Feistel-Type Structure-Based Construction of Linear Feedback Shift Registers

In 2023, Academician Feng et al. proposed LOL, a highly flexible stream cipher algorithm design framework. This framework utilizes a Linear Feedback Shift Register (LFSR) based on Feistel structure to generate pseudorandom sequences efficiently. Our paper extends this concept by proposing a method for constructing LFSRs based on generalized Feistel-type structures. We analyze the permutation-based equivalence classification of this generalized construction and provide specific examples of maximal-period LFSRs constructed using generalized Feistel structures with 4 and 8 branches. Notably, compared to traditional Feistel-structured LFSRs, our approach reduces computational complexity by 1/2 and 3/4 for 4-branch and 8-branch designs, respectively. These structures offer improved adaptability on domestic CPU platforms lacking SIMD instruction set support, providing diverse options for cryptographic sequence generator design.