Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Optimal ate pairing, twists of elliptic curves, jacobian coordinates, TNFS-secure, SexTNFS

Date: received 24 May 2019, last revised 22 Aug 2019

Contact author: georgios fotiadis at uni lu,chloemartindale@gmail com

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Version: 20190822:130319 (All versions of this report)

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