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Perhaps use https://cr.yp.to/papers/pippenger.pdf for an even faster exponentiation algorithm. See zcash issue 3128 for a potential discussion to see if this can be done in a side channel resistant manner.
(Not using a link to avoid a reference link showing up there, since this doesn't contribute to solving that problem)
Unmarshalling compressed G2 points can be sped up by using the montgomery reduction in that exponentiation.
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