Paper 2020/760

Curves with fast computations in the first pairing group

Rémi Clarisse and Sylvain Duquesne and Olivier Sanders

Abstract

Pairings are a powerful tool to build advanced cryptographic schemes. The most efficient way to instantiate a pairing scheme is through Pairing-Friendly Elliptic Curves. Because a randomly picked elliptic curve will not support an efficient pairing (the embedding degree will usually be too large to make any computation practical), a pairing-friendly curve has to be carefully constructed. This has led to famous curves, e.g. Barreto-Naehrig curves. However, the computation of the discrete logarithm problem on the finite-field side has received much interest and its complexity has recently decreased. Hence the need to propose new curves has emerged. In this work, we give one new curve that is specifically tailored to be fast over the first pairing-group, which is well suited for several cryptographic schemes, such as group signatures and their variants (EPID, anonymous attestation, etc) or accumulators.