# Perfect Nonlinearity of AES S Boxes

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?

• see Definition 2 at Perfect nonlinear functions and cryptography – kelalaka Oct 26 '18 at 19:11
• 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 – Richie Frame Oct 27 '18 at 0:27
• @kelalaka The link is apparently dead. – yyyy0000 Jul 17 '19 at 13:56
• @pushpen.paul little search – kelalaka Jul 17 '19 at 14:33