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Can someone give a clear definition of what a perfectly nonlinear function is? Can we say that AES s-boxes are perfectly nonlinear and why?

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    $\begingroup$ see Definition 2 at Perfect nonlinear functions and cryptography $\endgroup$ – kelalaka Oct 26 '18 at 19:11
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    $\begingroup$ as far as I know, an $m \times m$ boolean function where $m$ is an even number can never be as nonlinear (relative to its size) as when $m$ is an odd number, so an 8x8 boolean function such as the AES s-box (there is only 1) can never be perfectly nonlinear $\endgroup$ – Richie Frame Oct 27 '18 at 0:27

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