Construction of perfect diffusion layers from linear feedback shift registers

Maximum distance separable (MDS) matrices are widely used in the diffusion layers of block ciphers and hash functions. Inspired by Guo, Sajadieh and Wu et al.´s recursive construction of perfect diffusion layers from linear feedback shift registers (LFSRs), the authors further study how to construct perfect diffusion layers from LFSRs of Fibonacci and Galois architectures, and present a systematic analysis of 4 × 4 words diffusion layer constructed with those two structures. Compared with known results, the MDS matrices constructed by us have the advantage that their inverses are usually also MDS matrices, and can be efficiently implemented with the same computational complexity.