Advances in Mathematics of Communications (AMC)

On finite fields for pairing based cryptography

Pages: 281 - 286, Volume 1, Issue 3, August 2007      doi:10.3934/amc.2007.1.281

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Florian Luca - Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, Mexico (email)
Igor E. Shparlinski - Department of Computing, Macquarie University, Sydney, NSW 2109, Australia (email)

Abstract: Here, we improve our previous bound on the number of finite fields over which elliptic curves of cryptographic interest with a given embedding degree and small complex multiplication discriminant may exist. We also give some heuristic arguments which lead to a lower bound which in some cases is close to our upper bound.

Keywords:  Elliptic curves, pairing based cryptography, embedding degree.
Mathematics Subject Classification:  11G07, 11T71, 14H52.

Received: July 2006;      Revised: June 2007;      Available Online: July 2007.