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IEICE TRANSACTIONS on Fundamentals

A Note on the Pairing Computation Using Normalized Miller Functions

Naoki OGURA, Shigenori UCHIYAMA, Naoki KANAYAMA, Eiji OKAMOTO

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Summary :

This paper considers the normalization of Miller functions for computing “point-evaluation” pairings on an elliptic curve E over a finite field Fq, where the characteristic of Fq is neither 2 nor 3. It is shown that the normalized Miller functions for computing point-evaluation pairings on G2G1 when (i) the embedding degree k is even, or (ii) 3|k and E/Fq(q ≡ (1 mod 3)) is a curve of the form Y2=X3+b. Thus, there is no need to consider the normalization for computing pairings on many pairing-friendly elliptic curves.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.1 pp.196-203
Publication Date
2012/01/01
Publicized
Online ISSN
1745-1337
DOI
10.1587/transfun.E95.A.196
Type of Manuscript
Special Section PAPER (Special Section on Cryptography and Information Security)
Category
Mathematics

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