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The Research of the Properties of Normal Boolean Functions

Author: LiuZuo
Tutor: XiaoGuoZhen
School: Xi'an University of Electronic Science and Technology
Course: Cryptography
Keywords: Bent functions (Weakly) Normality (Weakly) Non-normality Algorithm
CLC: TN918.1
Type: Master's thesis
Year: 2010
Downloads: 51
Quote: 0
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Abstract


The Bent functions are those Boolean functions which satisfy the highest nonlinearity. So they are with very significant value of research. To be devoted to the construction of new Bent functions, Hans Dobbertin strengthened the interest for the study of the restrictions of Boolean functions on k-dimensional flats providing the concept of k-normality. The known classes of Bent functions, which are explicitly constructed, are normal functions. This leads to the main interest of normality concerning Bent functions:a Bent function which is non-normal does not belong to any known class of Bent functions. And then some researches about the properties and the construction of normal Boolean functions follow.With the basis of recent results of the authors from home and abroad on normality of Boolean functions, we introduce the concept, the properties, the function construction and the algorithm of checking normality systematically. In the paper, first, we make a summarization on the research situation and value of the normality. Second, we discuss some preliminaries, including the basis of Boolean functions, the cryptographic properties relating to the normality, and the Bent functions. Third, we state the research conditions of the non-normal Boolean functions. Last, we discuss the algorithm of checking normality, and improve the algorithm of checking Bent functions in [1].

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CLC: > Industrial Technology > Radio electronics, telecommunications technology > Communicate > Confidentiality of communications and communications security > Theory
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