Title :
Ordinary pairing friendly curve of embedding degree 1 whose order has two large prime factors
Author :
Izuta, Tetsuya ; Nogami, Yasuyuki ; Morikawa, Yoshitaka
Author_Institution :
Grad. Sch. of Natural Sci. & Technol., Okayama Univ., Okayama, Japan
Abstract :
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.
Keywords :
polynomials; public key cryptography; RSA cryptography; cyclotomic polynomial; elliptic curve; embedding degree; friendly curve;
Conference_Titel :
TENCON 2010 - 2010 IEEE Region 10 Conference
Conference_Location :
Fukuoka
Print_ISBN :
978-1-4244-6889-8
DOI :
10.1109/TENCON.2010.5686593