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For BW6-761, explanation is here: https://hackmd.io/@gnark/BW6-761-changes
For BW6-633, it follows the same logic.
I chose to port here an optimal Tate (Alg.2 in HG21) because it is the fastest for both single pairing and multi-pairing and also for both BW6-761 (over BLS12) and BW6-633 (over BLS24). The result of BW6-761 pairing is not the same as previously but it's not a problem since we are using pairings as a a product check (e.g.
e([]A, []B)==1
rather than exact values.Benchmarks:
BW6-761
BW6-633