相关论文: Further Results of the Cryptographic Properties on…
In this paper, we present infinite families of permutations of $\mathbb{F}_{2^{2n}}$ with high nonlinearity and boomerang uniformity $4$ from generalized butterfly structures. Both open and closed butterfly structures are considered. It…
As a generalization of Dillon's APN permutation, butterfly structure and generalizations have been of great interest since they generate permutations with the best known differential and nonlinear properties over the field of size…
This paper is concerned with the fast computation of Fourier integral operators of the general form $\int_{\R^d} e^{2\pi\i \Phi(x,k)} f(k) d k$, where $k$ is a frequency variable, $\Phi(x,k)$ is a phase function obeying a standard…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…
Butterfly algorithms are an effective multilevel technique to compress discretizations of integral operators with highly oscillatory kernel functions. The particular version of the butterfly algorithm considered here realizes the transfer…
This paper explains the recent developments in security and encryption. The Butterfly cipher and quantum cryptography are reviewed and compared. Examples of their relative uses are discussed and suggestions for future developments…
Based on the author's previous work on the Jacobi identity for twisted relative vertex operator algebras and modules and on the generating function identities for affine Lie algebras, we interpret the second difference sequence of the…
We study natural evaluation and interpolation problems for elliptic functions and prove that they allow a recursive treatment using a variant of classical butterflies first introduced by Gauss. We deduce the existence of straight-line…
A cryptarithm (or alphametic) is a mathematical puzzle in which numbers are represented with words in such a way that identical letters stand for equal digits and distinct letters for unequal digits. An alphametic puzzle is usually given in…
Cohesive subgraph mining in bipartite graphs becomes a popular research topic recently. An important structure k-bitruss is the maximal cohesive subgraph where each edge is contained in at least k butterflies (i.e., (2, 2)-bicliques). In…
Bipartite graphs characterize relationships between two different sets of entities, like actor-movie, user-item, and author-paper. The butterfly, a 4-vertices 4-edges (2,2)-biclique, is the simplest cohesive motif in a bipartite graph and…
With the idea of an eventual classification of 3-bridge links,\ we define a very nice class of 3-balls (called butterflies) with faces identified by pairs, such that the identification space is $S^{3},$ and the image of a prefered set of…
Plotting spectra of a range of almost Mathieu operators reveals a beautiful fractal-like image that contains multiple copies of a butterfly image. We demonstrate that plotting the butterflies using a gap-labelling scheme based on K-theory…
This study reports on an implementation of cryptographic pairings in a general purpose computer algebra system. For security levels equivalent to the different AES flavours, we exhibit suitable curves in parametric families and show that…
We construct cryptographic trilinear maps that involve simple, non-ordinary abelian varieties over finite fields. In addition to the discrete logarithm problems on the abelian varieties, the cryptographic strength of the trilinear maps is…
We consider the problem of counting motifs in bipartite affiliation networks, such as author-paper, user-product, and actor-movie relations. We focus on counting the number of occurrences of a "butterfly", a complete $2 \times 2$ biclique,…
S-boxes are an important primitive that help cryptographic algorithms to be resilient against various attacks. The resilience against specific attacks can be connected with a certain property of an S-box, and the better the property value,…
Bipartite graphs are ubiquitous in many domains, e.g., e-commerce platforms, social networks, and academia, by modeling interactions between distinct entity sets. Within these graphs, the butterfly motif, a complete 2*2 biclique, represents…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
In this paper, we investigate the butterfly factorization problem, i.e., the problem of approximating a matrix by a product of sparse and structured factors. We propose a new formal mathematical description of such factors, that encompasses…