On the constructions of resilient Boolean functions with five-valued Walsh spectra and resilient semi-bent functions

2022 ◽  
Vol 309 ◽  
pp. 1-12
Author(s):  
Sihong Su ◽  
Bingxin Wang ◽  
Jingjing Li
Keyword(s):  
Boolean Functions ◽  
Bent Functions ◽  
Walsh Spectra

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.

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.

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.

Quantum algorithms for learning Walsh spectra of multi-output Boolean functions

2019 ◽  
Vol 18 (6) ◽  
Author(s):  
Jingyi Cui ◽  
Jiansheng Guo ◽  
Linhong Xu ◽  
Mingming Li
Keyword(s):  
Boolean Functions ◽  
Quantum Algorithms ◽  
Walsh Spectra

scholarly journals THE DEUTSCH–JOZSA ALGORITHM REVISITED IN THE DOMAIN OF CRYPTOGRAPHICALLY SIGNIFICANT BOOLEAN FUNCTIONS

2005 ◽  
Vol 03 (02) ◽  
pp. 359-370 ◽  
Author(s):  
SUBHAMOY MAITRA ◽  
PARTHA MUKHOPADHYAY
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Block Cipher ◽  
Quantum Algorithm ◽  
Building Blocks ◽  
Linear Functions ◽  
Constant Time ◽  
Exponential Time ◽  
Classical Algorithm ◽  
Walsh Spectra

Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems, one tries to find out linear functions that are correlated to the Boolean functions used in the crypto system. Let f be an n-variable Boolean function and its Walsh spectra is denoted by Wf(ω) at the point ω ∈ {0, 1}n. The Boolean function is available in the form of an oracle. We like to find a ω such that Wf(ω) ≠ 0 as this will provide one of the linear functions which are correlated to f. We show that the quantum algorithm proposed by Deutsch and Jozsa7 solves this problem in constant time. However, the best known classical algorithm to solve the problem requires exponential time in n. We also analyze certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch–Jozsa algorithm performs on them.

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