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

Tetsuya Izuta, Yasuyuki Nogami, Yoshitaka Morikawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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(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.

Original languageEnglish
Title of host publicationIEEE Region 10 Annual International Conference, Proceedings/TENCON
Pages769-772
Number of pages4
DOIs
Publication statusPublished - 2010
Event2010 IEEE Region 10 Conference, TENCON 2010 - Fukuoka, Japan
Duration: Nov 21 2010Nov 24 2010

Other

Other2010 IEEE Region 10 Conference, TENCON 2010
CountryJapan
CityFukuoka
Period11/21/1011/24/10

Fingerprint

Cryptography
Polynomials
Composite materials

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Science Applications

Cite this

Izuta, T., Nogami, Y., & Morikawa, Y. (2010). Ordinary pairing friendly curve of embedding degree 1 whose order has two large prime factors. In IEEE Region 10 Annual International Conference, Proceedings/TENCON (pp. 769-772). [5686593] https://doi.org/10.1109/TENCON.2010.5686593

Ordinary pairing friendly curve of embedding degree 1 whose order has two large prime factors. / Izuta, Tetsuya; Nogami, Yasuyuki; Morikawa, Yoshitaka.

IEEE Region 10 Annual International Conference, Proceedings/TENCON. 2010. p. 769-772 5686593.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Izuta, T, Nogami, Y & Morikawa, Y 2010, Ordinary pairing friendly curve of embedding degree 1 whose order has two large prime factors. in IEEE Region 10 Annual International Conference, Proceedings/TENCON., 5686593, pp. 769-772, 2010 IEEE Region 10 Conference, TENCON 2010, Fukuoka, Japan, 11/21/10. https://doi.org/10.1109/TENCON.2010.5686593
Izuta T, Nogami Y, Morikawa Y. Ordinary pairing friendly curve of embedding degree 1 whose order has two large prime factors. In IEEE Region 10 Annual International Conference, Proceedings/TENCON. 2010. p. 769-772. 5686593 https://doi.org/10.1109/TENCON.2010.5686593
Izuta, Tetsuya ; Nogami, Yasuyuki ; Morikawa, Yoshitaka. / Ordinary pairing friendly curve of embedding degree 1 whose order has two large prime factors. IEEE Region 10 Annual International Conference, Proceedings/TENCON. 2010. pp. 769-772
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