Related papers: Bilinear cryptography using finite $p$-groups of n…

The MOR cryptosystem is a natural generalization of the El-Gamal cryptosystem to non-abelian groups. Using a $p$-group, a cryptosystem was built by this author in 'A simple generalization of El-Gamal cryptosystem to non-abelian groups'. It…

Englisch: In this paper we study the paillier cryptosystem and derive form it to new schemes. First we transform the signature of paillier in a Blind signature. Secondly we propose a three-pass protocol wich use the homomorphic property…

In this paper, we consider a nonlinear beam equation with the p-biharmonic operator, where $1 < p < \infty$. Using a change of variable, we transform the problem into a system of differential equations and prove the existence, uniqueness…

Let $p$ be a prime number, $G$ be a finite $p$-group and $K$ be a field of characteristic $p$. The Modular Isomorphism Problem (MIP) asks whether the group algebra $KG$ determines the group $G$. Dealing with MIP, we investigated a question…

In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time…

Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…

We show that a special class of (nonconvex) NMPC problems admits an exact solution by reformulating them as a finite number of convex subproblems, extending previous results to the multi-input case. Our approach is applicable to a special…

We describe an algorithm for determining the algebraic subgroup of GL(n,C) that is defined as the closure of the group generated by a finite number of elements of GL(n,C). The algorithm avoids the use of Groebner bases and can be used on…

Cryptography protects users by providing functionality for the encryption of data and authentication of other users. This technology lets the receiver of an electronic message verify the sender, ensures that a message can be read only by…

In this article, we have proposed a generalized Lucas matrix (recursive matrix of higher order) having relation with generalized Fibonacci sequences and established many special properties in addition to that usual matrix algebra. Further,…

In a XOR-based alternating block cipher the plaintext is masked by a sequence of layers each performing distinct actions: a highly nonlinear permutation, a linear transformation, and the bitwise key addition. When assessing resistance…

The notion of inner linear Hopf algebra is a generalization of the notion of discrete linear group. In this paper, we prove two general results that enable us to enlarge the class of Hopf algebras that are known to be inner linear: the…

Modern advances in general-purpose computer algebra systems offer solutions to a variety of problems, which in the past required substantial time investments by trained mathematicians. An excellent example of such development are the…

Spiking Neural P systems are a class of membrane computing models inspired directly by biological neurons. Besides the theoretical progress made in this new computational model, there are also numerous applications of P systems in fields…

The orbits of the group B of upper-triangular matrices acting on 2-nilpotent complex matrices via conjugation are classified via oriented link patterns, generalizing A. Melnikov's classification of the B-orbits on upper-triangular such…

Two novel extended semi-discrete KP-type systems, namely partial differential-difference systems with one continuous and two discrete variables, are investigated. Introducing an arbitrary function into the Cauchy matrix function or the…

As a special type of factorization of finite groups, logarithmic signature (LS) is used as the main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST1, MST2 and MST3. An LS with…

Since 1870s, scientists have been taking deep insight into Lie groups and Lie algebras. With the development of Lie theory, Lie groups have got profound significance in many branches of mathematics and physics. In Lie theory, exponential…

We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…

Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a…