Related papers: Permutation rotation-symmetric S-boxes, liftings a…

We investigate shift-invariant transformations, also known as rotation-symmetric vectorial Boolean functions, on $n$ bits that are induced from Boolean functions on $k$ bits, for $k\leq n$. We consider such transformations that are not…

Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The…

Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…

Rotation symmetric Boolean functions have important applications in the design of cryptographic algorithms. In this paper, the Conjecture about rotation symmetric Boolean functions (RSBFs) of degree 3 proposed by Cusik and St\u{a}nic\u{a}…

Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…

Finding permutation polynomials with low differential and boomerang uniformityis an important topic in S-box designs of many block ciphers. For example, AES chooses the inverse function as its S-box, which is differentially 4-uniform and…

Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential…

We consider the action on $\mathbb{F}_2^n$ by cyclic permutations ($\mathbb{Z}/n\mathbb{Z}$). Two elements $x, y\in \mathbb{F}_2^n$ are in the same orbit if they are cyclic shifts of each other. Cryptographic properties of rotation…

Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well…

Let $(0, a_1, \ldots, a_{d-1})_n$ denote the function $f_n(x_0, x_1, \ldots, x_{n-1})$ of degree $d$ in $n$ variables generated by the monomial $x_0x_{a_1} \cdots x_{a_{d-1}}$ and having the property that $f_n$ is invariant under cyclic…

We address the correspondence-free alignment of two rotation sets on \(SO(3)\), a core task in calibration and registration that is often impeded by missing time alignment, outliers, and unknown axis conventions. Our key idea is to…

We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…

Let $f_n(x_0, x_1, \ldots, x_{n-1})$ denote the algebraic normal form (polynomial form) of a rotation symmetric (RS) Boolean function of degree $d$ in $n \geq d$ variables and let $wt(f_n)$ denote the Hamming weight of this function. Let…

Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…

Block ciphers use S-boxes to create confusion in the cryptosystems. Such S-boxes are functions over $\mathbb{F}_{2^{n}}$. These functions should have low differential uniformity, high nonlinearity, and high algebraic degree in order to…

The concept of rotation symmetric functions from the Boolean domain is extended to the multiple-valued (MV) domain. It is shown that symmetric functions are a subset of the rotation symmetric functions. Functions exhibiting these kinds of…

In 2006, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yucel.…

In Pasalic et al., IEEE Trans. Inform. Theory 69 (2023), 2702--2712, and in Anbar, Meidl, Cryptogr. Commun. 10 (2018), 235--249, two different vectorial negabent and vectorial bent-negabent concepts are introduced, which leads to seemingly…

The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is epsilon-far from having that property. The performance of the algorithm is judged by how many calls need to be made to…

We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…