COMPARATIVE ANALYSIS OF MATHEMATICAL MODELS OF SPEECH INFORMATION

Abstract

The aggravation of the cyber security situation around Ukraine requires a radical revision of the current approaches to ensuring the cyber security of information and telecommunication systems of the state. Anticipatory pace of development of means and technologies of cyberattack determines the need to find new non-trivial (asymmetric) and at the same time practical ideas aimed at ensuring cyber security of information regardless of the type of its presentation. Recently, speech information that circulates in IP networks has become the object of cyberattacks by unscrupulous competitors, foreign government institutions, and simply interested individuals. As known, one of the most effective measures of cyber security of speech information is its cryptographic protection. Well-known international and national cryptographic protocols provide sufficient cryptographic stability, but despite this, the number of cyber threats to speech information does not decrease, but, on the contrary, increases in proportion to the growth of its value. Therefore, the issue of increasing the level of security of speech information that circulates in IP networks remains relevant. One of the first stages on the way to the creation of the latest cryptographic means of protecting speech information is the analysis of relevant mathematical models. In order to establish the advantages and disadvantages of known mathematical models of speech information and choose among them with the same accuracy the one that will consider the individual features of the source of speech information, as well as have an acceptable realizability for a given system of parameters, the article presents the results of the analysis of two classes of models: dynamic and stochastic. It is shown that the main dynamic models of speech information, which belong to the models of the first class, are wavelet models, pulse-modulated and wave models, models of linear prediction, harmonic mathematical models. In the article, in addition to the well-known mathematical models of the first class, a new type of them is analyzed - Fredholm models of speech information. The second class of models considered in the article includes two of the most common types, namely: acoustic-phonetic models and speech traffic models. For each of the researched models of one or another class and type, developers were established, the mathematical apparatus underlying them was specified, and the researched mathematical model of speech information is formalized. On the basis of the introduced qualitative scale, based on the totality of the determined advantages and disadvantages of the analyzed models, the degree of achievement of the obtained results was assessed in accordance with the goal set in the article. Therefore, the conducted analysis covered the most common classes of mathematical models of speech information and made it possible to choose among them the one that will become the basis for the development of the latest cryptographic means of protection.