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-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.