# American Institute of Mathematical Sciences

August  2007, 1(3): 281-286. doi: 10.3934/amc.2007.1.281

## On finite fields for pairing based cryptography

 1 Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, Mexico 2 Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

Received  July 2006 Revised  June 2007 Published  July 2007

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.
Citation: Florian Luca, Igor E. Shparlinski. On finite fields for pairing based cryptography. Advances in Mathematics of Communications, 2007, 1 (3) : 281-286. doi: 10.3934/amc.2007.1.281
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