Secure Pseudo-Random Linear Binary Sequences Generators Based on Arithmetic Polynoms

  • Oleg FinkoEmail author
  • Sergey Dichenko
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 342)


We present a new approach to construction of pseudo-random binary sequences (PRBS) generators for the purpose of cryptographic data protection, secured from the perpetrator’s attacks, caused by generation of masses of hardware errors and faults. The new method is based on the use of linear polynomial arithmetic for the realization of systems of boolean characteristic functions of pseudo-random sequences (PRS) generators. “Arithmetization” of systems of logic formulas has allowed to apply mathematical apparatus of residue systems for multisequencing of the process of PRS generation and organizing control of computing errors, caused by hardware faults. This has guaranteed high security of PRS generator’s functioning and, consequently, security of tools for cryptographic data protection based on those PRSs.


Cryptographic data protection Pseudo-random binary sequences Residue number systems 


  1. 1.
    Forouzan, B.A.: Cryptography and Network Security. McGraw Hill (2008)Google Scholar
  2. 2.
    Schneier, B.: Applied Cryptography. Wiley, New York (1996)Google Scholar
  3. 3.
    Yang, B., Wu, K., Karri, R.: Scan based side channel attack on data encryption standard. Report 2004(324), 114–116 (2004)Google Scholar
  4. 4.
    Hetagurov, J.A., Prudnaya, Y.P.: Improving the reliability of digital devices redundant coding methods. Energiya, Moscow (1974)Google Scholar
  5. 5.
    Kelsey, J.: Protocol interactions and the chosen protocol attack. Security protocols. In: 5th International Workshop, pp. 91–104, Springer New York. (1996)Google Scholar
  6. 6.
    Ortega, J.M.: Introduction to Parallel & Vector Solution of Linear Systems. Plenum Press, New York (1988)CrossRefzbMATHGoogle Scholar
  7. 7.
    Shmerko, V.P.: Malyugin’s theorems: a new concept in logical control, VLSI design, and data structures for new technologies. Autom. Remote. Control. 65(6), 893–912 (2004). JuneCrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Finko, O.A.: Large systems of boolean functions: realization by modular arithmetic methods. Autom. Remote. Control. 65(6), 871–892 (2004). JuneCrossRefMathSciNetGoogle Scholar
  9. 9.
    Garner, H.L.: Number systems and arithmetic. Adv. Comput. 6, 131–194 (1965)CrossRefzbMATHGoogle Scholar
  10. 10.
    Omondi, A., Premkumar, B.: Residue Number System: Theory and Implementation. Imperial College Press, London (2007)Google Scholar
  11. 11.
    Soderstrand, M.A., Jenkins, W.K., Jullien, G.A., Tailor, F.J.: Residue Number System Arithmetic: Modern Application in Digital Signal Processing. IEEE Press, New York (1986)Google Scholar
  12. 12.
    Jenkins, W.K.: The design of error checkers for self-checking residue number arithmetic. IEEE Trans. Comput. 4, 388–396 (1983)CrossRefGoogle Scholar
  13. 13.
    Finko, O.A., Vishnevsky, A.K.: Parallel realization of systems of substitutions by numerical polynoms. In: Papers of the 5th International Conference Parallel Computing and Control Problems, pp. 935–943. Moscow (2010)Google Scholar
  14. 14.
    Finko, O.A., Vishnevsky, A.K.: Standard function hybrid cryptosystem arithmetic and logical multinomial realization. Theory and Techniques of Radio, pp. 32–38. Voronezh (2011)Google Scholar
  15. 15.
    Finko, O.A., Dichenko, S.A., Eliseev, N.I.: Error function generator binary PRS control implemented on arithmetic polynomials. St. Petersburg State Polytechnical University J. Comput. Sci. Telecommun. Control Syst. 176(4), 142–149 (2013)Google Scholar
  16. 16.
    Krasnobaev, V.A.: Reliable model in the computer residue number system. Electron. Model. 7(4), 44–46 (1985)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Computer Systems and Information Security of Kuban State Technological UniversityKrasnodarRussia

Personalised recommendations