Parallel Programming Strategies for Computing Walsh Spectra of Boolean Functions

2020 ◽  
pp. 138-152
Author(s):  
Dushan Bikov ◽  
Maria Pashinska
Keyword(s):  
Parallel Programming ◽  
Boolean Functions ◽  
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 Cryptographically significant Boolean functions with five valued Walsh spectra

2002 ◽  
Vol 276 (1-2) ◽  
pp. 133-146 ◽  
Author(s):  
Subhamoy Maitra ◽  
Palash Sarkar
Keyword(s):  
Boolean Functions ◽  
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.

scholarly journals Boolean Functions with Multiple-Valued Walsh Spectra

2019 ◽  
Vol 28 (6) ◽  
pp. 1165-1169
Author(s):  
Tianfeng Sun ◽  
Bin Hu
Keyword(s):  
Boolean Functions ◽  
Walsh Spectra

Boolean functions with six-valued Walsh spectra and their application

2021 ◽  
Author(s):  
Wengang Jin ◽  
Xiaoni Du ◽  
Yanzhong Sun ◽  
Cuiling Fan
Keyword(s):  
Boolean Functions ◽  
Walsh Spectra

A class of Boolean functions with four-valued Walsh spectra

2009 ◽  
Author(s):  
Yonghong Xie ◽  
Lei Hu ◽  
Wenfeng Jiang ◽  
Xiangyong Zeng
Keyword(s):  
Boolean Functions ◽  
Walsh Spectra
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