Memoirs of the Faculty of Engineering, Okayama University
Published by Faculty of Enginerring, Okayama University

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Memoirs of the School of Engineering, Okayama University

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Ordinary Pairing Friendly Curve of Embedding Degree 3 Whose Order Has Two Large Prime Factors

Nogami, Yasuyuki Graduate School of Natural Science and Technology, Okayama University
Morikawa, Yoshitaka Graduate School of Natural Science and Technology, Okayama University
抄録
This paper proposes a method for generating a certain composite order ordinary pairing–friendly elliptic curve of embedding degree 3. In detail, the order has two large prime factors such as the modulus of RSA cryptography. The method is based on the property that the order of the target pairing–friendly curve is given by a polynomial as r(X) of degree 2 with respect to the integer variable X. When the bit size of the prime factors is about 500 bits, the proposed method averagely takes about 15 minutes on Core 2 Quad (2.66Hz) for generating one.
ISSN
1349-6115
NCID
AA12014085
NAID