ABSTRACT
The mathematical model of cryptosystem based on the method of gamma superposition, in which the algorithm of the inverse transformation of the closed text is reduced to the impossibility of problem solution is developed. The multiplicative knapsack task is generalized and the problem of working out of alphabetic cryptosystems mathematical models is considered. The mathematical models of such cryptosystems are offered in the article. The investigation is based on the C. Shannon, who considered, that cryptosystems containing Diophantine difficulties, possesses the greatest uncertainty of key selection process. Necessary and suffitient conditions at which generalized multiplicative knapsack is injective on Zp, p . 2, are established. The problem of building the isomorphic additive and multiplicative knapsacks is also considered.
- Shannon C. Communication theory of secrecy systems, Bell System Techn. J. 28, No. 4 - 1949. P. 656-715.Google ScholarCross Ref
- 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 scheme // IEEE Transactions on Information Theory. - Jul 1984. - vol. IT-30, No. 4. - 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 nonstandard Knapsack Problem // Izv. vuzov. Tomsk Polytechnical University. - 2006. - v. 309. - No. 2. - 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. Building 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. Mathematical model of the polyalphabetic information security system based on the normal generalized knapsack // SIN'14 Proceedings of the 6th International Conference on Security of Information and Networks, ACM, 2014, pp.123-128. Google ScholarDigital Library
Index Terms
- Mathematical modelling of cryptosystems based on Diophantine problem with gamma superposition method
Recommendations
Building 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 NetworksThe theorems about equal power knapsacks, components of which are the parametrical solution of Tarry-Ascot multistage Diophantine equation system or the numerical solution of such a system were formulated. Mathematical models of alphabet cryptosystems, ...
Multivariate public key cryptosystems from diophantine equations
Wang et al. introduced in (A medium-field multivariate public-key encryption scheme. Topics in Cryptology--CTRSA 2006: The Cryptographers' Track at the RSA Conference, 2006) a multivariate public key cryptosystem, called MFE cryptosystem, and it is ...
Securely combining public-key cryptosystems
CCS '01: Proceedings of the 8th ACM conference on Computer and Communications SecurityIt is a maxim of sound computer-security practice that a cryptographic key should have only a single use. For example, an RSA key pair should be used only for public-key encryption or only for digital signatures, and not for both.In this paper we show ...
Comments