Parallel Computation of Optimal Ate Cryptographic Pairings at the $128$, $192$ and $256$-bit security levels using elliptic net algorithm
This work addresses performance bottlenecks in pairing-based cryptography, which is crucial for cryptographic applications, but it is incremental as it builds on existing methods like the elliptic net algorithm.
The paper tackled the problem of efficiently computing optimal Ate cryptographic pairings at various security levels by deriving formulae using elliptic nets for specific curves and parallelizing the computations, achieving more efficient theoretical results with 8 processors compared to the Miller algorithm in most cases, except for KSS curves at the 256-bit level.
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 $128$, $192$ and $256$-bit security levels, and Scott-Guillevic curve with embedding degree $54$. 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 $256$-bit security level, more efficient theoretical results with $8$ processors compared to the case where the Miller algorithm is used. This work still confirms that $BLS48$ curves are the best for pairing-based cryptography at $256$-bit security level \cite{NARDIEFO19}.