Testing an S-Box for Cryptographic Use

Generally, one faces two type of problems related to the selection of

an s-box (substitution box/function) before its cryptographic use can be

considered secure. First one is how to design (or search) a good s-box

and second one is how to verify a given s-box is indeed a good one in

a sense of meeting its requirements. The requirements contain the types

and quantitative values of desired properties for an s-box.