Behaviors of Single Attractor Cellular Automata over Galois Field GF(2p)

  • Sung-Jin Cho
  • Un-Sook Choi
  • Yoon-Hee Hwang
  • Han-Doo Kim
  • Hyang-Hee Choi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4173)

Abstract

In this paper, we analyze behaviors of state transitions of a linear Single Attractor Cellular Automata(SACA) C and the complemented SACA C′ derived from C over Galois Field GF(2p). And we propose the algorithm for the construction of the state transition diagram of C and C′ over GF(2p) by using the new concept of basic path. These results extend the results over GF(2) of Cho et al. for SACA.

References

  1. 1.
    Von Neumann, J.: Theory of self-reproducing automata. University of Illinois Press, Urbana (1966)Google Scholar
  2. 2.
    Wolfram, S.: Statistical mechanics of cellular automata. Rev. Modern Physics 55, 601–644 (1983)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Das, A.K., Chaudhuri, P.P.: Efficient characterization of cellular automata. Proc. IEE(Part E) 137, 81–87 (1990)Google Scholar
  4. 4.
    Das, A.K., Chaudhuri, P.P.: Vector space theoretic analysis of additive cellular automata and its application for pseudo-exhaustive test pattern generation. IEEE Trans. Comput. 42, 340–352 (1993)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Tsalides, P., York, T.A., Thanailakis, A.: Pseudo-random number generators for VLSI systems based on linear cellular automata. IEE Proc. E. Comput. Digit. Tech. 138, 241–249 (1991)CrossRefGoogle Scholar
  6. 6.
    Nandi, S., Kar, B.K., Chaudhuri, P.P.: Theory and applications of cellular automata in cryptography. IEEE Trans. Computers 43, 1346–1357 (1994)CrossRefGoogle Scholar
  7. 7.
    Paul, K.: Theory and application of GF(2p) cellular automata, Ph. D. Thesis, B.E. College (Deemed University), Howrah, India (2002)Google Scholar
  8. 8.
    Chattopadhyay, C.: Some studies on theory and applications of additive cellular automata, Ph. D. Thesis, I.I.T., Kharagpur, India (2002)Google Scholar
  9. 9.
    Sen, S., Shaw, C., Chowdhury, D.R., Ganguly, N., Chaudhuri, P.P.: Cellular automata based cryptosystem. In: Deng, R.H., Qing, S., Bao, F., Zhou, J. (eds.) ICICS 2002. LNCS, vol. 2513, pp. 303–314. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Cho, S.J., Choi, U.S., Hwang, Y.H., Pyo, Y.S., Kim, H.D., Heo, S.H.: Computing phase shifts of maximum-length 90/150 cellular automata sequences. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds.) ACRI 2004. LNCS, vol. 3305, pp. 31–39. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Cho, S.J., Choi, U.S., Kim, H.D.: Analysis of complemented CA derived from a linear TPMACA. Computers and Mathematics with Applications 45, 689–698 (2003)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Cho, S.J., Choi, U.S., Kim, H.D.: Behavior of complemented CA whose complement vector is acyclic in a linear TPMACA. Mathematical and Computer Modelling 36, 979–986 (2002)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Sikdar, B.K., Majumder, P., Mukherjee, M., Ganguly, N., Das, D.K., Chaudhuri, P.P.: Hierarchical cellular automata as an on-chip test pattern generator. In: VLSI Design, Fourteenth International Conference on 2001, pp. 403–408 (2001)Google Scholar
  14. 14.
    Sikdar, B.K., Ganguly, N., Majumder, P., Chaudhuri, P.P.: Design of multiple attractor GF(2p) cellular automata for diagnosis of VLSI circuits. In: VLSI Design, Fourteenth International Conference on 2001, pp. 454–459 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sung-Jin Cho
    • 1
  • Un-Sook Choi
    • 2
  • Yoon-Hee Hwang
    • 3
  • Han-Doo Kim
    • 4
  • Hyang-Hee Choi
    • 5
  1. 1.Division of Mathematical SciencesPukyong National UniversityBusanKorea
  2. 2.Department of Multimedia EngineeringTongmyong UniversityBusanKorea
  3. 3.Department of Information SecurityGraduate School, Pukyong National UniversityBusanKorea
  4. 4.Institute of Mathematical Sciences and School of Computer Aided ScienceInje UniversityGimhaeKorea
  5. 5.Department of Applied MathematicsPukyong National UniversityBusanKorea

Personalised recommendations