The choice of functions S : F_2~n → F_2~m to be used as substitution boxes (S-boxes), fastly implementable and contributing to resisting attacks is a crucial question for the design of block ciphers. We summary the state of the art in this domain, considering also the case m ＜ n which has been less studied. We also recall the method for protecting block ciphers against side channel attacks (SCA) by masking, and how the S-boxes can be processed in order to ensure this protection. We state a related open problem, also interesting for its own sake. We eventually see how Boolean functions, vectorial functions and error correcting codes can be used in different ways for reducing the cost of masking while keeping the same resistance to some SCA and also for allowing resisting fault injection attacks (FIA).
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