  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}.
