a coprocessor responsible for this task. An improved exponentiation algorithm allows us to save hardware resources. According to our place-and-route results on Xilinx FPGAs, our design improves both the computation time and the area-time trade-off compared to previoulsy published coprocessors.

Available format(s)
Category
Implementation
Publication info
Published elsewhere. Unknown where it was published
Keywords
Tate pairing$\eta_T$ pairingelliptic curvefinite field arithmeticKaratsuba-Ofman multiplierhardware acceleratorFPGA
Contact author(s)
jeanluc beuchat @ gmail com
History
2009-08-04: last of 2 revisions
See all versions
Short URL
https://ia.cr/2009/122

CC BY

BibTeX

@misc{cryptoeprint:2009/122,
author = {Jean-Luc Beuchat and Jérémie Detrey and Nicolas Estibals and Eiji Okamoto and Francisco Rodríguez-Henríquez},
title = {Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers},
howpublished = {Cryptology ePrint Archive, Paper 2009/122},
year = {2009},
note = {\url{https://eprint.iacr.org/2009/122}},
url = {https://eprint.iacr.org/2009/122}
}

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