Research on Design and Construction Method of Bent Functions

2014 ◽  
Vol 571-572 ◽  
pp. 114-117
Author(s):  
Guang Xue Meng ◽  
Yan Guang Shen ◽  
Tao Jiang
Keyword(s):  
Projective Geometry ◽  
Boolean Functions ◽  
Construction Method ◽  
Bent Function ◽  
Bent Functions ◽  
C Language ◽  
Walsh Spectra ◽  
Algebra Method ◽  
Design And Construction

Bent function is a class of the highest nonlinear Boolean functions. In this paper three methods of design and construction are discussed with examples, which are algebra method, the character function in projective geometry and random researching method. Also, the Bent function of class is implemented with C language. At last, the concatenate construction from m = 2n-k Bent functions of k variables to a Bent function of n variables is given and verified with Walsh spectra.

scholarly journals Construction of an S-Box Based on Chaotic and Bent Functions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 671
Author(s):  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Chaos Theory ◽  
Boolean Functions ◽  
Security Analysis ◽  
Bent Function ◽  
Bent Functions ◽  
Encryption Algorithm ◽  
Symmetric Encryption ◽  
Differential Uniformity ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

An S-box is the most important part of a symmetric encryption algorithm. Various schemes are put forward by using chaos theory. In this paper, a construction method of S-boxes with good cryptographic properties is proposed. The output of an S-box can be regarded as a group of Boolean functions. Therefore, we can use the different properties of chaos and Bent functions to generate a random Bent function with a high nonlinearity. By constructing a set of Bent functions as the output of an S-box, we can create an S-box with good cryptological properties. The nonlinearity, differential uniformity, strict avalanche criterion and the independence criterion of output bits are then analyzed and tested. A security analysis shows that the proposed S-box has excellent cryptographic properties.

Several Classes of Boolean Functions with Four-Valued Walsh Spectra

2017 ◽  
Vol 28 (04) ◽  
pp. 357-377
Author(s):  
Zhiqiang Sun ◽  
Lei Hu
Keyword(s):  
Boolean Functions ◽  
Bent Functions ◽  
Plateaued Functions ◽  
Walsh Spectra

In this paper, we give constructions of several classes of Boolean functions with four-valued Walsh spectra, which are derived from the indirect sum construction. The Walsh spectra and spectrum distributions of these functions are determined. The result of functions with four-valued Walsh spectra derived from Bent functions is used to research Bent functions and o-polynomials. By investigating the indirect sum, we also give constructions of plateaued functions and functions with five-valued Walsh spectra.

On Walsh Spectrum of Cryptographic Boolean Function

2017 ◽  
Vol 67 (5) ◽  
pp. 536
Author(s):  
Shashi Kant Pandey ◽  
B. K. Dass
Keyword(s):  
Boolean Function ◽  
General Expression ◽  
Significant Role ◽  
Boolean Functions ◽  
Diophantine Equations ◽  
Bent Function ◽  
Bent Functions ◽  
Necessary Condition ◽  
Walsh Spectrum ◽  
Walsh Transformation

<p>Walsh transformation of a Boolean function ascertains a number of cryptographic properties of the Boolean function viz, non-linearity, bentness, regularity, correlation immunity and many more. The functions, for which the numerical value of Walsh spectrum is fixed, constitute a class of Boolean functions known as bent functions. Bent functions possess maximum possible non-linearity and therefore have a significant role in design of cryptographic systems. A number of generalisations of bent function in different domains have been proposed in the literature. General expression for Walsh transformation of generalised bent function (GBF) is derived. Using this condition, a set of Diophantine equations whose solvability is a necessary condition for the existence of GBF is also derived. Examples to demonstrate how these equations can be utilised to establish non-existence and regularity of GBFs is presented.</p>

Construction Technology of Shallow Pipe- Jacking Working Shaft

2011 ◽  
Vol 480-481 ◽  
pp. 1266-1270
Author(s):  
Liu Hui
Keyword(s):  
Side Wall ◽  
Soil Mass ◽  
Construction Method ◽  
Construction Technology ◽  
Reactive Force ◽  
Small Height ◽  
Key Points ◽  
Pipe Jacking ◽  
Design And Construction

During the pipe jacking construction, the bearing plates of jack need the support of great reactive force which is provided by the side-wall of the working shaft and the soil mass behind the wall. In the shallow pipe-jacking working shaft, the soil mass only can provide limited reactive force due to the small height of the soil mass behind the side-wall, which becomes the difficult point in the design and construction of the shallow pipe-jacking working shaft. This thesis takes the actual projects for the examples to introduce the construction technology of shallow pipe-jacking working shaft in details, including the construction key points like pre-grouting injection consolidation, ring beam construction method as well as reverse construction method.

scholarly journals Two Boolean Functions with Five-Valued Walsh Spectra and High Nonlinearity

2015 ◽  
Vol 26 (05) ◽  
pp. 537-556 ◽  
Author(s):  
Xiwang Cao ◽  
Lei Hu
Keyword(s):  
Finite Fields ◽  
Boolean Functions ◽  
Exponential Sums ◽  
New Method ◽  
High Nonlinearity ◽  
Walsh Spectra ◽  
And Diffusion ◽  
Confusion And Diffusion

For cryptographic systems the method of confusion and diffusion is used as a fundamental technique to achieve security. Confusion is reflected in nonlinearity of certain Boolean functions describing the cryptographic transformation. In this paper, we present two Boolean functions which have low Walsh spectra and high nonlinearity. In the proof of the nonlinearity, a new method for evaluating some exponential sums over finite fields is provided.

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