Related papers: A Note on "On the Construction of Boolean Function…
Algebraic immunity of Boolean function $f$ is defined as the minimal degree of a nonzero $g$ such that $fg=0$ or $(f+1)g=0$. Given a positive even integer $n$, it is found that the weight distribution of any $n$-variable symmetric Boolean…
We describe several families of efficiently implementable Boolean functions achieving provable trade-offs between resiliency, nonlinearity, and algebraic immunity. In particular, the following statement holds for each of the function…
Algebraic immunity has been proposed as an important property of Boolean functions. To resist algebraic attack, a Boolean function should possess high algebraic immunity. It is well known now that the algebraic immunity of an $n$-variable…
To resist algebraic attack, a Boolean function should possess good algebraic immunity (AI). Several papers constructed symmetric functions with the maximum algebraic immunity $\lceil \frac{n}{2}\rceil $. In this correspondence we prove that…
We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\leq 20$, we show that there are functions…
From the motivation of algebraic attacks to stream and block ciphers([1,2,7,13,14,15]), the concept of {\em algebraic immunity} (AI) was introduced in [21] and studied in [3,5,10,11,17,18,19,20,21]. High algebraic immunity is a necessary…
In this paper, we explicitly construct a large class of symmetric Boolean functions on $2k$ variables with algebraic immunity not less than $d$, where integer $k$ is given arbitrarily and $d$ is a given suffix of $k$ in binary…
Constructing $2m$-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field $\mathbb{F}_{2^{2m}}$ seems to be a promising approach since Tu and Deng's work. In this paper, we…
In this correspondence, an equivalent definition of algebraic immunity of Boolean functions is posed, which can clear up the confusion caused by the proof of optimal algebraic immunity of the Carlet-Feng function and some other functions…
Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing binary minimal codes from sets, Boolean functions and vectorial Boolean…
This paper provides a serious attempt towards constructing a switching-algebraic theory for weighted monotone voting systems, whether they are scalar-weighted or vector-weighted. The paper concentrates on the computation of a prominent…
We propose a general approach to construct cryptographic significant Boolean functions of $(r+1)m$ variables based on the additive decomposition $\mathbb{F}_{2^{rm}}\times\mathbb{F}_{2^m}$ of the finite field $\mathbb{F}_{2^{(r+1)m}}$,…
A Boolean function $f({\vec x})$ is sensitive to bit $x_i$ if there is at least one input vector $\vec x$ and one bit $x_i$ in $\vec x$, such that changing $x_i$ changes $f$. A function has sensitivity $s$ if among all input vectors, the…
We explore the switching-algebraic computation of the Banzhaf indices for general and monotone or unrestricted systems. This computation is achieved via (a) two Boolean-quotient formulas that are valid when the voting system is not…
This paper employs switching-algebraic techniques for the calculation of a fundamental index of voting powers, namely, the total Banzhaf power. This calculation involves two distinct operations: (a) Boolean differencing or differentiation,…
We show a partial Boolean function $f$ together with an input $x\in f^{-1}\left(*\right)$ such that both $C_{\bar{0}}\left(f,x\right)$ and $C_{\bar{1}}\left(f,x\right)$ are at least $C\left(f\right)^{2-o\left(1\right)}$. Due to recent…
Suppose that $Y^n$ is obtained by observing a uniform Bernoulli random vector $X^n$ through a binary symmetric channel with crossover probability $\alpha$. The "most informative Boolean function" conjecture postulates that the maximal…
$\newcommand{\sp}{\mathsf{sparsity}}\newcommand{\s}{\mathsf{s}}\newcommand{\al}{\mathsf{alt}}$ The well-known Sensitivity Conjecture states that for any Boolean function $f$, block sensitivity of $f$ is at most polynomial in sensitivity of…
$\newcommand{\F}{\mathbb{F}}$We study the Boolean function parameters sensitivity ($s$), block sensitivity ($bs$), and alternation ($alt$) under specially designed affine transforms. For a function $f:\F_2^n\to \{0,1\}$, and $A=Mx+b$ for $M…
We pursue a systematic study of the following problem. Let f:{0,1}^n -> {0,1} be a (usually monotone) Boolean function whose behaviour is well understood when the input bits are identically independently distributed. What can be said about…