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Preprints, Working Papers, ... Year : 2023

An Algebraic Point of View on the Generation of Pairing-Friendly Curves

Abstract

In 2010, Freeman, Scott, and Teske published a well-known taxonomy compiling the best known families of pairing-friendly elliptic curves. Since then, the research effort mostly shifted from the generation of pairing-friendly curves to the improvement of algorithms or the assessment of security parameters to resist the latest attacks on the discrete logarithm problem. Consequently, very few new families were discovered. However, the need of pairing-friendly curves of prime order in some new applications such as SNARKs has reignited the interest in the generation of pairing-friendly curves, with hope of finding families similar to the one discovered by Barreto and Naehrig. Building on the work of Kachisa, Schaefer, and Scott, we show that some elements of extensions of a cyclotomic field have a higher probability of generating a family of pairing-friendly curves. We present a general framework which embraces the KSS families and many of the other families in the taxonomy paper, and provide an open-source SageMath implementation of our technique. We finally introduce a new family with embedding degree k = 20 which we estimate to provide a faster Miller loop compared to KSS16 and KSS18 at the 192-bit security level.
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Dates and versions

hal-04205681 , version 1 (13-09-2023)

Identifiers

  • HAL Id : hal-04205681 , version 1

Cite

Jean Gasnier, Aurore Guillevic. An Algebraic Point of View on the Generation of Pairing-Friendly Curves. 2023. ⟨hal-04205681⟩
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