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Abstract The article considers the choice of cycle functions in the provable persistent key universal hashing scheme, proposed model and method of forming codes of integrity and authenticity of data on the basis of modular transformations, computational complexity reduce algorithm of the hashing schemes implementation using cyclic functions. The object of the research is the process of improving the integrity and authenticity of data packets in security protocols of telecommunication networks. The subject of the study are models, methods and algorithms for monitoring the integrity and authenticity of data packets in security protocols of telecommunication networks. The purpose of the study is to increase the integrity and authenticity of data packets in security protocols of telecommunication networks. The developed enhanced method of forming a cascade MAC differs from the known (algorithm UMAC) using modular hashing on the last stage of the MAC forming that provides high collision properties of strictly universal hashing and safety performance at the level of modern means of demonstrable strength protection. Were obtained estimates of the computational complexity of the formation of the MAC using modular hashing, found, that with comparable rates of resistance the complexity of modular hashing exceeds by 1–2 orders of known schemes based on block symmetric ciphers. However, the use of modular transformations provides provable security and high collision properties of strictly universal hashing. References Stinson D. R. Some constructions and bounds for authentication codes / D. R. Stinson // J. Cryptology. – 1988. – № 1. – Р. 37–51. 2. Stinson D. R. The combinatorics of authentication and secrecy codes / D. R. Stinson // J. Cryptology. – 1990. – № 2. – Р. 23–49. 3. Кузнецов А. А. Исследование коллизионных свойств кодов аутентификации сообщений UMAC / А. А. Кузнецов, О. Г. Король, С. П. Евсеев // Прикладная радиоэлектроника. – Харьков : Изд-во ХНУРЭ, 2012. – Т. 11, № 2. – С. 171–183. 4. Hoholdt Т. An explicit construction of a sequence of codes attaining the Tsfasman-Vladut-Zink bound / T. Hoholdt // The first steps, IEEE Trans. Info. Theory. – 1997. – 135 p. 5. Maitra S. Further constructions of resilient Boolean functions with very high nonlinearity / S. Maitra, E. Pasalic // Accepted in SETA. – May, 2001. 6. Кузнецов О. О. Захист інформації в інформаційних системах / О. О. Кузнецов, С. П. Євсеєв, О. Г. Король. – Х. : Вид. ХНЕУ, 2011. – 504 с. 7. Final report of European project number IST-1999-12324, named New European Schemes for Signatures, Integrity, and Encryption, April 19, 2004 – Version 0.15 (beta), Springer-Verlag. 8. Столлингс В. Криптография и защита сетей: принципы и практика, 2-е изд. / В. Столлингс : пер. с англ. – М. : Вильям, 2001. – 672 с. 9. Король О. Г. Исследование методов обеспечения аутентичности и целостности данных на основе односторонних хеш-функций / О. Г. Король, С. П. Евсеев // Науково-технічний журнал «Захист інформації». – 2008. – Спецвипуск (40). – С. 50–55. 10. Bierbrauer J. Authentification via algebraic-geometric codes [Electronic resource] / J. Bierbrauer. – Access mode : http://www.math.mtu.edu/~jbierbra/ potpap.ps. 11. Bierbrauer J. On families of hash function via geometric codes and concatenation / J. Bierbrauer, T. Johansson, G. Kabatianskii // Advances in Cryptology – CRYPTO 93. Lecture Notes in Computer Science. – 1994 – № 773. – Р. 331–342. 12. Bierbrauer J. Universal hashing and geometric codes [Electronic resource] / J. Bierbrauer. – Access mode : http://www.math.mtu.edu/ ~jbierbra/ hashco1.ps.

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