Ordinary pairing friendly curve of embedding degree 1 whose order has two large prime factors

This paper proposes a method for generating a certain composite order ordinary pairing-friendly elliptic curve of embedding degree 1. In detail, the order has two large prime factors such as the modulus of RSA cryptography. The method is based on a property that the order of the target pairing-frien...

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Bibliographic Details
Published inTENCON 2010 - 2010 IEEE Region 10 Conference pp. 769 - 772
Main Authors Izuta, T, Nogami, Y, Morikawa, Y
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.11.2010
Subjects
Elliptic curve cryptography
Elliptic curves
Polynomials
Protocols
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Summary:This paper proposes a method for generating a certain composite order ordinary pairing-friendly elliptic curve of embedding degree 1. In detail, the order has two large prime factors such as the modulus of RSA cryptography. The method is based on a property that the order of the target pairing-friendly curve is given by a cyclotomic polynomial as r(χ) of degree 2 with respect to the integer variable χ. When the bit size of the prime factors is almost 1000 bits, the proposed method averagely takes about 20 hours on Core 2 Duo (3.0GHz) for generating one.
ISBN:9781424468898
1424468892
ISSN:2159-3442
2159-3450
DOI:10.1109/TENCON.2010.5686593