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A Method for Generating Full Cycles by a Composition of NLFSRs
KTH, School of Information and Communication Technology (ICT), Electronic Systems.ORCID iD: 0000-0001-7382-9408
2014 (English)In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 73, no 2, 469-486 p.Article in journal (Refereed) Published
Abstract [en]

Non-linear feedback shift registers (NLFSRs) are a generalization of linear feedback shift registers in which a current state is a non-linear function of the previous state. The interest in NLFSRs is motivated by their ability to generate pseudo-random sequences which are typically hard to break with existing cryptanalytic methods. However, it is still not known how to construct large -stage NLFSRs which generate full cycles of possible states. This paper presents a method for generating full cycles by a composition of NLFSRs. First, we show that an -stage register with period can be constructed from NLFSRs with -stages by adding to their feedback functions a logic block of size , for . This logic block implements Boolean functions representing pairs of states whose successors have to be exchanged in order to join cycles. Then, we show how to join all cycles into one by using one more logic block of size O(nk).

Place, publisher, year, edition, pages
2014. Vol. 73, no 2, 469-486 p.
Keyword [en]
LFSR, NLFSR, De Bruijn sequence, Full cycle, Maximum period
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
URN: urn:nbn:se:kth:diva-149958DOI: 10.1007/s10623-014-9947-3ISI: 000339826100014ScopusID: 2-s2.0-84905270747OAI: diva2:744917
Swedish Research Council, 621-2010-4388Swedish Foundation for Strategic Research , SM12-0005

QC 20150623

Available from: 2014-09-09 Created: 2014-08-29 Last updated: 2015-06-23Bibliographically approved

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Dubrova, Elena
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