In this paper, several new classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent functions.Numerical results show that the proposed class contains cubic bent functions that are affinely inequivalent to all known quadratic ones. Meanwhile, we determine the distribution of the Walsh spectrum of five-valued functions constructed in this paper.
Generic constructions of 5-valued spectra Boolean functions
Whereas the design and properties of bent and plateaued functions have been frequently addressed during the past few decades, there are only a few design methods of so-called 5-valued spectra Boolean functions whose Walsh spectra takes the values in $\{0, \pm 2^{λ_1}, \pm 2^{λ_2}\}$ . Moreover, these design methods mainly regards the specification of these functions in their ANF (algebraic normal form ) domain. In this article, we give a precise characterization of this class of functions in their spectral domain using the concept of a dual of plateaued functions. Both necessary and sufficient…
Designing plateaued Boolean functions in spectral domain and their classification
The design of plateaued functions over $GF(2)^n$ , also known as 3-valued Walsh spectra functions (taking the values from the set $\{0, \pm 2^{\lceil \frac{n+s}{2} \rceil}\}$ ), has been commonly approached by specifying a suitable algebraic normal form which then induces this particular Walsh spectral characterization. In this article, we consider the reversed design method which specifies these functions in the spectral domain by specifying a suitable allocation of the nonzero spectral values and their signs. We analyze the properties of trivial and nontrivial plateaued functions (as affine …
Some New Constructions of Generalized Plateaued Functions
Plateaued functions as an extension of bent functions play a significant role in cryptography, coding theory, sequences and combinatorics. In \cite{Mesnager9} , Mesnager \emph{et al.} introduced generalized plateaued functions in order to study plateaued functions in the general context of generalized $p$ -ary functions. In this paper, we focus on the constructions of generalized $p$ -ary $s$ -plateaued functions from $V_{n}$ to $\mathbb{Z}_{p^k}$ , where $V_{n}$ is an $n$ -dimensional vector space over $\mathbb{F}_{p}$ , $p$ is a prime, $k\geq 1$ and $n+s$ is even when $p=2$ . In particular, …
The Maximum Nonlinearity of 8-variable Balanced Boolean Functions is 116
School of Computer and Electronic Information/School of Artificial Intelligence, Nanjing Normal University（南京师范大学计算机与电子信息学院/人工智能学院）；China Telecom Corporation Limited, Huaibei Branch（中国电信股份有限公司淮北分公司）
On the Differential Linear Connectivity Table of Vectorial Boolean Functions
Vectorial Boolean functions are crucial building blocks in symmetric ciphers. Different known attacks on block ciphers have resulted in diverse cryptographic criteria of vectorial Boolean functions,such as differential distribution table and nonlinearity. Very recently, Bar-On et al. introduced at Eurocrypt'19 a new tool, called the Differential-Linear Connectivity Table (DLCT).This paper is a follow-up work, which presents further theoretical characterization of the DLCT of vectorial Boolean functions and also investigates this new criterion of functions with certain forms. In this paper we i…
On the Differential-Linear Connectivity Table of Vectorial Boolean Functions
Vectorial Boolean functions are crucial building-blocks in symmetric ciphers. Different known attacks on block ciphers have resulted in diverse cryptographic criteria for vectorial Boolean functions, such as differential uniformity and nonlinearity. Very recently, Bar-On et al. introduced at Eurocrypt'19 a new tool, called the differential-linear connectivity table (DLCT), which allows for taking into account the dependency between the two subciphers $E_0$ and $E_1$ involved in differential-linear attacks. This new notion leads to significant improvements of differential-linear attacks on seve…
