short-paper

Mathematical modelling of cryptosystems based on Diophantine problem with gamma superposition method

Author:

V. O. OsipyanAuthors Info & Claims

SIN '15: Proceedings of the 8th International Conference on Security of Information and Networks

Pages 338 - 341

https://doi.org/10.1145/2799979.2800026

Published: 08 September 2015 Publication History

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.

References

[1]

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

[2]

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

Digital Library

[3]

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

[4]

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

Digital Library

[5]

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

[6]

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

[7]

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.

Digital Library

[8]

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

[9]

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

[10]

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

Digital Library

[11]

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

Digital Library

[12]

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

Digital Library

[13]

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

Digital Library

[14]

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

[15]

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

[16]

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.

[17]

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

[18]

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

[19]

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

[20]

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.

Digital Library

[21]

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

[22]

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.

Digital Library

Cited By

Osipyan VLitvinov KZhuck A(2022)Research and development of the mathematic models of cryptosystems based on the universal Diophantine languageSHS Web of Conferences10.1051/shsconf/202214101020141(01020)Online publication date: 24-Jun-2022
https://doi.org/10.1051/shsconf/202214101020
Osipyan VLitvinov KBurnap PElçi ARana OReinecke PMoradpoor NTheodorakopoulos GKarabina K(2018)A mathematical model of the cryptosystem based on the linear Diophantine equationProceedings of the 11th International Conference on Security of Information and Networks10.1145/3264437.3264464(1-4)Online publication date: 10-Sep-2018
https://dl.acm.org/doi/10.1145/3264437.3264464
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

Index Terms

Mathematical modelling of cryptosystems based on Diophantine problem with gamma superposition method
1. Security and privacy
  1. Cryptography
    1. Public key (asymmetric) techniques
      1. Public key encryption

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 Networks

The 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 Security

It 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

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Other conferences

SIN '15: Proceedings of the 8th International Conference on Security of Information and Networks

September 2015

350 pages

ISBN:9781450334532

DOI:10.1145/2799979

Conference Chairs:
Oleg Makarevich
Southern Federal University, Russia
,
Ron Poet
University of Glasgow, UK
,
Atilla Elçi
Aksaray University, Turkey
,
Manoj Singh Gaur
Malaviya National Institute of Technology, India
,
Mehmet Orgun
Macquarie University, Australia
,
Program Chairs:
Ludmila Babenko
Southern Federal University, Russia
,
Sadek Ferdous
University of Glasgow, UK
,
Anthony T. S. Ho
University of Surrey, UK
,
Vijay Laxmi
Malaviya National Institute of Technology, India
,
Josef Pieprzyk
Queensland University of Technology, Australia

Copyright © 2015 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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 September 2015

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Short-paper

Conference

SIN '15

SIN '15: The 8th International Conference on Security of Information and Networks

September 8 - 10, 2015

Sochi, Russia

Acceptance Rates

SIN '15 Paper Acceptance Rate 34 of 92 submissions, 37%;

Overall Acceptance Rate 102 of 289 submissions, 35%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
39
Total Downloads

Downloads (Last 12 months)2
Downloads (Last 6 weeks)1

Reflects downloads up to 21 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Osipyan VLitvinov KZhuck A(2022)Research and development of the mathematic models of cryptosystems based on the universal Diophantine languageSHS Web of Conferences10.1051/shsconf/202214101020141(01020)Online publication date: 24-Jun-2022
https://doi.org/10.1051/shsconf/202214101020
Osipyan VLitvinov KBurnap PElçi ARana OReinecke PMoradpoor NTheodorakopoulos GKarabina K(2018)A mathematical model of the cryptosystem based on the linear Diophantine equationProceedings of the 11th International Conference on Security of Information and Networks10.1145/3264437.3264464(1-4)Online publication date: 10-Sep-2018
https://dl.acm.org/doi/10.1145/3264437.3264464
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

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents