On the Density of Irreducible NFSRs

Let n be a positive integer. An NFSR of n stages is called irreducible if the family of output sequences of any NFSR of stages less than n is not included in that of the NFSR. In this paper, we prove that the density of the irreducible NFSRs of n stages is larger than 0.39. This implies that it is e...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 59; no. 6; pp. 4006 - 4012
Main Authors Tian, Tian, Qi, Wen-Feng
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.06.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Applied sciences
Boolean functions
Ciphers
Cryptography
Exact sciences and technology
Families of NFSR sequences
Generators
Information theory
Information, signal and communications theory
irreducibility
Linear feedback shift registers
Mathematical analysis
nonlinear feedback shift registers
Periodic structures
Polynomials
Signal and communications theory
stream ciphers
Telecommunications and information theory
Shift register
Private key
Stream ciphering
Security of data
Families of NFSR sequences
Feedback regulation
irreducibility
nonlinear feedback shift registers
stream ciphers
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Summary:Let n be a positive integer. An NFSR of n stages is called irreducible if the family of output sequences of any NFSR of stages less than n is not included in that of the NFSR. In this paper, we prove that the density of the irreducible NFSRs of n stages is larger than 0.39. This implies that it is expected to find an irreducible NFSR of n stages among three randomly chosen NFSRs of n stages.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2247093