Efficient Search for Optimal Vector Permutations of uBlock-like Structures

The overall structure is an important feature of block cipher and also the primary research object. It has a great influence on the performance of hardware and software in the selection of rounds of block cipher. In the design process of the AES-like ciphers, when using a matrix with a non-optimal branch number for the MixColumns operation, the choice of the vector permutation, i.e., an alternative for ShiftRows, can actually improve the security of the primitive. uBlock-like structure is an AES-like structure. In this paper, we investigate the characteristics and diffusivity of uBlock-like structures, the lower bound of the number of full diffusion rounds and the equivalence class division criteria, and then we propose a search strategy for optimal vector permutations of uBlock-like structures. According to the optimal number of full diffusion rounds, the optimal branch number of the super diffusion layer, and the special properties of the diffusion layer of uBlock-like structure, we prove that the left and right vector permutations cannot be the identity transformation, and a series of optimal vector permutations of uBlock-like structures are given. The search strategy greatly reduces the number of permutation pairs that need to be tested and provides technical support for the design of uBlock-like algorithms.