Symmetry conditions of Boolean functions in complex Hadamard transform

1998 ◽  
Vol 34 (17) ◽  
pp. 1634 ◽  
Author(s):  
S. Rahardja ◽  
B.J. Falkowski
Keyword(s):  
Boolean Functions ◽  
Hadamard Transform

scholarly journals Metaheuristics in the Optimization of Cryptographic Boolean Functions

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1052 ◽  
Author(s):  
Isaac López-López ◽  
Guillermo Sosa-Gómez ◽  
Carlos Segura ◽  
Diego Oliva ◽  
Omar Rojas
Keyword(s):  
Boolean Functions ◽  
High Performance ◽  
Memetic Algorithm ◽  
Hadamard Transform ◽  
Gradual Change ◽  
Exploration And Exploitation ◽  
High Entropy ◽  
Lower Entropy ◽  
Optimization Mechanism ◽  
Proper Balance

Generating Boolean Functions (BFs) with high nonlinearity is a complex task that is usually addresses through algebraic constructions. Metaheuristics have also been applied extensively to this task. However, metaheuristics have not been able to attain so good results as the algebraic techniques. This paper proposes a novel diversity-aware metaheuristic that is able to excel. This proposal includes the design of a novel cost function that combines several information from the Walsh Hadamard Transform (WHT) and a replacement strategy that promotes a gradual change from exploration to exploitation as well as the formation of clusters of solutions with the aim of allowing intensification steps at each iteration. The combination of a high entropy in the population and a lower entropy inside clusters allows a proper balance between exploration and exploitation. This is the first memetic algorithm that is able to generate 10-variable BFs of similar quality than algebraic methods. Experimental results and comparisons provide evidence of the high performance of the proposed optimization mechanism for the generation of high quality BFs.

scholarly journals On the Walsh-Hadamard transform of monotone Boolean functions

2012 ◽  
Vol 5 (2) ◽  
pp. 19-35
Author(s):  
Charles Celerier ◽  
David Joyner ◽  
Caroline Melles ◽  
David Phillips
Keyword(s):  
Boolean Functions ◽  
Hadamard Transform ◽  
Monotone Boolean Functions ◽  
Walsh Hadamard Transform

scholarly journals On Negabent Functions and Nega-Hadamard Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Zepeng Zhuo ◽  
Jinfeng Chong
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Sum Of Squares ◽  
Hadamard Transform ◽  
Autocorrelation Coefficient ◽  
Equivalent Statement ◽  
Hadamard Transforms

The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called negabent function. In this paper, the special Boolean functions by concatenation are presented. We investigate their nega-Hadamard transforms, nega-autocorrelation coefficients, sum-of-squares indicators, and so on. We establish a new equivalent statement onf1∥f2which is negabent function. Based on them, the construction for generating the negabent functions by concatenation is given. Finally, the function expressed asf(Ax⊕a)⊕b·x⊕cis discussed. The nega-Hadamard transform and nega-autocorrelation coefficient of this function are derived. By applying these results, some properties are obtained.

CLASS OF BOOLEAN FUNCTIONS CONSTRUCTED USING SIGNIFICANT BITS OF LINEAR RECURRENCES OVER THE RING ℤ2n

2019 ◽  
Vol 6 (2) ◽  
pp. 90-94
Author(s):  
Hernandez Piloto Daniel Humberto
Keyword(s):  
Linear Function ◽  
Boolean Functions ◽  
Hamming Distance ◽  
Linear Recurrences ◽  
Maximum Period ◽  
Non Linear ◽  
The Given ◽  
Class Of Functions

In this work a class of functions is studied, which are built with the help of significant bits sequences on the ring ℤ2n. This class is built with use of a function ψ: ℤ2n → ℤ2. In public literature there are works in which ψ is a linear function. Here we will use a non-linear ψ function for this set. It is known that the period of a polynomial F in the ring ℤ2n is equal to T(mod 2)2α, where α∈ , n01- . The polynomials for which it is true that T(F) = T(F mod 2), in other words α = 0, are called marked polynomials. For our class we are going to use a polynomial with a maximum period as the characteristic polyomial. In the present work we show the bounds of the given class: non-linearity, the weight of the functions, the Hamming distance between functions. The Hamming distance between these functions and functions of other known classes is also given.

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