79 research outputs found
The Framework for Simulation of Bioinspired Security Mechanisms against Network Infrastructure Attacks
The paper outlines a bioinspired approach named βnetwork nervous system" and methods of simulation of infrastructure attacks and protection mechanisms based on this approach. The protection mechanisms based on this approach consist of distributed prosedures of information collection and processing, which coordinate the activities of the main devices of a computer network, identify attacks, and determine nessesary countermeasures. Attacks and protection mechanisms are specified as structural models using a set-theoretic approach. An environment for simulation of protection mechanisms based on the biological metaphor is considered; the experiments demonstrating the effectiveness of the protection mechanisms are described
Agent-Based Modeling and Simulation of Network Infrastructure Cyber-Attacks and Cooperative Defense Mechanisms
Graphical & digital media application
Intrusion detection in unlabeled data with quarter-sphere Support Vector Machines
Practical application of data mining and machine learning techniques to
intrusion detection is often hindered by the difficulty to produce clean data for the
training. To address this problem a geometric framework for unsupervised anomaly
detection has been recently proposed. In this framework, the data is mapped into a
feature space, and anomalies are detected as the entries in sparsely populated regions.
In this contribution we propose a novel formulation of a one-class Support Vector
Machine (SVM) specially designed for typical IDS data features. The key idea of our
βquarter-sphereβ algorithm is to encompass the data with a hypersphere anchored at
the center of mass of the data in feature space. The proposed method and its behavior
on varying percentages of attacks in the data is evaluated on the KDDCup 1999 dataset
Attack graph based evaluation of network security.
Abstract. The perspective directions in evaluating network security are simulating possible malefactor's actions, building the representation of these actions as attack graphs (trees, nets), the subsequent checking of various properties of these graphs, and determining security metrics which can explain possible ways to increase security level. The paper suggests a new approach to security evaluation based on comprehensive simulation of malefactor's actions, construction of attack graphs and computation of different security metrics. The approach is intended for using both at design and exploitation stages of computer networks. The implemented software system is described, and the examples of experiments for analysis of network security level are considered
Enhancing intrusion detection through data perturbation augmentation strategy.
Intrusion data augmentation is an approach used to increase the size of the training data sample to improve the classification capabilities of machine-learning algorithms applied to intrusion detection. In this study, we introduced data perturbation by adding Gaussian noise to the minority class representing the intrusion scenarios. Employing the Divide-Sort, Augment, and Combined (SAC) technique, we performed oversampling on the minority class of two datasets used for training the model. Subsequently, we validated the model to achieve high overall accuracy indicating reliable intrusion detection. The performance of the model on the perturbed dataset was compared with that of the SMOTE and ROSE data augmentation methods. The results revealed that the perturbation of oversampled data exhibited superior and near perfect classification compared with the SMOTE and ROSE data augmentation techniques. The effectiveness of the proposed intrusion detection approach has been demonstrated on the BoT-IoT and smart grid imbalanced datasets, previously used for benchmarking
ΠΠ½ΡΠ΅Π»Π»Π΅ΠΊΡΡΠ°Π»ΡΠ½Π°Ρ ΡΠΈΡΡΠ΅ΠΌΠ° Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ ΡΠΈΡΡΠΎΠ²ΠΎΠ³ΠΎ ΡΠ΅ΡΠ΅Π²ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΠ΅Π½ΡΠ° Π΄Π»Ρ Π·Π°ΡΠΈΡΡ ΠΎΡ Π½Π΅ΠΆΠ΅Π»Π°ΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ
Π Π½Π°ΡΡΠΎΡΡΠ΅Π΅ Π²ΡΠ΅ΠΌΡ ΠΠ½ΡΠ΅ΡΠ½Π΅Ρ ΠΈ ΡΠΎΡΠΈΠ°Π»ΡΠ½ΡΠ΅ ΡΠ΅ΡΠΈ ΠΊΠ°ΠΊ ΡΡΠ΅Π΄Π° ΡΠ°ΡΠΏΡΠΎΡΡΡΠ°Π½Π΅Π½ΠΈΡ ΡΠΈΡΡΠΎΠ²ΠΎΠ³ΠΎ ΡΠ΅ΡΠ΅Π²ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΠ΅Π½ΡΠ° ΡΡΠ°Π½ΠΎΠ²ΡΡΡΡ ΠΎΠ΄Π½ΠΎΠΉ ΠΈΡ
Π²Π°ΠΆΠ½Π΅ΠΉΡΠΈΡ
ΡΠ³ΡΠΎΠ· ΠΏΠ΅ΡΡΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ, ΠΎΠ±ΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΠΈ Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ. ΠΠΎΠ·Π½ΠΈΠΊΠ°Π΅Ρ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡ Π·Π°ΡΠΈΡΡ Π»ΠΈΡΠ½ΠΎΡΡΠΈ, ΠΎΠ±ΡΠ΅ΡΡΠ²Π° ΠΈ Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π° ΠΎΡ Π½Π΅ΠΆΠ΅Π»Π°ΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ. Π Π½Π°ΡΡΠ½ΠΎ-ΠΌΠ΅ΡΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΎΠΌ ΠΏΠ»Π°Π½Π΅ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ° Π·Π°ΡΠΈΡΡ ΠΎΡ Π½Π΅ΠΆΠ΅Π»Π°ΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ ΠΈΠΌΠ΅Π΅Ρ ΠΊΡΠ°ΠΉΠ½Π΅ Π½Π΅Π±ΠΎΠ»ΡΡΠΎΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ. ΠΡΠΈΠΌ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΡΡΡ Π°ΠΊΡΡΠ°Π»ΡΠ½ΠΎΡΡΡ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π½ΡΡ
Π² ΡΡΠ°ΡΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ², Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΡΡ
Π½Π° ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΡ ΠΈΠ½ΡΠ΅Π»Π»Π΅ΠΊΡΡΠ°Π»ΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ ΡΠΈΡΡΠΎΠ²ΠΎΠ³ΠΎ ΡΠ΅ΡΠ΅Π²ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΠ΅Π½ΡΠ° Π΄Π»Ρ Π·Π°ΡΠΈΡΡ ΠΎΡ Π½Π΅ΠΆΠ΅Π»Π°ΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ. Π ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΡΠ°Π»ΡΠ½ΡΠ΅ ΠΎΡΠ½ΠΎΠ²Ρ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ ΡΠ°ΠΊΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ, ΡΠ°ΡΠΊΡΡΠ²Π°ΡΡΠΈΠ΅ ΡΠΎΠ΄Π΅ΡΠΆΠ°Π½ΠΈΠ΅ ΠΏΠΎΠ½ΡΡΠΈΡ Π½Π΅ΠΆΠ΅Π»Π°ΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ ΠΈ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡΠΈΠ΅ ΠΎΠ±ΡΡΡ Π°ΡΡ
ΠΈΡΠ΅ΠΊΡΡΡΡ ΡΠΈΡΡΠ΅ΠΌΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΈ Π°Π»Π³ΠΎΡΠΈΡΠΌΡ ΡΡΠ½ΠΊΡΠΈΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ½ΡΡ
ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠΎΠ² ΡΠΈΡΡΠ΅ΠΌΡ, ΡΠ°ΠΊΠΈΡ
ΠΊΠ°ΠΊ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠΊΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΠΈ, ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ ΠΌΠ½ΠΎΠ³ΠΎΠ°ΡΠΏΠ΅ΠΊΡΠ½ΠΎΠΉ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΡΠ΅ΡΠ΅Π²ΡΡ
ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ
ΠΎΠ±ΡΠ΅ΠΊΡΠΎΠ², ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ ΡΡΡΡΠ°Π½Π΅Π½ΠΈΡ Π½Π΅ΠΏΠΎΠ»Π½ΠΎΡΡ ΠΈ ΠΏΡΠΎΡΠΈΠ²ΠΎΡΠ΅ΡΠΈΠ²ΠΎΡΡΠΈ ΠΈ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ ΠΏΡΠΈΠ½ΡΡΠΈΡ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ. ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠΉ ΠΎΡΠ΅Π½ΠΊΠΈ ΡΠΈΡΡΠ΅ΠΌΠ½ΡΡ
ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠΎΠ², ΠΊΠΎΡΠΎΡΡΠ΅ ΠΏΡΠΎΠ΄Π΅ΠΌΠΎΠ½ΡΡΡΠΈΡΠΎΠ²Π°Π»ΠΈ ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΠΎΡΠ²Π΅ΡΠ°ΡΡ ΠΏΡΠ΅Π΄ΡΡΠ²Π»ΡΠ΅ΠΌΡΠΌ ΡΡΠ΅Π±ΠΎΠ²Π°Π½ΠΈΡΠΌ ΠΏΠΎ ΠΏΠΎΠ»Π½ΠΎΡΠ΅ ΠΈ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΈ ΠΏΡΠΎΡΠΈΠ²ΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ Π½Π΅ΠΆΠ΅Π»Π°ΡΠ΅Π»ΡΠ½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
Π΅Π΅ Π½Π΅ΠΏΠΎΠ»Π½ΠΎΡΡ ΠΈ ΠΏΡΠΎΡΠΈΠ²ΠΎΡΠ΅ΡΠΈΠ²ΠΎΡΡΠΈ
ΠΠ΅ΡΠΎΠ΄ΠΈΠΊΠ° ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ Π°Π½ΠΎΠΌΠ°Π»ΠΈΠΉ ΠΈ ΠΊΠΈΠ±Π΅ΡΠ°ΡΠ°ΠΊ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΈΠ½ΡΠ΅Π³ΡΠ°ΡΠΈΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΡΡΠ°ΠΊΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° ΠΈ ΠΌΠ°ΡΠΈΠ½Π½ΠΎΠ³ΠΎ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ
Π ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΠ΅ΡΡΡ
ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Π΄Π°Π½Π½ΡΡ
Π΄Π»Ρ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ½ΠΈΡΠΎΡΠΈΠ½Π³Π° ΡΠ΅ΡΠ΅Π²ΠΎΠ³ΠΎ ΡΡΠ°ΡΠΈΠΊΠ° ΠΈ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ Π² Π½Π΅ΠΌ Π°Π½ΠΎΠΌΠ°Π»ΡΠ½ΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ, Π° ΡΠ°ΠΊΠΆΠ΅ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΠΊΠΈΠ±Π΅ΡΠ°ΡΠ°ΠΊ, Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎ ΡΡΠΈΡΡΠ²Π°ΡΡ Π±ΠΎΠ»ΡΡΠΎΠ΅ ΡΠΈΡΠ»ΠΎ ΡΠ°ΠΊΡΠΎΡΠΎΠ² ΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ², Π²ΠΊΠ»ΡΡΠ°Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΠ΅ ΡΠ΅ΡΠ΅Π²ΡΠ΅ ΠΌΠ°ΡΡΡΡΡΡ, Π²ΡΠ΅ΠΌΠ΅Π½Π° Π·Π°Π΄Π΅ΡΠΆΠΊΠΈ Π΄Π°Π½Π½ΡΡ
, ΠΏΠΎΡΠ΅ΡΠΈ ΠΏΠ°ΠΊΠ΅ΡΠΎΠ² ΠΈ Π½ΠΎΠ²ΡΠ΅ ΡΠ²ΠΎΠΉΡΡΠ²Π° ΡΡΠ°ΡΠΈΠΊΠ°, ΠΎΡΠ»ΠΈΡΠ°ΡΡΠΈΠ΅ΡΡ ΠΎΡ Π½ΠΎΡΠΌΠ°Π»ΡΠ½ΡΡ
. ΠΡΠ΅ ΡΡΠΎ ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΏΠΎΠ±ΡΠ΄ΠΈΡΠ΅Π»ΡΠ½ΡΠΌ ΠΌΠΎΡΠΈΠ²ΠΎΠΌ ΠΊ ΠΏΠΎΠΈΡΠΊΡ Π½ΠΎΠ²ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ ΠΊΠΈΠ±Π΅ΡΠ°ΡΠ°ΠΊ ΠΈ Π·Π°ΡΠΈΡΡ ΠΎΡ Π½ΠΈΡ
ΡΠ΅ΡΠ΅ΠΉ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Π΄Π°Π½Π½ΡΡ
. Π ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠ° ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΡ Π°Π½ΠΎΠΌΠ°Π»ΠΈΠΉ ΠΈ ΠΊΠΈΠ±Π΅ΡΠ°ΡΠ°ΠΊ, ΠΏΡΠ΅Π΄Π½Π°Π·Π½Π°ΡΠ΅Π½Π½Π°Ρ Π΄Π»Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π² ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΠ΅ΡΡΡ
ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Π΄Π°Π½Π½ΡΡ
, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΎΡΠ½ΠΎΠ²ΡΠ²Π°Π΅ΡΡΡ Π½Π° ΠΈΠ½ΡΠ΅Π³ΡΠ°ΡΠΈΠΈ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΡΡΠ°ΠΊΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° ΠΈ ΠΌΠ°ΡΠΈΠ½Π½ΠΎΠ³ΠΎ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ. ΠΠ΅ΡΠΎΠ΄ΠΈΠΊΠ° ΠΎΡΠΈΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½Π° Π½Π° Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΠ΅ Π² ΡΠ΅Π°Π»ΡΠ½ΠΎΠΌ ΠΈΠ»ΠΈ Π±Π»ΠΈΠ·ΠΊΠΎΠΌ ΠΊ ΡΠ΅Π°Π»ΡΠ½ΠΎΠΌΡ ΠΌΠ°ΡΡΡΠ°Π±Π΅ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΠΈ Π²ΠΊΠ»ΡΡΠ°Π΅Ρ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ ΡΡΠ°ΠΏΠΎΠ²: (1) Π²ΡΡΠ²Π»Π΅Π½ΠΈΡ Π°Π½ΠΎΠΌΠ°Π»ΠΈΠΉ Π² ΡΠ΅ΡΠ΅Π²ΠΎΠΌ ΡΡΠ°ΡΠΈΠΊΠ΅, (2) ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π² Π°Π½ΠΎΠΌΠ°Π»ΠΈΡΡ
ΠΊΠΈΠ±Π΅ΡΠ°ΡΠ°ΠΊ ΠΈ (3) ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΠΊΠΈΠ±Π΅ΡΠ°ΡΠ°ΠΊ. ΠΠ΅ΡΠ²ΡΠΉ ΡΡΠ°ΠΏ ΡΠ΅Π°Π»ΠΈΠ·ΡΠ΅ΡΡΡ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΡΡΠ°ΠΊΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π° (ΠΎΡΠ΅Π½ΠΊΠΈ ΡΠ°ΠΌΠΎΠΏΠΎΠ΄ΠΎΠ±ΠΈΡ ΡΠ΅ΡΠ΅Π²ΠΎΠ³ΠΎ ΡΡΠ°ΡΠΈΠΊΠ°), Π²ΡΠΎΡΠΎΠΉ ΠΈ ΡΡΠ΅ΡΠΈΠΉ β Ρ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΌΠ°ΡΠΈΠ½Π½ΠΎΠ³ΠΎ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ, ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΠΈΡ
ΡΡΠ΅ΠΉΠΊΠΈ ΡΠ΅ΠΊΡΡΡΠ΅Π½ΡΠ½ΡΡ
Π½Π΅ΠΉΡΠΎΠ½Π½ΡΡ
ΡΠ΅ΡΠ΅ΠΉ Ρ Π΄ΠΎΠ»Π³ΠΎΠΉ ΠΊΡΠ°ΡΠΊΠΎΡΡΠΎΡΠ½ΠΎΠΉ ΠΏΠ°ΠΌΡΡΡΡ. Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ Π²ΠΎΠΏΡΠΎΡΡ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΠΎΠΉ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ, Π²ΠΊΠ»ΡΡΠ°Ρ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Π½Π°Π±ΠΎΡΠ° Π΄Π°Π½Π½ΡΡ
, ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠ΅Π³ΠΎ ΡΠ΅ΡΠ΅Π²ΡΠ΅ ΠΏΠ°ΠΊΠ΅ΡΡ, ΡΠΈΡΠΊΡΠ»ΠΈΡΡΡΡΠΈΠ΅ Π² ΡΠ΅ΡΠΈ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Π΄Π°Π½Π½ΡΡ
. ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠΉ ΠΎΡΠ΅Π½ΠΊΠΈ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΡΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ Π½Π°Π±ΠΎΡΠ° Π΄Π°Π½Π½ΡΡ
. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎ Π²ΡΡΠΎΠΊΡΡ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΉ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ ΠΈ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π½ΡΡ
Π΄Π»Ρ Π½Π΅Π΅ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΡ
ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΡΡ ΡΠ°Π½Π½Π΅Π΅ ΠΎΠ±Π½Π°ΡΡΠΆΠ΅Π½ΠΈΠ΅ ΠΊΠ°ΠΊ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
, ΡΠ°ΠΊ ΠΈ Π½Π΅ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
ΠΊΠΈΠ±Π΅ΡΠ°ΡΠ°ΠΊ
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