Constructions of bent functions on the minimal distance from the quadratic bent function

2011 ◽  
Author(s):  
Nikolay Kolomeec
Keyword(s):  
Bent Function ◽  
Bent Functions ◽  
Minimal Distance

scholarly journals A Construction of Bent Functions of n+2 Variables from a Bent Function of n Variables and Its Cyclic Shifts

Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Joan-Josep Climent ◽  
Francisco J. García ◽  
Verónica Requena
Keyword(s):  
Bent Function ◽  
Bent Functions ◽  
Cyclic Shift ◽  
Cyclic Shifts

We present a method to iteratively construct new bent functions of n+2 variables from a bent function of n variables and its cyclic shift permutations using minterms of n variables and minterms of 2 variables. In addition, we provide the number of bent functions of n+2 variables that we can obtain by applying the method here presented, and finally we compare this method with a previous one introduced by us in 2008 and with the Rothaus and Maiorana-McFarland constructions.

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.

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.

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