ABSTRACT
This publication is an expanded text of some works and implementations of new ideas of the author, so it does not purport to light-theoretic studies of non-standard knapsack problem. More information can be found in works the author. This paper considers class of polyalphabetic cryptosystems with the open key based on a non-standard knapsack with new generalized Merkle-Hellman scheme. We propose the algorithm of packing the normal generalized knapsack with predetermined threshold value p and cryptosystem with the open key based on p-ary Warshamov's code with generalized knapsack's function. Unlike standard knapsacks, components of the normal generalized knapsack can may be various as be-tween themselves and repeat given set number of times.
- Shannon C. Communication theory of secrecy systems, Bell System Techn. J. 28, No 4--1949. P. 656--715.Google Scholar
- Ginzburg B.D.// Problems of cybernetics 1967, v.19, p. 249--252.Google Scholar
- Diffie W., Hellman M. New directions in cryptography // IEEE Transactions on Information Theory. -- 1976. -- Vol. 22. -- P. 644--654. Google ScholarDigital Library
- Merkle R., Hellman M. Hiding information and signatures in trapdoor knapsacks // IEEE Transactions on Information Theory. 1978. Vol. IT -- 24. P. 525--530. Google ScholarDigital Library
- Merkle R., Hellman M. On the security of multiple encryption // Communications of the ACM. -- 1981. -- Vol. 24. P. 465--467. Google ScholarDigital Library
- Lenstra A.K., Lenstra H.W., Lovasz L. Factoring polynomials with rational coefficients // Mathematische Annalen. 1982. Vol. 261. P. 515--534.Google Scholar
- Shamir A. A polynomial-time algorithm for breaking the basic Merkle-Hellman cryptosystem // Information Theory, IEEE Transactions. -- 1984. -- Vol. 30, No 5. -- P. 699--704. Google ScholarDigital Library
- Odlyzhko A.O. Cryptanalytic attacks on the multiplicative knapsack cryptosystem and on Shamir's fast signature sceme // IEEE Transactions on Information Theory. -- Jul 1984. -- vol. IT-30, No4. -- p. 594--601. Google ScholarDigital Library
- Chor B., Rivest R. A knapsack-type public key cryptoystem based on arithmetic in finite fields//IEEE Transactions on Information Theory. 1988. Vol. IT -- 34. P. 901--909. Google ScholarDigital Library
- Salomaa A. Public-Key Cryptography Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona.Google Scholar
- Koblitz N. A Course in Number Theory and Cryptography. Springer-Verlag New York. 1987. Google ScholarDigital Library
- Schneir B. Applied Cryptography: Protocols, Algorithms and Source Code in C, 2nd edition. New York: J. Wiley & Sons, 1996. Google ScholarDigital Library
- Martello S. T.P. Knapsack problems: algorithms and computer implementations // Chichester: JOHN WILEY & SONS. --1990.-- P. 137--138. Google ScholarDigital Library
- Vaudenay S. Cryptanalysis of the Chor-Rivest cryptosystem // CRYPTO. -- 1998. -- P. 243--256. Google ScholarDigital Library
- Osipyan V.O. On One Generalization of Knapsack Cryptosystems // Izv. vuzov. Northern-Caucasus area. Tech. science. -- 2003. -- Appendix No 5. -- p. 18--25.Google Scholar
- Osipyan V.O. Information protection systems based on functional knapsack problem // Voprosi zachiti informatsi. -- M., 2004.-- No 4. -- c.16--19.Google Scholar
- Osipyan V.O. On Information Protection System Based on the Knapsack Problem // Izv. vuzov. Tomsk Polytechnical University. -- 2006. -- v. 309. -- No2. -- p. 209--212.Google Scholar
- Osipyan V.O. Generalization of open key knapsack cryptosystems // Security of Information and Networks (SIN 2007). Trafford, 2008. P. 58--63.Google Scholar
- Osipyan V.O. Different models of information protection system, based on the functional knapsack // SIN'11 Proceedings of the 4th international conference on Security of information and networks, ACM, 2011. pp 215--218. Google ScholarDigital Library
- Osipyan V.O. Building of data protection knapsacks cryptosystems with Diophantine problems. LAP LAMBERT Academic Publishing, 2012.Google Scholar
- Osipyan V.O. Buiding of alphabetic data protection cryptosystems on the base of equal power knapsacks with Diophantine problems // SIN'12 Proceedings of the Fifth International Conference on Security of Information and Networks, ACM, 2012, pp.124--129. Google ScholarDigital Library
- 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, pp.343--346. Google ScholarDigital Library
- Osipyan V.O., Karpenko Y.A., Zhuck A.S., Arutyunyan A.H. Diophantine difficulties of attacks on non-standard knapsacks information security systems // Izvestiya YFU, No12(149), 2013, pp. 209--215.Google Scholar
Index Terms
Mathematical model of the polyalphabetic information security system based on the normal generalized knapsack
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