perf(bw6-756): optimize GT subgroup membership#351
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ThomasPiellard
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Mar 6, 2023
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Instead of checking
z^r==1in GT (whereris 378 bit), we do the following sequential check:z^(Phi_k(p)) == 1(wherePhi_k(p)is the kth-cyclotomic polynomial) andz^(p+1-t) == 1wheret, the Frobenius trace, happens to be defined by the polynomialt(x) = (-x⁶ + 5x⁵ - 9x⁴ + 7x³ - 4x + 5)/3 + 1in the case of the BW6-756 curve