APPLICATION OF MATRIX AND OPERATOR-MATRIX METHODS IN ENCRYPTING TEXT OBJECTS USING BIGRAMS AND TRIGRAMS

The article discusses the application of matrix and operator-matrix methods for encrypting textual objects based on bigrams and trigrams. The algorithm involves transforming the original text using an auxiliary key, splitting it into bigrams and trigrams, and then sequentially encrypting it using matrix substitutions. Matrices of arbitrary size are used as keys, ensuring the flexibility of the method. The operator-matrix method is a generalization of the matrix coefficient and allows for a reliable number and dimensionality of the matrix. The use of various data input and extraction methods, up to 480 options, enhances the robustness of the transformation. The proposed methods can be used to protect textual information of various structures, including documents, messages, and other data. The operator-matrix method expands encryption capabilities, increases key variability, and introduces complex character processing algorithms. The flexibility in selecting matrix parameters and their correction algorithms allows the method to be adapted to various security requirements. Thus, the described methods and approaches to constructing substitution keys can be applied to textual objects in an arbitrary manner. The operator-matrix method is a generalized method of matrix substitution for textual objects. The application of this approach ensures a high level of protection for textual objects, making their decryption without knowledge of the key significantly more difficult.

method, object, encryption, coding, decryption, element, symbol, key, option, matrix, operator-matrix, stability, cybercrime.

1. Gafurov M.Kh. About one way to encrypt an object using language elements. / M.Kh. Gafurov // Polytechnic Bulletin. Series: Intelligence. Innovation. Investments. – 2023. – No. 2 (62). – P. 22-29.

2. Gafurov M.Kh. About one way to encrypt an object using a double key. (in Tajik) / M.Kh. Gafurov // Polytechnic Bulletin. Series: Intelligence. Innovation. Investments. – 2023. – No. 1 (61). – P. 38-41.

3. Gafurov M.Kh. Operator application of encryption of language elements with Polybeus square. / M.Kh. Gafurov // Bulletin of the Technological University of Tajikistan. – 2024. – No. 1 (56). – P. 159-164.

4. Gafurov M.Kh. The use of bigrams and trigrams when encrypting an object using a Polybeus square. / M.Kh. Gafurov // Polytechnic Bulletin. Series: Intelligence. Innovation. Investments. – 2024. – No. 1 (65). – P. 72-75.

5. Gafurov М.Kh. Application of trigrams in encryption of objects using the Polybius square and a double key. / М.Kh. Gafurov, A.S. Rajabova,, R.B. Ghiyosov // Bulletin of the Tajik National University. Series of natural sciences. – 2024. – №3. – Р. 28-31. doi.org/10.62965/tnu.sns.2024.3.3

6. Gafurov M.Kh. Application of the operator in the Polybey encryption method (in Tajik) / M.Kh. Gafurov // Materials of the international scientific and practical conference “Technical sciences and engineering education for sustainable development”. Part 2. – Dushanbe: Tajik Technical University named after academician. M.S. Oshimi. – 2021. – pp. 78-82.

7. Gafurov M.Kh. Encrypting an object using operator-matrix methods. / M.Kh. Gafurov // Public safety, legality and order in the 3rd millennium. – 2018. – No. 4-2. – pp. 14–21.

8. Gafurov M.Kh. Encrypting an object using trigrams and a double key. / M.Kh. Gafurov, A.A. Kosimov, S. Isfandiyor // Polytechnic Bulletin. Series: Intelligence. Innovation. Investments. – 2023. – No. 4 (64). – P. 45-49.

9. Gafurov M.Kh. Encryption of a text object when using language symbols (in Tajik) / M.Kh. Gafurov // Polytechnic Bulletin. Series: Intelligence. Innovation. Investments. – 2020. – No. 4 (52). – P. 31-35.

10. Gafurov M.Kh. Encryption of text elements using matrix and operator-matrix methods. / M.Kh. Gafurov // Polytechnic Bulletin. Series: Intelligence. Innovation. Investments. – 2024. – No. 4 (68). – pp. 26-32.

11. Kosimov A.A. On recognizing the author of a text fragment based on syllable frequency. / A.A. Kosimov // Polytechnic Bulletin, Series: intelligence, innovation, investment. – 2021. – 4(56). – pp. 59-64.

12. Kosimov A.A. Evaluating the effectiveness of using trigrams in text identification. / A.A. Kosimov // News of the Academy of Sciences of the Republic of Tajikistan. Department of physical, mathematical, chemical, geological and technical sciences. – 2017. – No. 1 (166). – pp. 51-57.

13. Usmanov Z.D. Morphological analysis of word forms of the Tajik language: monograph. / Z.D. Usmanov, G.M. Dovudov / Dushanbe: “Donish”. – 2015. – 130 p.

14. Usmanov Z.D. About the variety of postfixes in the Tajik literary language. / Z.D. Usmanov, O.M. Soliev, G.M. Dovudov // Reports of the Academy of Sciences of the Republic of Tajikistan. – 2009. – vol. 53. – no. 2. – P. 99-103.

15. Usmanov Z.D. On the formation of a database of prefixes of the Tajik literary language. / Z.D. Usmanov, G.M. Dovudov // Reports of the Academy of Sciences of the Republic of Tajikistan. – 2009. – vol. 52. – no. 6. – P. 431-436.

16. Usmanov, Z.D. Frequency of bigrams in Tajik literature / Z.D. Usmanov, A.A. Kosimov // Reports of the Academy of Sciences of the Republic of Tajikistan. – 2016. – t.59. – No. 1-2. – P. 28-32.

17. Khudoiberdiev Kh.A. On recognizing the author of a text based on syllable frequency. / H.A. Khudoiberdiev, A.A. Kosimov // Reports of the Academy of Sciences of the Republic of Tajikistan. – 2019. – T.62. – No. 11-12. – pp. 641-645.

2026-03-25