research-article

Mathematical model of the polyalphabetic information security system based on the normal generalized knapsack

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Osipyan V.O.Authors Info & Claims

SIN '14: Proceedings of the 7th International Conference on Security of Information and Networks

Pages 180 - 185

https://doi.org/10.1145/2659651.2659658

Published: 09 September 2014 Publication History

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.

References

[1]

Shannon C. Communication theory of secrecy systems, Bell System Techn. J. 28, No 4--1949. P. 656--715.

[2]

Ginzburg B.D.// Problems of cybernetics 1967, v.19, p. 249--252.

[3]

Diffie W., Hellman M. New directions in cryptography // IEEE Transactions on Information Theory. -- 1976. -- Vol. 22. -- P. 644--654.

Digital Library

[4]

Merkle R., Hellman M. Hiding information and signatures in trapdoor knapsacks // IEEE Transactions on Information Theory. 1978. Vol. IT -- 24. P. 525--530.

Digital Library

[5]

Merkle R., Hellman M. On the security of multiple encryption // Communications of the ACM. -- 1981. -- Vol. 24. P. 465--467.

Digital Library

[6]

Lenstra A.K., Lenstra H.W., Lovasz L. Factoring polynomials with rational coefficients // Mathematische Annalen. 1982. Vol. 261. P. 515--534.

[7]

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.

Digital Library

[8]

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.

Digital Library

[9]

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.

Digital Library

[10]

Salomaa A. Public-Key Cryptography Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona.

[11]

Koblitz N. A Course in Number Theory and Cryptography. Springer-Verlag New York. 1987.

Digital Library

[12]

Schneir B. Applied Cryptography: Protocols, Algorithms and Source Code in C, 2nd edition. New York: J. Wiley & Sons, 1996.

Digital Library

[13]

Martello S. T.P. Knapsack problems: algorithms and computer implementations // Chichester: JOHN WILEY & SONS. --1990.-- P. 137--138.

Digital Library

[14]

Vaudenay S. Cryptanalysis of the Chor-Rivest cryptosystem // CRYPTO. -- 1998. -- P. 243--256.

Digital Library

[15]

Osipyan V.O. On One Generalization of Knapsack Cryptosystems // Izv. vuzov. Northern-Caucasus area. Tech. science. -- 2003. -- Appendix No 5. -- p. 18--25.

[16]

Osipyan V.O. Information protection systems based on functional knapsack problem // Voprosi zachiti informatsi. -- M., 2004.-- No 4. -- c.16--19.

[17]

Osipyan V.O. On Information Protection System Based on the Knapsack Problem // Izv. vuzov. Tomsk Polytechnical University. -- 2006. -- v. 309. -- No2. -- p. 209--212.

[18]

Osipyan V.O. Generalization of open key knapsack cryptosystems // Security of Information and Networks (SIN 2007). Trafford, 2008. P. 58--63.

[19]

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.

Digital Library

[20]

Osipyan V.O. Building of data protection knapsacks cryptosystems with Diophantine problems. LAP LAMBERT Academic Publishing, 2012.

[21]

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.

Digital Library

[22]

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.

Digital Library

[23]

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.

Cited By

Osipyan VTlusten VLaktionova NVakhrusheva NShekhawat RGaur MElci AVaidya JMakarevich OPoet ROrgun MDhaka VBohra MSingh VBabenko LSheykhkanloo NRahnama B(2017)The duality principle in the theory of development generalized A-M knapsack cryptosystemsProceedings of the 10th International Conference on Security of Information and Networks10.1145/3136825.3136898(200-205)Online publication date: 13-Oct-2017
https://dl.acm.org/doi/10.1145/3136825.3136898
Osipyan VMakarevich OPoet RElçi AGaur MOrgun MBabenko LFerdous SHo ALaxmi VPieprzyk J(2015)Mathematical modelling of cryptosystems based on Diophantine problem with gamma superposition methodProceedings of the 8th International Conference on Security of Information and Networks10.1145/2799979.2800026(338-341)Online publication date: 8-Sep-2015
https://dl.acm.org/doi/10.1145/2799979.2800026

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Mathematical model of the polyalphabetic information security system based on the normal generalized knapsack

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SIN '14: Proceedings of the 7th International Conference on Security of Information and Networks

September 2014

518 pages

ISBN:9781450330336

DOI:10.1145/2659651

Conference Chair:
Ron Poet
University of Glasgow, UK
,
Program Chair:
Raj Muttukrishnan
City University, UK

Copyright © 2014 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

In-Cooperation

SIGSAC: ACM Special Interest Group on Security, Audit, and Control
MNIT: Malaviya National Institute of Technology
Aksaray Univ.: Aksaray University
SICSA: The Scottish Informatics and Computer Science Alliance
University of Glasgow: University of Glasgow

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Association for Computing Machinery

New York, NY, United States

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Published: 09 September 2014

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SIN '14

SIN '14: The 7th International Conference on Security of Information and Networks

September 9 - 11, 2014

Scotland, Glasgow, UK

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SIN '14 Paper Acceptance Rate 32 of 109 submissions, 29%;

Overall Acceptance Rate 102 of 289 submissions, 35%

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Cited By

Osipyan VTlusten VLaktionova NVakhrusheva NShekhawat RGaur MElci AVaidya JMakarevich OPoet ROrgun MDhaka VBohra MSingh VBabenko LSheykhkanloo NRahnama B(2017)The duality principle in the theory of development generalized A-M knapsack cryptosystemsProceedings of the 10th International Conference on Security of Information and Networks10.1145/3136825.3136898(200-205)Online publication date: 13-Oct-2017
https://dl.acm.org/doi/10.1145/3136825.3136898
Osipyan VMakarevich OPoet RElçi AGaur MOrgun MBabenko LFerdous SHo ALaxmi VPieprzyk J(2015)Mathematical modelling of cryptosystems based on Diophantine problem with gamma superposition methodProceedings of the 8th International Conference on Security of Information and Networks10.1145/2799979.2800026(338-341)Online publication date: 8-Sep-2015
https://dl.acm.org/doi/10.1145/2799979.2800026

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