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Major families of pairing-friendly elliptic curves, including BN, BLS12,BLS24, KSS16, and KSS18 have recently been vulnerable to number field sieve(NFS) attacks. Due to the recent attacks on discrete logs in F_(q^k ),selecting such curves became relevant again. This paper revisited the topic ofselecting pairing-friendly curves at different security levels. First, weexpanded the classification given by Freeman et al. [1] by identifying newfamilies that were not previously mentioned, such as a complete family withvariable differentiation and new sparse families of curves. We discussedindividual curves and a comprehensive framework for constructing parametricfamilies. We estimated the security and assessed families of thepairing-friendly curve to discover families of curves better than BN, KSS, andBLS in terms of the required key size. We also evaluated the complexity of theoptimal ate pairing that has never been discussed before, except by Barbulescuet al. [2]. We demonstrated that the recent attack (TNFS) on pairing needs toincrease the key size. We compared families of curves in the context of keysize and selected a suitable alternative to an elliptic curve.

Pairing-Friendly Elliptic Curves: Revisited Taxonomy, Attacks and Security Concern