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BN optimal ate Miller loop looks like:
f_{v,Q} * line1 * line2
which is implemented this way(f_{v,Q} * line1) * line2
costing 2 full-sparse multiplicationsMulBy034()
(2 x 13M = 26M
withM
inFp2
). This small PR changes it tof_{u,Q} * (line1 * line2)
costing 1 sparse-sparse multiplicationMul034By034()
and 1 full-sparse multiplicationMul()
(6M + 18M = 24M
). This might be particularly interesting for multi-pairing as we would multiply the two lines 2-by-2 exploiting full sparsity.Note: we can save
1M
more when multiplying the product of lines byf
as the product has always oneFp2
zero, but this is not worth it.