Related papers: Rotation Symmetric Bent Boolean Functions for n = …

Starting from a consistency requirement between T-duality symmetry and renormalization group flows, the two-loop metric beta function is found for a d=2 bosonic sigma model on a generic, torsionless background. The result is obtained…

It is disproved the Tokareva's conjecture that any balanced boolean function of appropriate degree is a derivative of some bent function. This result is based on new upper bounds for the numbers of bent and plateaued functions.

The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high…

Dillon-like Boolean functions are known, in the literature, to be those trace polynomial functions from $\mathbb{F}_{2^{2n}}$ to $\mathbb{F}_{2}$, with all the exponents being multiples of $2^n-1$ often called Dillon-like exponents. This…

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…

Let $\mathcal{F}_{n}^*$ be the set of Boolean functions depending on all $n$ variables. We prove that for any $f\in \mathcal{F}_{n}^*$, $f|_{x_i=0}$ or $f|_{x_i=1}$ depends on the remaining $n-1$ variables, for some variable $x_i$. This…

The Bregman distance is a central tool in convex optimization, particularly in first-order gradient descent and proximal-based algorithms. Such methods enable optimization of functions without Lipschitz continuous gradients by leveraging…

We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…

The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N=1 supersymmetric version of the classical…

Boolean functions with good cryptographic properties like high nonlinearity and algebraic degree play an important in the security of stream and block ciphers. Such functions may be designed, for instance, by algebraic constructions or…

Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…

We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if…

A Boolean function $f$ on $n$ variables is said to be a bent function if the absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on…

N=2 superconformal many-body quantum mechanics in arbitrary dimensions is governed by a single scalar prepotential which determines the bosonic potential and the boson-fermion couplings. We present a special class of such models, for which…

Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs since their duals are also…

Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant…

Depending on the parity of $n$ and the regularity of a bent function $f$ from $\mathbb F_p^n$ to $\mathbb F_p$, $f$ can be affine on a subspace of dimension at most $n/2$, $(n-1)/2$ or $n/2- 1$. We point out that many $p$-ary bent functions…

The r-th order nonlinearity of a Boolean function is the minimum number of elements that have to be changed in its truth table to arrive at a Boolean function of degree at most r. It is shown that the (suitably normalised) r-th order…

A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…

We present necessary and sufficient conditions for a Boolean function to be a negabent function for both even and odd number of variables, which demonstrate the relationship between negabent functions and bent functions. By using these…