title: 'Computing Optimal Ate Pairing' -> 'Computing the Optimal Ate Pairing' or 'Computing Optimal Ate Pairings'
sen 1: optimal -> the optimal; subfunctions -> the subfunctions
par 3: 'its twisted curve' -> 'its twist'; 'such isomorphism' -> 'such an isomorphism'
par 4: 'Computation of optimal Ate pairing for BN curves uses Frobenius map'
-> 'The computation of the optimal Ate pairing for BN curves uses the Frobenius map'
last sentence: 'Let a Frobenius' -> 'The p-power Frobenius'; 'be' -> 'is'
Comments from Chloe (Expert Reviewer)