相关论文: A new APN function which is not equivalent to a po…
In this paper, we show that there is no vectorial Boolean function of degree 4e, with e satisfaying certain conditions, which is APN over infinitely many extensions of its field of definition. It is a new step in the proof of the conjecture…
The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out…
APN functions play a fundamental role in cryptography against attacks on block ciphers. Several families of quadratic APN functions have been proposed in the recent years, whose construction relies on the existence of specific families of…
The approximation power of general feedforward neural networks with piecewise linear activation functions is investigated. First, lower bounds on the size of a network are established in terms of the approximation error and network depth…
The Feistel Boomerang Connectivity Table and the related notion of $F$-Boomerang uniformity (also known as the second-order zero differential uniformity) has been recently introduced by Boukerrou et al.~\cite{Bouk}. These tools shall…
We prove a necessary condition for some polynomials of Kasami degree to be APN over F_{q^n} for large n.
We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal…
Filters are key devices in optical systems and are usually applied to signal suppression or selection based on their amplitude frequency responses. Different from amplitude filtering, an all-pass filter (APF) is a unique type of filter that…
In this paper we present a new class of perfect nonlinear %Dembowski-Ostrom polynomials over $\mathbb{F}_{p^{2k}}$ for any odd prime $p$. In addition, we show that the new perfect nonlinear functions are CCZ-inequivalent to all the…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
Let $F$ be a function from $\mathbb{F}_{p^n}$ to itself and $\delta$ a positive integer. $F$ is called zero-difference $\delta$-balanced if the equation $F(x+a)-F(x)=0$ has exactly $\delta$ solutions for all non-zero $a\in\mathbb{F}_{p^n}$.…
Let $n$ be an even number such that $n\equiv 0 \pmod{4}$. We show that a power function $x^d$, with $d=2^{\frac{n+2}{2}}+2^{\frac{n-2}{2}}-1$, on $\mathbb{F}_{2^n}$ is an APN function of degree $n/2$ which is CCZ-equivalent to Kasami…
APN permutations in even dimension are vectorial Boolean functions that play a special role in the design of block ciphers. We study their properties, providing some general results and some applications to the low-dimension cases. In…
We construct a new partial geometry with parameters pg(5,5,2), not isomorphic to the partial geometry of van Lint and Schrijver.
A new type of an integrable mapping is presented. This map is equipped with fractional difference and possesses an exact solution, which can be regarded as a discrete analogue of the Mittag-Leffler function.
A novel algorithm for producing smooth nonlinearities on digital hardware is presented. The non-linearities are inherently quadratic and have both symmetrical and asymmetrical variants. The integer (and fixed point) implementation is highly…
In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert…
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…
Recently, a new concept called multiplicative differential was introduced by Ellingsen et al. Inspired by this pioneering work, power functions with low c-differential uniformity were constructed. Wang et al. defined the c-differential…
Boolean functions with good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the recent FLIP stream cipher. In this paper, we propose a large class of weightwise perfectly…