Scalable Method of Searching for Full-period Nonlinear Feedback Shift Registers with GPGPU. New List of Maximum Period NLFSRs.

Abstract

This paper addresses the problem of efficient searching for Nonlinear Feedback Shift Registers (NLFSRs) with a guaranteed full period. The maximum possible period for an $n$-bit NLFSR is $2^n-1$ (all-zero state is omitted). %but omitting all-0 state makes the period $2^n-1$ in their longest cycle of states. A multi-stages hybrid algorithm which utilizes Graphics Processor Units (GPU) power was developed for processing data-parallel throughput computation. Usage of abovementioned algorithm allows to give an extended list of n-bit NLFSR with maximum period for 7 cryptographically applicable types of feedback functions.