Related papers: On Another Two Cryptographic Identities In Univers…
Two signed graphs are called switching isomorphic if one of them is isomorphic to a switching equivalent of the other. To determine the number of switching non-isomorphic signed graphs on a specific graph, we will establish a method based…
It is classically known that generic smooth maps of R^2 into R^3 admit only cross cap singularities. This suggests that the class of cross caps might be an important object in differential geometry. We show that the standard cross cap…
We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.
We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular. We give theoretical and experimental results on the spectral and statistical properties…
Osburn and Schneider derived several combinatorial identities involving harmonic numbers using the computer programm Sigma. Here, they are derived by partial fraction decomposition and creative telescoping.
Authentication is a process by which an entity,which could be a person or intended computer,establishes its identity to another entity.In private and public computer networks including the Internet,authentication is commonly done through…
We derive several identities for arbitrary homogeneous second order recurrence sequences with constant coefficients. The results are then applied to present a unified study of six well known integer sequences, namely the Fibonacci sequence,…
Metaverse in general holds a potential future for cyberspace. At the beginning of Web 2.0, it was witnessed that people were signing in with various pseudonyms or 'nyms', risking their online identities by increasing presence of fake…
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…
There are quantum circuit identities that simplify quantum circuits, reducing the effort needed physically to implement them. This paper constructs all identities made from 3 or fewer operations taken from a common set of one qubit…
We derive a "switching identity" that can be stated for critical Brownian loop-soups or for the Gaussian free field on a cable graph: It basically says that at the level of cluster configurations and at the more general level of the…
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…
It is well known that in every inverse semigroup the binary operation and the unary operation of inversion satisfy the following three identities: [\quad x=(xx')x \qquad \quad (xx')(y'y)=(y'y)(xx') \qquad \quad (xy)z=x(yz"). ] The goal of…
In this work, we study the secure index coding problem where there are security constraints on both legitimate receivers and eavesdroppers. We develop two performance bounds (i.e., converse results) on the symmetric secure capacity. The…
Short Weierstrass's elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problems was widely used in Cryptographic applications. This paper introduces a new security notation 'trusted security' for computation methods of…
This paper summarizes basic properties of PPTs and shows that each PPT belongs to one of six different classes. Mapping an ordered sequence of PPTs into a corresponding sequence of these six classes makes it possible to use them in…
The excessiveness of integration-by-part (IBP) identities is discussed. The Lie-algebraic structure of the IBP identities is used to reduce the number of the IBP equations to be considered. It is shown that Lorentz-invariance (LI)…
We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…
Given a real representation of the Clifford algebra corresponding to $R^{p+q}$ with metric of signature $(p,q)$, we demonstrate the existence of two natural bilinear forms on the space of spinors. With the Clifford action of $k$-forms on…
Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity…