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Thank you for reporting this. It looks like a rather severe regression. With

S = [x for x in range(256)];shuffle(S)
S = sage.crypto.sbox.SBox(S)
%prun -s cumtime S.nonlinearity()

on 8.1 and 8.2+ you can see that the call graph has changed significantly. Recent changes on sbox have been made by Friedrich Wiemer. You should file a trac ticket and CC him on it. He would likely have a good idea what the cause of the slowdown is and if it can be fixed.