Related papers: Generating S-Boxes from Semi-fields Pseudo-extensi…
This note reports on the number of s-partitions of a natural number n. In an s-partition each cell has the form $2^k-1$ for some integer k. Such partitions have potential applications in cryptography, specifically in distributed…
Civino et al. (2019) have shown how some diffusion layers can expose a Substitution-Permutation Network to vulnerability from differential cryptanalysis when employing alternative operations coming from groups isomorphic to the translation…
In a topological quantum computer, universality is achieved by braiding and quantum information is natively protected from small local errors. We address the problem of compiling single-qubit quantum operations into braid representations…
The paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. As the starting point of our programme, we construct Frobenius maps on black box groups of untwisted Lie type in odd…
A Sidon set $S$ in $\mathbb{F}_2^n$ is a set such that $x+y=z+w$ has no solutions $x,y,z,w \in S$ with $x,y,z,w$ all distinct. In this paper, we prove various results on Sidon sets by using or generalizing known cryptographic results. In…
In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to…
In this paper, we identify many important properties and develop criteria for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of subquasigroup of…
Algebraic Branching Programs(ABPs) are standard models for computing polynomials. Syntactic multilinear ABPs (smABPs) are restrictions of ABPs where every variable is allowed to occur at most once in every path from the start to the…
This paper explores semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NPPP-Complete. We then show that existing qualitative relations in…
We provide a new property, called Non-Type-Preserving, for a mixing layer which guarantees protection against algebraic attacks based on the imprimitivity of the group generated by the round functions. Our main result is to present…
Internet of Things is an ecosystem of interconnected devices that are accessible through the internet. The recent research focuses on adding more smartness and intelligence to these edge devices. This makes them susceptible to various kinds…
We describe a general purpose Mathematica package for computing Superfield Operator Product Expansions in meromorphic $N=2$ superconformal field theory. Given the SOPEs for a set of ``basic" superfields, SOPEs of arbitrarily complicated…
We investigate properties of equivalence classes in AES which arise naturally from properties of MixColumns and InvMixColumns. These two operations have the property that the XOR of the 4 input bytes equals the XOR of 4 output bytes. We…
Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing binary minimal codes from sets, Boolean functions and vectorial Boolean…
Asymmetric quantum error-correcting codes (AQCs) may offer some advantage over their symmetric counterparts by providing better error-correction for the more frequent error types. The well-known CSS construction of $q$-ary AQCs is extended…
Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle…
In this article we describe the Java library that we have recently constructed to automatize the S-expansion method, a powerful mathematical technique allowing to relate different Lie algebras. An important input in this procedure is the…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
Chaos and its applications in the field of secure communications have attracted a lot of attention. Chaos-based pseudo-random number generators are critical to guarantee security over open networks as the Internet. We have previously…
In poly alphabetic substitution the plain texts letters are enciphered differently according to their position. The name poly alphabetic suggests that there are more than one key so we have used two keys combination instead of just one, in…