Cellular automata (CA) based S-boxes are the type of S-boxes with good cryptography and low cost of hardware as well as software implementation

which are used in Keccak

SIMON

and other cryptographic algorithms. This paper studied the properties of CA-based S-boxes

and the three important properties were given and proved

including shift invariance

mirror symmetry and complementarity. Meanwhile

the neural network implementation for CA-based S-boxes was studied

which demonstrated that the CA-based S-boxes could be implemented with simpler structure and less resources than the general one. In addition

a weight threshold search algorithm which could easily and quickly implement the neural network structure of CA-based S-boxes was shown.