Mathematical modeling of non-standard multiplicative knapsack cryptosystems

Authors

  • Osipyan V.O. Kuban State University, Krasnodar, Российская Федерация
  • Leyman A.V. Kuban State University, Krasnodar, Российская Федерация
  • Chesebiev A.A. Kuban State University, Krasnodar, Российская Федерация
  • Zhuk A.S. Kuban State University, Krasnodar, Российская Федерация
  • Harutyunyan A.Kh. Kuban State University, Krasnodar, Российская Федерация
  • Karpenko Yu.A. Adyghe State University, Krasnodar, Российская Федерация

UDC

519.72

Abstract

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 knapsack

Author Infos

Valeriy O. Osipyan

д-р физ.-мат. наук, доцент, профессор кафедры информационных технологий Кубанского государственного университета

e-mail: rrwo@mail.ru

Antonina V. Leyman

преподаватель кафедры информационных технологий Кубанского государственного университета

e-mail: antonina.leyman@gmail.com

Asker A. Chesebiev

соискатель кафедры информационных технологий Кубанского государственного университета

e-mail: kit@fpm.kubsu.ru

Arseniy S. Zhuk

соискатель кафедры информационных технологий Кубанского государственного университета

e-mail: arseniyzhuck@mail.ru

Ashot Kh. Harutyunyan

преподаватель кафедры прикладной математики Кубанского государственного университета

e-mail: ashotikmail.ru@mail.ru

Yuriy A. Karpenko

старший преподаватель кафедры алгебры и геометрии Адыгейского государственного университета

e-mail: nart27@gmail.com

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Issue

2017. No. 2

Pages

57-64

Submitted

2017-04-18

Published

2017-06-30

How to Cite

Osipyan V.O., Leyman A.V., Chesebiev A.A., Zhuk A.S., Harutyunyan A.Kh., Karpenko Yu.A. Mathematical modeling of non-standard multiplicative knapsack cryptosystems. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2017, no. 2, pp. 57-64. (In Russian)

Copyright (c) 2017 Osipyan V.O., Leyman A.V., Chesebiev A.A., Zhuk A.S., Harutyunyan A.Kh., Karpenko Yu.A.

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