Summary
International Technical Conference on Circuits/Systems, Computers and Communications
2008
Session Number:E2
Session:
Number:E2-4
An Improvement of Twisted Ate Pairing Using Integer Variable with Small Hamming Weight
Yumi Sakemi, Hidehiro Kato, Yasuyuki Nogami, Yoshitaka Morikawa,
pp.-
Publication Date:2008/7/7
Online ISSN:2188-5079
Summary:
Barreto-Naehrig (BN) curve has been introduced as a pairing-friendly elliptic curve over prime field Fp which has embedding degree 12. Characteristic and Frobenius trace are given as polynomials of integer variable $\chi$. This paper proposes an improvement of Miller's algorithm of twisted Ate pairing with BN curve by $\chi$ of small hamming weight. Then, in order to show the efficiency of the proposed method, twisted Ate pairings with BN curve of order $r\approx 2^{158}$ and $r\approx 2^{254}$ are simulated and it is shown that these twisted Ate pairings are carried out with 7.21 milliseconds and 16.5 milliseconds by Pentium4 (3.6GHz), respectively.