Advances in Mathematics of Communications (AMC)

Heuristics of the Cocks-Pinch method

Pages: 103 - 118, Volume 8, Issue 1, February 2014      doi:10.3934/amc.2014.8.103

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Min Sha - Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351, Cours de la Libération, 33405 Talence Cedex, France (email)

Abstract: We heuristically analyze the Cocks-Pinch method by using the Bateman-Horn conjecture. Especially, we present the first known heuristic which suggests that any efficient construction of pairing-friendly elliptic curves can efficiently generate such curves over pairing-friendly fields, naturally including the Cocks-Pinch method. Finally, some numerical evidence is given.

Keywords:  Pairing-friendly elliptic curve, Cocks-Pinch method, Bateman-Horn conjecture, pairing-friendly field.
Mathematics Subject Classification:  Primary: 14H52, 11T71; Secondary: 11G20.

Received: April 2013;      Revised: December 2013;      Available Online: January 2014.