Parallel Computation of Optimal Ate Cryptographic Pairings at the $128$, $192$ and $256$-bit security levels using elliptic net algorithm
Abstract
Efficient computations of pairings with Miller Algorithm have recently received a great attention due to the many applications in cryptography. In this work, we give formulae for the optimal Ate pairing in terms of elliptic nets associated to twisted Barreto-Naehrig (BN) curve, Barreto-Lynn-Scott(BLS) curves and Kachisa-Schaefer-Scott(KSS) curves considered at the , and -bit security levels, and Scott-Guillevic curve with embedding degree . We show how to parallelize the computation of these pairings when the elliptic net algorithm instead is used and we obtain except in the case of Kachisa-Schaefer-Scott(KSS) curves considered at the -bit security level, more efficient theoretical results with processors compared to the case where the Miller algorithm is used. This work still confirms that curves are the best for pairing-based cryptography at -bit security level \cite{NARDIEFO19}.
Cite
@article{arxiv.2003.11286,
title = {Parallel Computation of Optimal Ate Cryptographic Pairings at the $128$, $192$ and $256$-bit security levels using elliptic net algorithm},
author = {Narcisse Bang Mbang and Emmanuel Fouotsa and Celestin Lele},
journal= {arXiv preprint arXiv:2003.11286},
year = {2021}
}