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.

scholarly journals Estimation of Cyclic Shift with Delayed Correlation and Matched Filtering in Time Domain Cyclic-SLM for PAPR Reduction

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Panca Dewi Pamungkasari ◽  
Yukitoshi Sanada
Keyword(s):  
Time Domain ◽  
Side Information ◽  
Average Power ◽  
Matched Filtering ◽  
Cyclic Shift ◽  
Ofdm Systems ◽  
High Power Amplifier ◽  
Critical Issues ◽  
Cyclic Shifts ◽  
Selective Mapping

Time domain cyclic-selective mapping (TDC-SLM) reduces the peak-to-average power ratio (PAPR) in OFDM systems while the amounts of cyclic shifts are required to recover the transmitted signal in a receiver. One of the critical issues of the SLM scheme is sending the side information (SI) which reduces the throughputs in wireless OFDM systems. The proposed scheme implements delayed correlation and matched filtering (DC-MF) to estimate the amounts of the cyclic shifts in the receiver. In the proposed scheme, the DC-MF is placed after the frequency domain equalization (FDE) to improve the accuracy of cyclic shift estimation. The accuracy rate of the propose scheme reaches 100% at Eb/N0 = 5 dB and the bit error rate (BER) improves by 0.2 dB as compared with the conventional TDC-SLM. The BER performance of the proposed scheme is also better than that of the conventional TDC-SLM even though a nonlinear high power amplifier is assumed.

Calculating the number of solutions of a difference equation

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
Sergey D. Loshkarev
Keyword(s):  
Difference Equation ◽  
Boolean Function ◽  
Boolean Functions ◽  
Hash Function ◽  
Differential Cryptanalysis ◽  
Cyclic Shift ◽  
Number Of Solutions ◽  
Special Equation ◽  
Cyclic Shifts ◽  
The Impact

AbstractThe hash algorithms of the MDx family involve cyclic shifts, computation of primitive Boolean functions, and addition of constants. So far, very few works have been published in which the authors attempt to explain the impact that the choice of constants, shifts, and Boolean functions has on the cryptographic properties of the algorithms. G. A. Karpunin and H. T. Nguyen suggested a model in which the resistance against differential cryptanalysis may be quantitatively estimated in terms of the number of solutions of a special equation. In this work, in the framework of the aforementioned model, an equation for the MD5 hash function is derived. Examination of one Boolean function and one value of the cyclic shift through exhaustive search requires 2

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.

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>

Bent functions from a finite abelian group into a finite abelian group

2002 ◽  
Vol 12 (2) ◽  
Author(s):  
V.I. Solodovnikov
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Bent Function ◽  
Bent Functions ◽  
Primary Case ◽  
Minimal Function

AbstractWe introduce the notions of an absolutely non-homomorphic function, a minimal function (farthest from homomorphisms) and a bent function, and prove that the class of bent functions coincides with the class of absolutely non-homomorphic functions, a function is uniquely determined by the distances to homomorphisms with shifts, and that in the primary case the bent functions are absolutely minimal.

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