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A Note on the Pairing Computation Using Normalized Miller Functions
Naoki OGURA Shigenori UCHIYAMA Naoki KANAYAMA Eiji OKAMOTO
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2012/01/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
pairing, Miller's algorithm, rational functions, normalization,
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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.