Searching for nonlinear feedback shift registers with parallel computing

Abstract

Abstract. Nonlinear feedback shift registers (NLFSRs) are used to construct pseudorandom generators for stream ciphers. Their theory is not so complete as that of linear feedback shift registers (LFSRs). In general, it is not known how to construct all NLFSRs with maximum period. The direct method is to search for such registers with suitable properties. Advanced technology of parallel computing has been applied both in software and hardware to search for maximum period NLFSRs having a fairly simple algebraic normal form.

On cross joining de Bruijn sequences

“…Gong and Mandal [15] following Mykkeltveit et al [18] developed a recursive method for constructing maximum period NLFSRs. Chan, Games and Rushanan [2] conjectured existence of quadratic m-sequences for each order n. In [3] we have verified this conjecture experimentally up to order n = 29, finding simple quadratic NLFSRs by searching methods. In the present note we aim to relate the existence of NLFSRs generating quadratic m-sequences to the construction of cross joining.…”

“…Methods for finding NLFSRs with simple ANF of the feedback function were presented in [8,2,19,3]. Gong and Mandal [15] following Mykkeltveit et al [18] developed a recursive method for constructing maximum period NLFSRs.…”

Modified Alternating Step Generators with Non-Linear Scrambler

“…We concentrated on selecting proper non-linear functions -as feedback functions and the others as filtering and combining functions. In [21,22,23] there are described methods for constructing non-linear feedback functions for shift registers. At this time we can achieve registers with the maximal period for the length up to n = 31.…”

“…The output sequence from the alternating step generator is applied to the input of the scrambler, where bit after bit is added (mod 2) to its non-linear feedback. The example of the non-linear feedback function of the scrambler might look like this [23]…”

The search of square m-sequences with maximum period via GPU and CPU

“…The most critical NLFSR related problem is finding a systematic procedure for constructing NLFSRs with a long confirmed period. Available algorithms either consider some individual cases or apply to low order NLFSRs only [7,14,16]. Nikolay Poluyanenko developed the most efficient method.…”