On pseudorandom subsets in finite fields I: measure of pseudorandomness and support of Boolean functions

2021 ◽  
Author(s):  
Huaning Liu ◽  
Xiaolin Chen
Keyword(s):  
Finite Fields ◽  
Boolean Functions

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.

scholarly journals Pairs of Quadratic Forms over Finite Fields

10.37236/4072 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Alexander Pott ◽  
Kai-Uwe Schmidt ◽  
Yue Zhou
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Boolean Functions ◽  
Quadratic Forms ◽  
Symmetric Matrices ◽  
Explicit Expressions

Let $\mathbb{F}_q$ be a finite field with $q$ elements and let $X$ be a set of matrices over $\mathbb{F}_q$. The main results of this paper are explicit expressions for the number of pairs $(A,B)$ of matrices in $X$ such that $A$ has rank $r$, $B$ has rank $s$, and $A+B$ has rank $k$ in the cases that (i) $X$ is the set of alternating matrices over $\mathbb{F}_q$ and (ii) $X$ is the set of symmetric matrices over $\mathbb{F}_q$ for odd $q$. Our motivation to study these sets comes from their relationships to quadratic forms. As one application, we obtain the number of quadratic Boolean functions that are simultaneously bent and negabent, which solves a problem due to Parker and Pott.

scholarly journals Laced Boolean functions and subset sum problems in finite fields

2011 ◽  
Vol 159 (11) ◽  
pp. 1059-1069 ◽  
Author(s):  
David Canright ◽  
Sugata Gangopadhyay ◽  
Subhamoy Maitra ◽  
Pantelimon Stănică
Keyword(s):  
Finite Fields ◽  
Boolean Functions ◽  
Subset Sum ◽  
Subset Sum Problems

scholarly journals Bent and bent 4 spectra of Boolean functions over finite fields

2017 ◽  
Vol 46 ◽  
pp. 163-178 ◽  
Author(s):  
Nurdagül Anbar ◽  
Wilfried Meidl
Keyword(s):  
Finite Fields ◽  
Boolean Functions
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