Design of Iterative MDS Matrices Based on MISTY Structure

The security of symmetric-key ciphers critically depends on the diffusion efficiency of their linear components. Iterative maximum distance separable (MDS) matrices, as fundamental elements of diffusion layer, play a pivotal role in constructing secure cryptographic systems. This study focuses on the construction of iterative MDS matrices based on the iterative MISTY structure. First, we present iterative MISTY structures with same round functions over F2m22n & times;n, along with the corresponding necessary conditions for constructing iterative MDS matrices. Then, we investigate the construction of 4th-order iterative MDS matrices over F2m44 & times; for m = 4, 5, 6, 8, and evaluate the implementation cost in terms of gate count for some instances. Second, we extend this paradigm to MISTY structures with distinct round functions, establishing corresponding necessary conditions and generating 4th-order iterative MDS matrices over F2m44 & times; for m = 3, 4. Based on which, we investigate 4th-order iterative MDS matrices over F2m44 & times; for m = 3, 4 and exhibit some instances selected from the resulting matrices.