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This paper introduced the concept of soft quasigroup, its parastrophes, soft nuclei, left (right) coset, distributive soft quasigroups and normal soft quasigroups. Necessary and sufficient conditions for a soft set over a quasigroup (loop)…
As quantum computing matures into a practical paradigm, the need for secure and private quantum computation on untrusted hardware becomes increasingly urgent. While classical fully homomorphic encryption has enabled computation over…
Large language models (LLMs) are increasingly used to assist developers with code, yet their implementations of cryptographic functionality often contain exploitable flaws. Minor design choices (e.g., static initialization vectors or…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
The CMOS integrated chips at advanced technology nodes are becoming more vulnerable to various sources of faults like manufacturing imprecisions, variations, aging, etc. Additionally, the intentional fault attacks (e.g., high power…
In 2022, Persianom, Phan and Yung outlined the creation of Anamorphic Cryptography. With this, we can create a public key to encrypt data, and then have two secret keys. These secret keys are used to decrypt the cipher into different…
The piggy bank idea allows one-way encryption of information that can be accessed only by authorized parties. Here we show how the piggy bank idea can be used to authenticate parties to counter man-in-the-middle (MIM) attack that can…
In this paper we investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which admit a compact semigroup topology and describe graph…
In this paper we model a class of stream and block ciphers as systems of (ordinary) explicit difference equations over a finite field. We call this class "difference ciphers" and we show that ciphers of application interest, as for example…
The architecture scalability afforded by recent proposals of a large scale photonic based quantum computer, utilizing the theoretical developments of topological cluster states and the photonic chip, allows us to move on to a discussion of…
A partial automorphism of a semigroup $S$ is any isomorphism between its subsemigroups, and the set all partial automorphisms of $S$ with respect to composition is the inverse monoid called the partial automorphism monoid of $S$. Two…
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
Let $G$ be a finite group and $H$ a subgroup of $G$. Each left transversal (with identity) of $H$ in $G$ has a left loop (left quasigroup with identity) structure induced by the binary operation of $G$. We say two left transversals are…
For a complex or real algebraic group G, with g:=Lie(G), quantizations of global type are suitable Hopf algebras F_q[G] or U_q(g) over C[q,q^{-1}]. Any such quantization yields a structure of Poisson group on G, and one of Lie bialgebra on…
We apply the abelianization technique to obtain an explicit ring presentation for the quasimap quantum cohomology of GIT quotients. As an application, for quiver varieties associated with oriented-acyclic quivers, we establish a cluster…
Drinfeld showed that any finite dimensional Hopf algebra \G extends to a quasitriangular Hopf algebra \D(\G), the quantum double of \G. Based on the construction of a so--called diagonal crossed product developed by the authors, we…
It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…
A \emph{mixed dihedral group} is a group $H$ with two disjoint subgroups $X$ and $Y$, each elementary abelian of order $2^n$, such that $H$ is generated by $X\cup Y$, and $H/H'\cong X\times Y$. In this paper we give a sufficient condition…
The double quantum groups are the Hopf algebras underlying the complex quantum groups of which the simplest example is the quantum Lorentz group. They are non- standard quantizations of the double group $G \times G$. We construct a…
A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the…