Construction of Kind of S-box with Good Cryptographic Properties

The construction principle of nonlinear transformation S-box in Rijndael algorithm was studied,and based on the principle,a number of 4×4 and 6×6 S-boxes with some good cryptographic properties that are close to the best ones were constructed in the paper.These small S-boxes can be used as resources to further construct large S-boxes with several good cryptographic properties.The avalanche probabilities of these S-boxes were statistically analyzed,and several rules were discovered,it will be a great help to construct safer and larger S-boxes.