Automatic Search And Analysis For Cryptographic S-Boxes

The design and security analysis of cryptographic S-boxes have always been the focus of block cipher research.As the key component of block cipher,the cryptographic S-boxes provide confusion for the cryptographic algorithm and determine the security of the algorithm.The indicators to measure the security strength of the cryptographic S-boxes include algebraic degree,linearity,differential uniformity,transparency order,etc.The traditional construction method has certain limitations for designing S-boxes.For example,due to the limited search space,the complexity of the construction of S-boxes is not easy to be attacked,or the efficiency is too low.Computational intelligent algorithms are excellent in the design of S-boxes and have better optimization performance.This article focuses on the automatic search and analysis of 4×4 and 8×8 cryptographic S-boxes.The main contents are as follows:1)Based on the rules of Cellular Automata(CA),a new search method for 4×4 S boxes is proposed.Based on the design mechanism of the CA rule S-boxes,the generation form of the CA rule S-boxes algebraic expression is analyzed.By optimizing the CA rules,new 4×4 S-boxes are searched out,and the generated cryptographic indicators of the 4×4S-boxes are analyzed,and 4×4 optimal S-boxes with excellent properties is selected.It is shown that more 4×4 optimal S-boxes are attained,which is conducive to the expansion of S-boxes.In particular,three classes of 4×4 sub-optimal S-boxes can also be transformed to some 4×4 optimal S-boxes under the CA rules of this method.Compared with the previous well-known results,these new 4×4 optimal S-boxes have lower transparency order so that they have a robuster ability against differential power attack(DPA).2)Based on the Feistel-SP structure,an 8×8 S-boxes design scheme SB_F is proposed,and the corresponding search algorithm for the SB_F design scheme is given.This solution selects small S-boxes with light weight,low cost,and high efficiency.It uses a 3-round Feistel-SP structure to automatically search for new 8×8 S-boxes,and the traditional cryptography indexes and transparency order of the new 8×8 S-boxes were tested.The experimental results show that the 8×8 cipher S-boxes designed based on SB_F scheme has good cipher properties,and the hardware realization of the S-boxes is theoretically analyzed.3)Based on the mixed structure of Feistel and L-M,a design method of 8×8 S-boxes are proposed.The S-boxes design is realized based on two rounds of Feistel structure and one round of L-M structure.The results show that the 8×8 cryptographic S-boxes designed based on the SB_L scheme have an algebraic number of 7,a non-linearity of 96,and a minimum RTO of 7.5029.Compared with the existing algorithm structure to generate S-boxes,the newly-generated 8×8 S-boxes have reached the optimal algebraic degree,which reduces the transparency order to some extent.