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On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions
Author
Source
International Journal of Engineering Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-01
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Engineering Sciences and Information Technology
Civil Engineering
Abstract EN
The rth-order nonlinearity of Boolean function plays a central role against several known attacks on stream and block ciphers.
Because of the fact that its maximum equals the covering radius of the rth-order Reed-Muller code, it also plays an important role in coding theory.
The computation of exact value or high lower bound on the rth-order nonlinearity of a Boolean function is very complicated problem, especially when r>1.
This paper is concerned with the computation of the lower bounds for third-order nonlinearities of two classes of Boolean functions of the form Tr1nλxd for all x∈?2n, λ∈?2n*, where a d=2i+2j+2k+1, where i, j, and k are integers such that i>j>k≥1 and n>2i, and b d=23ℓ+22ℓ+2ℓ+1, where ℓ is a positive integer such that gcdℓ,?=1 and n>6.
American Psychological Association (APA)
Singh, Brajesh Kumar. 2014. On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions. International Journal of Engineering Mathematics،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-509658
Modern Language Association (MLA)
Singh, Brajesh Kumar. On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions. International Journal of Engineering Mathematics No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-509658
American Medical Association (AMA)
Singh, Brajesh Kumar. On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions. International Journal of Engineering Mathematics. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-509658
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-509658