On Near-Maximum-Length Galois Nonlinear Feedback Shift Registers

Nonlinear feedback shift registers (NLFSRs) are well-positioned to play the key role in securing variety of digital ecosystems. They have already been deployed as major building blocks of several hardware stream ciphers, and are expected to become an essential part of hardware roots of trust that protect integrated circuits (ICs) against hardware security threats and mitigate risks associated with an unauthorized access and usage of ICs. In this article, we present two new sets of Galois NLFSRs with maximum and near maximum prime periods, respectively. All reported registers have been identified by virtue of an FPGA-based engine running in parallel around 8000 search processes. This article provides a detailed description of metrics used to characterize output sequences produced by NLFSRs, such as the number of n-tuples each output sequence is comprised of, linear complexity of output sequences, and the total number of different maximum-length sequences obtained by means of simple linear filters driven by the examined registers. This article is accompanied by tables listing all found and never presented before NLFSRs, altogether with their architectural details and the corresponding metrics.