Abstract
This study presents a technique for investigating the cyclic properties of substitution boxes (S-boxes) in the Cipher Block Chaining (CBC) mode of operation. S-boxes provide nonlinear transformations in cryptographic algorithms to create confusion. The CBC mode design is used in block ciphers to hide periodic patterns and create diffusion of the effect. The main objective of this study was to evaluate the cryptographic strength of S-boxes using periodicity detection in CBC mode. The study of S-boxes using the presented technique allows us to examine them in a different manner and study their diffusion levels, the metrics of which are the periodicities of S-box element sequences. To apply the diffusion of the effect of the CBC mode on the S-boxes, the encryption functions used in the block ciphers were replaced with the substitution functions used for the S-boxes. An S-box was selected for use in the Advanced Encryption Standard (AES) to demonstrate the experiments and results of the study. In this study, the cyclic properties of the S-box were considered from two different aspects: the periodicity detection of the S-box with respect to iterations and blocks. According to our study, the results of the AES S-box and other S-boxes exhibited very long periods, which indicates that the influence of the CBC mode spread over many iterations and blocks, indicating a high level of cryptographic strength for S-boxes.