  Pairings have been widely used since their introduction to cryptography. They
can be applied to identity-based encryption, tripartite Diffie-Hellman key
agreement, blockchain and other cryptographic schemes. The Acceleration of
pairing computations is crucial for these cryptographic schemes or protocols.
In this paper, we will focus on the Elliptic Net algorithm which can compute
pairings in polynomial time, but it requires more storage than Miller's
algorithm. We use several methods to speed up the Elliptic Net algorithm.
Firstly, we eliminate the inverse operation in the improved Elliptic Net
algorithm. In some circumstance, this finding can achieve further improvements.
Secondly, we apply lazy reduction technique to the Elliptic Net algorithm,
which helps us achieve a faster implementation. Finally, we propose a new
derivation of the formulas for the computation of the Optimal Ate pairing on
the twisted curve. Results show that the Elliptic Net algorithm can be
significantly accelerated especially on the twisted curve. The algorithm can be
$80\%$ faster than the previous ones on the twisted 381-bit BLS12 curve and
$71.5\%$ faster on the twisted 676-bit KSS18 curve respectively.
