TY - GEN
T1 - Ordinary pairing friendly curve of embedding degree 1 whose order has two large prime factors
AU - Izuta, Tetsuya
AU - Nogami, Yasuyuki
AU - Morikawa, Yoshitaka
PY - 2010
Y1 - 2010
N2 - 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(x) of degree 2 with respect to the integer variable x. 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.
AB - 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(x) of degree 2 with respect to the integer variable x. 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.
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U2 - 10.1109/TENCON.2010.5686593
DO - 10.1109/TENCON.2010.5686593
M3 - Conference contribution
AN - SCOPUS:79951612039
SN - 9781424468904
T3 - IEEE Region 10 Annual International Conference, Proceedings/TENCON
SP - 769
EP - 772
BT - TENCON 2010 - 2010 IEEE Region 10 Conference
T2 - 2010 IEEE Region 10 Conference, TENCON 2010
Y2 - 21 November 2010 through 24 November 2010
ER -