@inproceedings{3b23a8cd86b242d6b95d27b916e4e77f,

title = "Pairing-friendly elliptic curves of prime order",

abstract = "Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree k \leqslant 6 Unknown control sequence '\leqslant'. More general methods produce curves over \mathbb FpFp 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 ¿ = 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 \mathbb Fp4Fp4 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 ¿; 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 ¿ ~ q/(q–1).",

author = "P.S.L.M. Barreto and M. Naehrig",

year = "2006",

doi = "10.1007/11693383_22",

language = "English",

isbn = "978-3-540-33108-7",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "319--331",

editor = "B. Preneel and S. Tavares",

booktitle = "Selected Areas in Cryptography (12th International Workshop, SAC 2005, Kingston ON, Canada, August 11-12, 2005, Revised Selected Papers)",

address = "Germany",

}