arXiv subjects

Anwar Irmatov

Publications and source records attributed to Anwar Irmatov.

4 recordsLinked to original sources

arXiv2026

On a necessary condition for the matching cryptosystem stability

The article contains a description of a possible attack on a matching cryptosystem and a defense with limited noise. A public key of a matching cryposystem consists of a graph and a weight vector-function on the edges of the graph with values from a finite field, where a private key contains another weight function, for which the corresponding alternating weighted path problem can be solved in polynomial time. There is a specific family of these secret weight functions that is considered in this article, for which some of the coordinates of its vector values are described as limited noise. We suggest a necessary condition for the matching cryptosystem stability in terms of dimensions of spans of weight vectors that correspond to specific sets of edges of the graph from the public key.

cs.CR↗

arXiv2024

On the matching arrangement of a graph, improper weight function problem and its application

This article presents examples of an application of the finite field method for the computation of the characteristic polynomial of the matching arrangement of a graph. Weight functions on edges of a graph with weights from a finite field are divided into proper and improper functions in connection with proper colorings of vertices of the matching polytope of a graph. An improper weight function problem is introduced, a proof of its NP-completeness is presented, and a knapsack-like public key cryptosystem is constructed based on the improper weight function problem.

math.CO↗

arXiv2018

A Lower Bound of the Number of Threshold Functions in Terms of Combinatorial Flags on the Boolean Cube

Let $ E=\{ (1, b_1, \ldots , b_n)\in R^{n+1} \mid \; b_i= \pm 1 ,\; i=1, \ldots, n \}$, $E^{\times n}_{\ne 0} := \{ W=(w_{i_1}, \ldots , w_{i_n}) \mid w_{i_k}\in E, \, k=1, \ldots, n, \, dim \, span(w_{i_1}, \ldots , w_{i_n}) = n \},$ and $q^W_l := |span(w_{i_{n-l+1}}, \ldots , w_{i_n}) \cap E|.$ Then for any weights $p=(p_1, \ldots, p_{2^n})$, $p_i\in R$, $\sum_{i=1}^{2^n}{p_i} =1$ we have for the number of threshold functions $P(2,n)$ the following lower bound $$P(2, n) \geq 2\sum_{W\in E^{\times n}_{\ne 0}}{\frac{1- p_{i_1} -p_{i_2} - \cdots - p_{i_{q_n^W}}}{q_n^W\cdot q_{n-1}^W\cdots q_1^W}},$$ and the right side of the inequality doesn't depend on the choice of $p$. Here the indices used in the numerator correspond to vectors from $span(w_{i_1}, \ldots , w_{i_n})\cap E = \left\{w_{i_1}, \ldots, w_{i_n}, \ldots w_{i_{q_n^W}}\right\}$.

math.CO↗

arXiv2018

Application of the Ranking Relative Principal Component Attributes Network Model (REL-PCANet) for the Inclusive Development Index Estimation

In 2018, at the World Economic Forum in Davos it was presented a new countries' economic performance metric named the Inclusive Development Index (IDI) composed of 12 indicators. The new metric implies that countries might need to realize structural reforms for improving both economic expansion and social inclusion performance. That is why, it is vital for the IDI calculation method to have strong statistical and mathematical basis, so that results are accurate and transparent for public purposes. In the current work, we propose a novel approach for the IDI estimation - the Ranking Relative Principal Component Attributes Network Model (REL-PCANet). The model is based on RELARM and RankNet principles and combines elements of PCA, techniques applied in image recognition and learning to rank mechanisms. Also, we define a new approach for estimation of target probabilities matrix to reflect dynamic changes in countries' inclusive development. Empirical study proved that REL-PCANet ensures reliable and robust scores and rankings, thus is recommended for practical implementation.

cs.CE↗