Apart form the following, what are the other properties of a good cryptographic Substitution box or the S-Box:
- Changing one input bit should change about half of the output bits.
- Each output bit should depend on every input bit.
Cryptography Stack Exchange is a question and answer site for software developers, mathematicians and others interested in cryptography. It only takes a minute to sign up.
Sign up to join this communityApart form the following, what are the other properties of a good cryptographic Substitution box or the S-Box:
Another very common criteria for an S-box with $n$ input bits and $m$ output bits with $m\le n$ (as most commonly used S-boxes are) is that each of the $2^m$ output values should be reached for exactly (or at least near) $2^{n-m}$ input values.
The question's criterion 1 can be made strict and become the Strict Avalanche Criterion. There are even stricter /higher-order versions. There also is the Bit independence criterion. The desirability of these properties depends on the overall design of the cryptographic construction using the S-box, and is not easy to assess.
More generally, S-boxes are typically optimized with use as part of a particular cryptographic construction in mind, aiming at improving it's overall resistance against cryptanalytic attacks, as pointed in comment.