Cryptology ePrint Archive: Report 2005/302

Elliptic Curves for Pairing Applications

Angela Murphy and Noel Fitzpatrick

Abstract: In this paper we address the question of representing the discriminant of an imaginary quadratic field with respect to the basis of a cyclotomic field. This representation allows us to parameterize new families of ordinary elliptic curves over finite prime fields suitable for pairing applications. In particular these curves have small discriminants greater than four and arbitrary embedding degree. Computational results are presented which support the theoretical findings.

Category / Keywords: public-key cryptography / Pairing Based Cryptosystem, Elliptic Curves.

Date: received 1 Sep 2005, last revised 2 Dec 2005

Contact author: noelfitz at redbrick dcu ie

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Note: Corrected an error in the representation of sqrt{-15} in Q(\zeta_30). Corrected a typo in step 4.b of algorithm 2.3

Version: 20051202:131232 (All versions of this report)

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