Mathematical modeling of non-standard multiplicative knapsack cryptosystems
UDC
519.72EDN
ZHXFOFAbstract
It investigates the development of mathematical models of alphabet cryptosystems based on the tasks a non-standard multiplicative knapsacks. Mathematical models of the cryptosystems in the form of tuples. Establishes necessary and sufficient conditions under which the generalized multiplicative injective knapsack vector over $Z_p$, $p\ge 2$. Developed mathematical model of the cryptosystem by overlapping scales, in which the algorithm of the inverse transformation of the closed text is reduced to an algorithmically non-solvable problem for the analyst. On the basis of the analysis previously offered a different backpack models are revealed qualitative features of non-standard multiplicative knapsack systems that increase their resistance to known attacks. We also study the problem of constructing isomorphic additive and multiplication knapsacks. Moreover, in contrast to the standard knapsack-teams, in which when determining the entrance of a knapsack or other components of the knapsack vector are either present or not, and here we consider the case when they can be repeated a specified number of times for a given array for both generic and super generic multiplicative knapsack.
Keywords:
alphabetic cryptosystem, mathematical model of cryptosystems, symmetric and asymmetric knapsack system of information protection, non-additive (multiplicative) knapsack, generalized (generalized super) multiplicative knapsackReferences
- Shannon C. Communication theory of secrecy systems // Bell System Techn. J. 1949. Vol. 28. No. 4. P. 656-715.
- Merkle R., Hellman M. Hiding information and signatures in trapdoor knapsacks // IEEE Transactions on Information Theory. 1978. Vol. IT-24. P. 525-530.
- Rivest R.L., Chor B. A knapsack-type public key cryptosystem based on arithmetic in finite fields // IEEE Transactions on Information Theory. 1988. Vol. 34. No. 5. P. 901-909.
- Shamir A. A polynomial-time algorithm for breaking the basic Merkle-Hellman cryptosystem // IEEE Transactions on Information Theory. 1984. Vol. 30. No. 5. P. 699-704.
- Koblitz N. A course in number theory and cryptography. New York, Springer-Verlag, 1987.
- Осипян В.О. Об одном обобщении рюкзачной криптосистемы // Известия вузов. Сев.-Кавк. регион. Техн. науки. 2003. Прил. № 5. С. 18-25. [Osipyan V.O. Ob odnom obobshchenii rukzachnoi kriptosistemi [On a generalization of a knapsack cryptosystem]. Izv. vuzov Sev.-Kavk. reg. [Bulletin of the Universities of the Nord Caucasus region], 2003, no. 5, pp. 18-25.]
- Осипян В.О. О системе защиты информации на основе функционального рюкзака // Вопросы защиты информации. 2004. № 4. С. 16-18. [Osipyan V.O. O sisteme zashchity informatcii na osnove funktcional'nogo rukzaka [On a security system based on functional knapsack]. Voprosy zashchity informatcii [Question of information's security], 2004, no. 4, pp. 16-18.]
- Осипян В.О. О системе защиты информации на основе проблемы рюкзака // Известия Томского политехнического университета. 2006. Т. 309. № 2. С. 209-212. [Osipyan V.O. O sisteme zashchity informatcii na osnove problemy rukzaka [On a security system based on knapsack's problem]. Izvestiya Tomskogo Politekhnicheskogo universiteta [Bulletin of Tomsk politechnical University], 2006, vol. 309, no 2, pp. 209-212.]
- Осипян В.О., Арутюнян А.С., Спирина С.Г. Моделирование ранцевых криптосистем, содержащих диофантовую трудность // Чебышевский сборник. 2010. Т. XI. Вып. 1. С. 209-217. [Osipyan V.O., Harutunyan A.S., Spirina C.G. Modelirovanie rantcevyh kriptosistem, sodergashchikh diophantovuyu trudnost' [Modelling of knapsack cryptosystem Diophantine difficulty contains]. Chebyshevskii sbornik [Chebyshev's digest], 2010, vol. XI, no. 1, pp. 209-217.]
- Осипян В.О., Карпенко Ю.А., Жук А.С., Арутюнян А.Х. Диофантовы трудности атак на нестандартные рюкзачные системы защиты информации // Известия ЮФУ. Технические науки. 2013. № 12. С. 209-215. [Osipyan V.O., Kerpenko Y.A., Zhuk A.S., Harutunyan A.H. Diofantovy trudnosti atak na nestandartnye rukzachnye sistemy zashchity informatcii [Diophantine difficulties of attacks on non-standard knapsack security systems]. Izvestiya UFU. Tekhnicheskie nauki [Bulletin of South Federal University. Technical sciences]. 2013, no. 12, pp. 209-215.]
- Osipyan V.O. Information protection systems based on universal knapsack problem // SIN'13 Proceedings of the 6th International Conference on Security of Information and Networks, ACM, 2013. P. 343-346.
- Lenstra, Jr. H.W. Integer Programming with a Fixed Number of Variables // Mathematics of Operations Research. 1983. Vol. 8. No. 4. pp. 538-548.
- Vaudenay S. Cryptanalysis of the Chor-Rivest cryptosystem. Advances in Cryptology - CRYPTO '98: Proc. of 18th Annual International Cryptology Conference Santa Barbara, California, USA August 23–27, 1998. P. 243-256. DOI: 10.1007/BFb0055732
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Copyright (c) 2017 Осипян В.О., Лейман А.В., Чесебиев А.А., Жук А.С., Арутюнян А.Х., Карпенко Ю.А.
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