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

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 2ⁿ - 1 (an all-zero state is omitted). A multi-stages hybrid algorithm which utilizes Graphics Processor Units (GPU) power was developed for processing data-parallel throughput computation. Usage of the abovementioned algorithm allows giving an extended list of n-bit NLFSR with maximum period for 7 cryptographically applicable types of feedback functions.