Skew Frobenius Map and Efficient Scalar Multiplication for Pairing---Based Cryptography

Authors:
Yumi Sakemi;Yasuyuki Nogami;Katsuyuki Okeya;Hidehiro Kato;Yoshitaka Morikawa
Affiliations:
Okayama University, Okayama, Japan 700-8530;Okayama University, Okayama, Japan 700-8530;Hitachi, Ltd., Systems Development Laboratory, Yokohama, Japan 244-0817;Okayama University, Okayama, Japan 700-8530;Okayama University, Okayama, Japan 700-8530
Venue:
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
Year:
2008

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Abstract

This paper considers a new skew Frobenius endomorphism with pairing---friendly elliptic curve $E(\mathbb{F}{p}{})$ defined over prime field $\mathbb{F}{p}{}$. Then, using the new skew Frobenius map, an efficient scalar multiplication method for pairing---friendly elliptic curve $E(\mathbb{F}{p}{})$ is shown. According to the simulation result, a scalar multiplication by the proposed method with multi---exponentiation technique is about 40% faster than that by plain binary method.