Paper 2019/555
Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
Georgios Fotiadis and Chloe Martindale
Abstract
In this paper we present a comprehensive comparison between pairing-friendly elliptic curves, considering different curve forms and twists where possible. We define a measure of the efficiency of a parametrized pairing-friendly family that takes into account the number field sieve (NFS) attacks (unlike the $\rho$-value). This measure includes an approximation of the security of the discrete logarithm problem in $\mathbb F_{p^k}^*$, computed via the method of Barbulescu and Duquesne [4]. We compute the security of the families presented by Fotiadis and Konstantinou in [13], compute some new families, and compare the efficiency of both of these with the (adjusted) BLS, KSS, and BN families, and with the new families of [19]. Finally, we present an optimal pairing-friendly elliptic curve for security level 128 and recommend two pairing-friendly elliptic curves for security level 192.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Optimal ate pairingtwists of elliptic curvesjacobian coordinatesTNFS-secureSexTNFS
- Contact author(s)
-
georgios fotiadis @ uni lu
chloemartindale @ gmail com - History
- 2019-08-22: revised
- 2019-05-25: received
- See all versions
- Short URL
- https://ia.cr/2019/555
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/555,
author = {Georgios Fotiadis and Chloe Martindale},
title = {Optimal {TNFS}-secure pairings on elliptic curves with composite embedding degree},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/555},
year = {2019},
url = {https://eprint.iacr.org/2019/555}
}
