An Algorithm for Constructing a Minimal Register with Non-linear Update Generating a Given Sequence

Registers with Non-Linear Update (RNLUs) are a generalization of Non-Linear Feedback Shift Registers (NLFSRs) in which both, feedback and feedforward, connections are allowed and no chain connection between the stages is required. An RNLU can be used to generate any given 2^p-ary sequence, p ≥ 1. In this paper, a new algorithm for constructing RNLUs is presented. Expected size of RNLUs constructed by the presented algorithm is proved to be asymptotically smaller than the expected size of RNLUs constructed by previous algorithms generating the same sequence. The presented algorithm can potentially be useful for applications such as testing, wireless communications, and cryptography.