@inproceedings{barreto2006pairing-friendly,
author = {Barreto, Paulo S. L. M. and Naehrig, Michael},
title = {Pairing-friendly elliptic curves of prime order},
series = {Lecture Notes in Computer Science},
booktitle = {Selected Areas in Cryptography - SAC 2005},
year = {2006},
month = {January},
abstract = {Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree k ≤ 6. More general methods produce curves over Fp where the bit length of p is often twice as large as that of the order r of the subgroup with embedding degree k; the best published results achieve ρ = log (p)/log (r)   5/4. In this paper we make the first step towards surpassing these limitations by describing a method to construct elliptic curves of prime order and embedding degree k = 12. The new curves lead to very efficient implementation: non-pairing operations need no more than Fp4-arithmetic, and pairing values can be compressed to one third of their length in a way compatible with point reduction techniques. We also discuss the role of large CM discriminants D to minimize ρ; in particular, for embedding degree k = 2q where q is prime we show that the ability to handle log (D)/log (r)   (q − 3)/(q − 1) enables building curves with ρ   q/(q − 1)$.},
publisher = {Springer},
url = {http://approjects.co.za/?big=en-us/research/publication/pairing-friendly-elliptic-curves-of-prime-order/},
pages = {319-331},
volume = {3897},
edition = {Selected Areas in Cryptography - SAC 2005},
}