### TNFS Resistant Families of Pairing-Friendly Elliptic Curves

##### Abstract

Recently there has been a significant progress on the tower number field sieve (TNFS) method, reducing the complexity of the discrete logarithm problem (DLP) in finite field extensions of composite degree. These new variants of the TNFS attacks have a major impact on pairing-based cryptography and particularly on the selection of the underlying elliptic curve groups and extension fields. In this paper we revise the criteria for selecting pairing-friendly elliptic curves considering these new TNFS attacks in finite extensions of composite embedding degree. Additionally we update the criteria for finite extensions of prime degree in order to meet today’s security requirements.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Journal of Theoretical Computer Science, Elsevier (to appear)
Keywords
Pairingselliptic curvespairing-friendly parametersembedding degreeTNFS attacks
Contact author(s)
History
Short URL
https://ia.cr/2018/1017

CC BY

BibTeX

@misc{cryptoeprint:2018/1017,
author = {Georgios Fotiadis and Elisavet Konstantinou},
title = {TNFS Resistant Families of Pairing-Friendly Elliptic Curves},
howpublished = {Cryptology ePrint Archive, Paper 2018/1017},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/1017}},
url = {https://eprint.iacr.org/2018/1017}
}

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