Related papers: Differentially low uniform permutations from known…
We investigate the bi-Hamiltonian structures associated with constrained dispersionless modified KP hierarchies which are constructed from truncations of the Lax operator of the dispersionless modified KP hierarchy. After transforming their…
We introduce a new family of invariant differential operators associated with $\lambda$-cosine and Funk-Radon transforms on Stiefel and Grassmann manifolds. These operators reduce the order of the $\lambda$-cosine transforms and yield new…
Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradient estimates. Modern variance reduction techniques mostly consider categorical distributions and have…
For an elliptic, semilinear differential operator of the form $S(u) = A : D^2 u + b(x, u , Du)$, consider the functional $E_\infty(u) = \mathop{\mathrm{ess \, sup}}_\Omega |S(u)|$. We study minimisers of $E_\infty$ for prescribed boundary…
The article is devoted to different aspects of the question "What can be done with a matrix by low rank perturbation?" It is proved that one can change a geometrically simple spectrum drastically by a rank 1 permutation, but the situation…
This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions…
Commutative rings of one-dimensional difference operators of rank l>1 and their deformations are effectively constructed. Our analytical constructions are based on the so-called ''Tyurin parameters'' for the stable framed holomorphic vector…
Physical Unclonable Functions evaluate manufacturing variations to generate secure cryptographic keys for embedded systems without secure key storage. It is explained how methods from coding theory are applied in order to ensure reliable…
We study orbifolds by permutations of two identical N=2 minimal models within the Gepner construction of four dimensional heterotic strings. This is done using the new N=2 supersymmetric permutation orbifold building blocks we have recently…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
We consider a class of "box-like" statistically self-affine functions, and compute the almost-sure box-counting dimension of their graphs. Furthermore, we consider the differentiability of our functions, and prove that, depending on an…
In this paper, we propose a new design method of irregular spatially-coupled low-density parity-check (SC-LDPC) codes with non-uniform degree distributions by linear programming (LP). In general, irregular SC-LDPC codes with non-uniform…
We study the combinatorial equivalence of separable elements in types $A$ and $B$. A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}$ to the set of separable signed permutations in the…
The analysis of quantum algorithms which query random, invertible permutations has been a long-standing challenge in cryptography. Many techniques which apply to random oracles fail, or are not known to generalize to this setting. As a…
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…
The study of S-box properties relations is an interesting problem. In this work we develop and apply a local search method to create trajectories over S-box space. These trajectories shows the existence of an strong linear correlation…
We construct 8 x 8 bijective cryptographically strong S-boxes. Our construction is based on using non-bijective power functions over the finite filed.
The use of permutation polynomials has appeared, along to their compositional inverses, as a good choice in the implementation of cryptographic systems. Hence, there has been a demand for constructions of these polynomials which…
We provide two sufficient conditions to guarantee that the round functions of a translation based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and…
Substitution boxes with thorough cryptographic strengths are essential for the development of strong encryption systems. They are the only portions capable of inducing nonlinearity in symmetric encryption systems. Bijective substitution…