Hybrid Key Pre-Distribution and Multiple Keyspace Schemes Using Unitals
DOI:
https://doi.org/10.24160/1993-6982-2025-4-156-166Keywords:
combinatorial block design, security parameter, unital, parallel class, resolutionAbstract
The article considers the features of using key pre-distribution schemes based on combinatorial block designs (CBDs) that differ in the scale and power of the set of keys used with a limited amount of key memory, in combination with smaller-scale schemes. Such CBDs are based on a unital, a certain subset of projective plane elements, and are balanced incomplete combinatorial block designs (BICDs) that have a large number of blocks with a relatively small number of elements, a feature which determines the advisability of using them in wireless sensor networks (WSNs). A method for constructing such schemes is proposed, which involves the use of a limited number of "trusted" nodes as intermediate ones, mapped to a parallel class of the specified CBD, and united by a smaller-scale scheme for switching between the "trusted" nodes. The latter one can have a projective plane structure or it can be a Blom scheme. The composition of two such schemes forms a hybrid scheme. The formalization of constructing hybrid schemes and communication protocols in them is based on the system of algorithms with the representation of blocks and dual blocks of the CBD by algebraic identifiers and numbers uniquely corresponding to them. The possibility of implementing such schemes using wireless sensor networks is shown, in which the nodes corresponding to the parallel class act as routers, and the remaining ones are sleeping. Communications between the nodes of one parallel class are performed by means of nodes of the trusted center; therefore, it is possible to use the scheme when not all nodes from among the nodes that are not trusted nodes are implemented.
References
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2. Beth T., Jungnickel D., Lenz H. Design Theory // Encyclopedia of Mathematics and its Appl. Cambridge: Cambridge University Press, 1999.
3. Таранников Ю.В. Комбинаторные свойства дискретных структур и приложения к криптологии. М.: МЦНМО, 2014.
4. Lee J., Stinson D. On the Construction of Practical Key Redistribution Schemes for Distributed Sensor Networks using Combinatorial Designs // ACM Trans. Information and Systems Security. 2008. V. 11(2). Pp. 1—35.
5. Paterson M.B., Stinson D.R. A Unified Approach to Combinatorial Key Predistribution Schemes for Sensor Networks // Designs Codes and Cryptography.·2014. V. 71. Pp. 433—457.
6. Urivskiy A. Key Predistribution Scheme Using Affine Planes and Blom’s Scheme // Proc. Intern. Math. Conf. 50 Years of IITP. 2011. Pp. 1—5.
7. Barwick S., Ebert G. Unitals in Projective Planes. N.-Y: Springer, 2008.
8. Chegeni V. e. a. A Scalable Key Pre-distribution Scheme Based on the Unital Design for the Internet of Things Security // IETE J. Research. 2021. V. 69(2). Pp. 1—12.
9. Shaik R. e. a. A Novel Hermitian Unital Based Key Pre Distribution Scheme // Intern. J. Electrical Engineering and Technol. 2020. V. 11(3). Pp. 297—308.
10. Aher R., Nandgave S., A Novel Approach for Scalability in Pre Key Distribution Using Unital Algorithm // Intern. J. Innovations & Advancement in Computer Sci. 2015. V. 4(6). Pp. 2347—8616.
11. Manoj Kumar A., Jaya Prakash P., Giri Dr.M. Providing Efficient Measurable Key by Using Unital Based Key Predistribution Scheme for Wireless Sensor Networks // J. Computer Eng. 2014. V. 16(5). Pp. 121—124.
12. Suba's R., Sugitha J. Unital Design Based Key Pre-distribution Scheme for Wireless Sensor Networks // Intern. J. Innovation Research Sci., Eng. and Technol. 2014. V. 3. Pp. 933—937.
13. Сесюкалов А.А., Фролов А.Б. Рабочий стол для изучения схем распределения ключей и схем множественных ключевых пространств со структурой юнитала // Математические методы в технологиях и технике. 2024. № 5. С. 86—91.
14. Frolov A.B, Kochetova N.P. Scaling Networks and Capturing Keys Using Combined Systems of Sets // Society 5.0. Studies in Systems. Desitions and Control. N.-Y.: Springer, 2023. Pp. 267—278.
15. Frolov A.B, Kochetova N.P., Klyagin A.O. Scaling Networks and Capturing Keys Using Combined Combinatorial Block Designs // Networks and Systems in Cybernetics. N.-Y.: Springer Nature, 2023. Pp. 269—289.
16. Bamberg J., Betten A., Praeger Ch.E., Wassermann A. Unitals in the Desarguesian Projective Plane of Order 16 // J. Statist. Plann. Inference. 2014. V. 144. Pp. 110—122.
17. Faina G., Korchmáros G. A Graphic Characterization of Hermitian Curves. Amsterdam, N.-Y.: North-Holland, 1983.
18. Mez'ofi D.C. Constructions, Classifications and Embeddings of Abstract Unitals. Szeged, 2020.
19. Nagy G.P., Mez'ofi D.C. GAP Package UnitalSZ [Электрон ресурс] https://nagygp.github.io/UnitalSZ/ (дата обращения 20.12.2024).
20. GAP. Groups, Algorithms, and Programming. Version 4.11.0 [Электрон ресурс] https://www.gap-system.org (дата обращения 20.12.2024).
21. Frolov A., Kochetova N., Vunnukov A., Sesiukalov A. Educational Desktop for Remote Modeling of Secure Cyber-physical Systems Protocols // Proc. VII Intern. Conf. Information Technol. Engineering Education. Moscow: NRU MPEI, 2024. Pp. 1—5.
22. Frolov A., Kochetova N., Klyagin A. Algorithmizing Aspects of Some Combinatorial Block-designs Implemented in Network Systems // Data Analytics in System Engineering. N.-Y.: Springer, 2023.
23. Gholami K.El., Yassine M.Y., Fatani I.F-E. The IEEE 802.15.4 Standard in Industrial Applications: a Survey // J. Theoretical and Appl. Information Technol. 2021. V. 99(15). Pp. 1—17.
24. Kim S.H., Chong P.K., Kim T. Performance Study of Routing Protocols in ZigBee Wireless Mesh Networks // Wireless Pers Commun. 2017. V. 95. Pp. 1829—1853.
25. Kim T. e. a. Neighbor Table-based Shortcut Tree Routing in Zigbee Wireless Networks // IEEE Trans. Parallel and Distributed Systems. 2014. V. 25(3). Pp. 706—716.
26. Кочетова Н.П., Фролов А.Б. Масштабирование сетей и их ключевых систем на основе совмещенных комбинаторных блок-дизайнов // Информационные технологии. 2023. № 4. Т. 29. С. 171—182.
27. Du W. e. a. A Pairwise Key Pre Distribution Scheme for Wireless Sensor Networks // ACM Trans. Inform. Syst. Secur. 2005. V. 8. Pp. 228—258.
28. Blom R. An Optimal Class of Symmetric Key Generation Systems // Advances in Cryptology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1958. V. 209. Pp. 335–338.
29. Винников А.М., Дедова М.А., Кочетова Н.П., Фролов А.Б. Компьютерное моделирование протоколов безопасной киберфизической системы умного дома // Вестник МЭИ. 2024. № 4. C. 158—168.
---
Для цитирования: Сесюкалов А.А., Фролов А.Б. Гибридные схемы предварительного распределения ключей и множественных ключевых пространств с использованием юниталов // Вестник МЭИ. 2025. № 4. С. 156—166. DOI: 10.24160/1993-6982-2025-4-156-166
---
Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
#
1. Stinson D. Combinatorial Designs: Constructions and Analysis. Berlin: Springer, 2003.
2. Beth T., Jungnickel D., Lenz H. Design Theory. Encyclopedia of Mathematics and its Appl. Cambridge: Cambridge University Press, 1999.
3. Tarannikov Yu.V. Kombinatornye Svoystva Diskretnykh Struktur i Prilozheniya k Kriptologii. M.: MTSNMO, 2014. (in Russian).
4. Lee J., Stinson D. On the Construction of Practical Key Redistribution Schemes for Distributed Sensor Networks using Combinatorial Designs. ACM Trans. Information and Systems Security. 2008;11(2):1—35.
5. Paterson M.B., Stinson D.R. A Unified Approach to Combinatorial Key Predistribution Schemes for Sensor Networks. Designs Codes and Cryptography. 2014;71:433—457.
6. Urivskiy A. Key Predistribution Scheme Using Affine Planes and Blom’s Scheme. Proc. Intern. Math. Conf. 50 Years of IITP. 2011:1—5.
7. Barwick S., Ebert G. Unitals in Projective Planes. N.-Y: Springer, 2008.
8. Chegeni V. e. a. A Scalable Key Pre-distribution Scheme Based on the Unital Design for the Internet of Things Security. IETE J. Research. 2021;69(2):1—12.
9. Shaik R. e. a. A Novel Hermitian Unital Based Key Pre Distribution Scheme. Intern. J. Electrical Engineering and Technol. 2020;11(3):297—308.
10. Aher R., Nandgave S., A Novel Approach for Scalability in Pre Key Distribution Using Unital Algorithm. Intern. J. Innovations & Advancement in Computer Sci. 2015;4(6):2347—8616.
11. Manoj Kumar A., Jaya Prakash P., Giri Dr.M. Providing Efficient Measurable Key by Using Unital Based Key Predistribution Scheme for Wireless Sensor Networks. J. Computer Eng. 2014;16(5):121—124.
12. Suba's R., Sugitha J. Unital Design Based Key Pre-distribution Scheme for Wireless Sensor Networks. Intern. J. Innovation Research Sci., Eng. and Technol. 2014;3:933—937.
13. Sesyukalov A.A., Frolov A.B. Rabochiy Stol dlya Izucheniya Skhem Raspredeleniya Klyuchey i Skhem Mnozhestvennykh Klyuchevykh Prostranstv so Strukturoy Yunitala. Matematicheskie Metody v Tekhnologiyakh i Tekhnike. 2024;5:86—91. (in Russian).
14. Frolov A.B, Kochetova N.P. Scaling Networks and Capturing Keys Using Combined Systems of Sets. Society 5.0. Studies in Systems. Desitions and Control. N.-Y.: Springer, 2023:267—278.
15. Frolov A.B, Kochetova N.P., Klyagin A.O. Scaling Networks and Capturing Keys Using Combined Combinatorial Block Designs. Networks and Systems in Cybernetics. N.-Y.: Springer Nature, 2023:269—289.
16. Bamberg J., Betten A., Praeger Ch.E., Wassermann A. Unitals in the Desarguesian Projective Plane of Order 16. J. Statist. Plann. Inference. 2014;144:110—122.
17. Faina G., Korchmáros G. A Graphic Characterization of Hermitian Curves. Amsterdam, N.-Y.: North-Holland, 1983.
18. Mez'ofi D.C. Constructions, Classifications and Embeddings of Abstract Unitals. Szeged, 2020.
19. Nagy G.P., Mez'ofi D.C. GAP Package UnitalSZ [Elektron Resurs] https://nagygp.github.io/UnitalSZ/ (Data Obrashcheniya 20.12.2024).
20. GAP. Groups, Algorithms, and Programming. Version 4.11.0 [Elektron Resurs] https://www.gap-system.org (Data Obrashcheniya 20.12.2024).
21. Frolov A., Kochetova N., Vunnukov A., Sesiukalov A. Educational Desktop for Remote Modeling of Secure Cyber-physical Systems Protocols. Proc. VII Intern. Conf. Information Technol. Engineering Education. Moscow: NRU MPEI, 2024:1—5.
22. Frolov A., Kochetova N., Klyagin A. Algorithmizing Aspects of Some Combinatorial Block-designs Implemented in Network Systems. Data Analytics in System Engineering. N.-Y.: Springer, 2023.
23. Gholami K.El., Yassine M.Y., Fatani I.F-E. The IEEE 802.15.4 Standard in Industrial Applications: a Survey. J. Theoretical and Appl. Information Technol. 2021;99(15):1—17.
24. Kim S.H., Chong P.K., Kim T. Performance Study of Routing Protocols in ZigBee Wireless Mesh Networks. Wireless Pers Commun. 2017;95:1829—1853.
25. Kim T. e. a. Neighbor Table-based Shortcut Tree Routing in Zigbee Wireless Networks. IEEE Trans. Parallel and Distributed Systems. 2014;25(3):706—716.
26. Kochetova N.P., Frolov A.B., Masshtabirovanie Setey i Ikh Klyuchevykh Sistem na Osnove Sovmeshchennykh Kombinatornykh Blok-dizaynov. Informatsionnye Tekhnologii. 2023;4;29:171—182. (in Russian).
27. Du W. e. a. A Pairwise Key Pre Distribution Scheme for Wireless Sensor Networks. ACM Trans. Inform. Syst. Secur. 2005;8:228—258.
28. Blom R. An Optimal Class of Symmetric Key Generation Systems. Advances in Cryptology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1958;209:335–338.
29. Vinnikov A.M., Dedova M.A., Kochetova N.P., Frolov A.B. Komp'yuternoe Modelirovanie Protokolov Bezopasnoy Kiberfizicheskoy Sistemy Umnogo Doma. Vestnik MEI. 2024;4:158—168. (in Russian)
---
For citation: Sesyukalov A.A., Frolov A.B. Hybrid Key Pre-distribution and Multiple Keyspace Schemes Using Unitals. Bulletin of MPEI. 2025;4:156—166. (in Russian). DOI: 10.24160/1993-6982-2025-4-156-166
---
Conflict of interests: the authors declare no conflict of interes
2. Beth T., Jungnickel D., Lenz H. Design Theory // Encyclopedia of Mathematics and its Appl. Cambridge: Cambridge University Press, 1999.
3. Таранников Ю.В. Комбинаторные свойства дискретных структур и приложения к криптологии. М.: МЦНМО, 2014.
4. Lee J., Stinson D. On the Construction of Practical Key Redistribution Schemes for Distributed Sensor Networks using Combinatorial Designs // ACM Trans. Information and Systems Security. 2008. V. 11(2). Pp. 1—35.
5. Paterson M.B., Stinson D.R. A Unified Approach to Combinatorial Key Predistribution Schemes for Sensor Networks // Designs Codes and Cryptography.·2014. V. 71. Pp. 433—457.
6. Urivskiy A. Key Predistribution Scheme Using Affine Planes and Blom’s Scheme // Proc. Intern. Math. Conf. 50 Years of IITP. 2011. Pp. 1—5.
7. Barwick S., Ebert G. Unitals in Projective Planes. N.-Y: Springer, 2008.
8. Chegeni V. e. a. A Scalable Key Pre-distribution Scheme Based on the Unital Design for the Internet of Things Security // IETE J. Research. 2021. V. 69(2). Pp. 1—12.
9. Shaik R. e. a. A Novel Hermitian Unital Based Key Pre Distribution Scheme // Intern. J. Electrical Engineering and Technol. 2020. V. 11(3). Pp. 297—308.
10. Aher R., Nandgave S., A Novel Approach for Scalability in Pre Key Distribution Using Unital Algorithm // Intern. J. Innovations & Advancement in Computer Sci. 2015. V. 4(6). Pp. 2347—8616.
11. Manoj Kumar A., Jaya Prakash P., Giri Dr.M. Providing Efficient Measurable Key by Using Unital Based Key Predistribution Scheme for Wireless Sensor Networks // J. Computer Eng. 2014. V. 16(5). Pp. 121—124.
12. Suba's R., Sugitha J. Unital Design Based Key Pre-distribution Scheme for Wireless Sensor Networks // Intern. J. Innovation Research Sci., Eng. and Technol. 2014. V. 3. Pp. 933—937.
13. Сесюкалов А.А., Фролов А.Б. Рабочий стол для изучения схем распределения ключей и схем множественных ключевых пространств со структурой юнитала // Математические методы в технологиях и технике. 2024. № 5. С. 86—91.
14. Frolov A.B, Kochetova N.P. Scaling Networks and Capturing Keys Using Combined Systems of Sets // Society 5.0. Studies in Systems. Desitions and Control. N.-Y.: Springer, 2023. Pp. 267—278.
15. Frolov A.B, Kochetova N.P., Klyagin A.O. Scaling Networks and Capturing Keys Using Combined Combinatorial Block Designs // Networks and Systems in Cybernetics. N.-Y.: Springer Nature, 2023. Pp. 269—289.
16. Bamberg J., Betten A., Praeger Ch.E., Wassermann A. Unitals in the Desarguesian Projective Plane of Order 16 // J. Statist. Plann. Inference. 2014. V. 144. Pp. 110—122.
17. Faina G., Korchmáros G. A Graphic Characterization of Hermitian Curves. Amsterdam, N.-Y.: North-Holland, 1983.
18. Mez'ofi D.C. Constructions, Classifications and Embeddings of Abstract Unitals. Szeged, 2020.
19. Nagy G.P., Mez'ofi D.C. GAP Package UnitalSZ [Электрон ресурс] https://nagygp.github.io/UnitalSZ/ (дата обращения 20.12.2024).
20. GAP. Groups, Algorithms, and Programming. Version 4.11.0 [Электрон ресурс] https://www.gap-system.org (дата обращения 20.12.2024).
21. Frolov A., Kochetova N., Vunnukov A., Sesiukalov A. Educational Desktop for Remote Modeling of Secure Cyber-physical Systems Protocols // Proc. VII Intern. Conf. Information Technol. Engineering Education. Moscow: NRU MPEI, 2024. Pp. 1—5.
22. Frolov A., Kochetova N., Klyagin A. Algorithmizing Aspects of Some Combinatorial Block-designs Implemented in Network Systems // Data Analytics in System Engineering. N.-Y.: Springer, 2023.
23. Gholami K.El., Yassine M.Y., Fatani I.F-E. The IEEE 802.15.4 Standard in Industrial Applications: a Survey // J. Theoretical and Appl. Information Technol. 2021. V. 99(15). Pp. 1—17.
24. Kim S.H., Chong P.K., Kim T. Performance Study of Routing Protocols in ZigBee Wireless Mesh Networks // Wireless Pers Commun. 2017. V. 95. Pp. 1829—1853.
25. Kim T. e. a. Neighbor Table-based Shortcut Tree Routing in Zigbee Wireless Networks // IEEE Trans. Parallel and Distributed Systems. 2014. V. 25(3). Pp. 706—716.
26. Кочетова Н.П., Фролов А.Б. Масштабирование сетей и их ключевых систем на основе совмещенных комбинаторных блок-дизайнов // Информационные технологии. 2023. № 4. Т. 29. С. 171—182.
27. Du W. e. a. A Pairwise Key Pre Distribution Scheme for Wireless Sensor Networks // ACM Trans. Inform. Syst. Secur. 2005. V. 8. Pp. 228—258.
28. Blom R. An Optimal Class of Symmetric Key Generation Systems // Advances in Cryptology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1958. V. 209. Pp. 335–338.
29. Винников А.М., Дедова М.А., Кочетова Н.П., Фролов А.Б. Компьютерное моделирование протоколов безопасной киберфизической системы умного дома // Вестник МЭИ. 2024. № 4. C. 158—168.
---
Для цитирования: Сесюкалов А.А., Фролов А.Б. Гибридные схемы предварительного распределения ключей и множественных ключевых пространств с использованием юниталов // Вестник МЭИ. 2025. № 4. С. 156—166. DOI: 10.24160/1993-6982-2025-4-156-166
---
Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
#
1. Stinson D. Combinatorial Designs: Constructions and Analysis. Berlin: Springer, 2003.
2. Beth T., Jungnickel D., Lenz H. Design Theory. Encyclopedia of Mathematics and its Appl. Cambridge: Cambridge University Press, 1999.
3. Tarannikov Yu.V. Kombinatornye Svoystva Diskretnykh Struktur i Prilozheniya k Kriptologii. M.: MTSNMO, 2014. (in Russian).
4. Lee J., Stinson D. On the Construction of Practical Key Redistribution Schemes for Distributed Sensor Networks using Combinatorial Designs. ACM Trans. Information and Systems Security. 2008;11(2):1—35.
5. Paterson M.B., Stinson D.R. A Unified Approach to Combinatorial Key Predistribution Schemes for Sensor Networks. Designs Codes and Cryptography. 2014;71:433—457.
6. Urivskiy A. Key Predistribution Scheme Using Affine Planes and Blom’s Scheme. Proc. Intern. Math. Conf. 50 Years of IITP. 2011:1—5.
7. Barwick S., Ebert G. Unitals in Projective Planes. N.-Y: Springer, 2008.
8. Chegeni V. e. a. A Scalable Key Pre-distribution Scheme Based on the Unital Design for the Internet of Things Security. IETE J. Research. 2021;69(2):1—12.
9. Shaik R. e. a. A Novel Hermitian Unital Based Key Pre Distribution Scheme. Intern. J. Electrical Engineering and Technol. 2020;11(3):297—308.
10. Aher R., Nandgave S., A Novel Approach for Scalability in Pre Key Distribution Using Unital Algorithm. Intern. J. Innovations & Advancement in Computer Sci. 2015;4(6):2347—8616.
11. Manoj Kumar A., Jaya Prakash P., Giri Dr.M. Providing Efficient Measurable Key by Using Unital Based Key Predistribution Scheme for Wireless Sensor Networks. J. Computer Eng. 2014;16(5):121—124.
12. Suba's R., Sugitha J. Unital Design Based Key Pre-distribution Scheme for Wireless Sensor Networks. Intern. J. Innovation Research Sci., Eng. and Technol. 2014;3:933—937.
13. Sesyukalov A.A., Frolov A.B. Rabochiy Stol dlya Izucheniya Skhem Raspredeleniya Klyuchey i Skhem Mnozhestvennykh Klyuchevykh Prostranstv so Strukturoy Yunitala. Matematicheskie Metody v Tekhnologiyakh i Tekhnike. 2024;5:86—91. (in Russian).
14. Frolov A.B, Kochetova N.P. Scaling Networks and Capturing Keys Using Combined Systems of Sets. Society 5.0. Studies in Systems. Desitions and Control. N.-Y.: Springer, 2023:267—278.
15. Frolov A.B, Kochetova N.P., Klyagin A.O. Scaling Networks and Capturing Keys Using Combined Combinatorial Block Designs. Networks and Systems in Cybernetics. N.-Y.: Springer Nature, 2023:269—289.
16. Bamberg J., Betten A., Praeger Ch.E., Wassermann A. Unitals in the Desarguesian Projective Plane of Order 16. J. Statist. Plann. Inference. 2014;144:110—122.
17. Faina G., Korchmáros G. A Graphic Characterization of Hermitian Curves. Amsterdam, N.-Y.: North-Holland, 1983.
18. Mez'ofi D.C. Constructions, Classifications and Embeddings of Abstract Unitals. Szeged, 2020.
19. Nagy G.P., Mez'ofi D.C. GAP Package UnitalSZ [Elektron Resurs] https://nagygp.github.io/UnitalSZ/ (Data Obrashcheniya 20.12.2024).
20. GAP. Groups, Algorithms, and Programming. Version 4.11.0 [Elektron Resurs] https://www.gap-system.org (Data Obrashcheniya 20.12.2024).
21. Frolov A., Kochetova N., Vunnukov A., Sesiukalov A. Educational Desktop for Remote Modeling of Secure Cyber-physical Systems Protocols. Proc. VII Intern. Conf. Information Technol. Engineering Education. Moscow: NRU MPEI, 2024:1—5.
22. Frolov A., Kochetova N., Klyagin A. Algorithmizing Aspects of Some Combinatorial Block-designs Implemented in Network Systems. Data Analytics in System Engineering. N.-Y.: Springer, 2023.
23. Gholami K.El., Yassine M.Y., Fatani I.F-E. The IEEE 802.15.4 Standard in Industrial Applications: a Survey. J. Theoretical and Appl. Information Technol. 2021;99(15):1—17.
24. Kim S.H., Chong P.K., Kim T. Performance Study of Routing Protocols in ZigBee Wireless Mesh Networks. Wireless Pers Commun. 2017;95:1829—1853.
25. Kim T. e. a. Neighbor Table-based Shortcut Tree Routing in Zigbee Wireless Networks. IEEE Trans. Parallel and Distributed Systems. 2014;25(3):706—716.
26. Kochetova N.P., Frolov A.B., Masshtabirovanie Setey i Ikh Klyuchevykh Sistem na Osnove Sovmeshchennykh Kombinatornykh Blok-dizaynov. Informatsionnye Tekhnologii. 2023;4;29:171—182. (in Russian).
27. Du W. e. a. A Pairwise Key Pre Distribution Scheme for Wireless Sensor Networks. ACM Trans. Inform. Syst. Secur. 2005;8:228—258.
28. Blom R. An Optimal Class of Symmetric Key Generation Systems. Advances in Cryptology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1958;209:335–338.
29. Vinnikov A.M., Dedova M.A., Kochetova N.P., Frolov A.B. Komp'yuternoe Modelirovanie Protokolov Bezopasnoy Kiberfizicheskoy Sistemy Umnogo Doma. Vestnik MEI. 2024;4:158—168. (in Russian)
---
For citation: Sesyukalov A.A., Frolov A.B. Hybrid Key Pre-distribution and Multiple Keyspace Schemes Using Unitals. Bulletin of MPEI. 2025;4:156—166. (in Russian). DOI: 10.24160/1993-6982-2025-4-156-166
---
Conflict of interests: the authors declare no conflict of interes
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2025-06-24
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