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.
This work was supported by grant No.(R01-2003-000-10663-0) from the Basic Research Program of the Korea Science and Engineering Foundation.
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References
Von Neumann, J.: Theory of self-reproducing automata. University of Illinois Press, Urbana (1966)
Wolfram, S.: Statistical mechanics of cellular automata. Rev. Modern Physics 55, 601–644 (1983)
Das, A.K., Chaudhuri, P.P.: Efficient characterization of cellular automata. Proc. IEE(Part E) 137, 81–87 (1990)
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)
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)
Nandi, S., Kar, B.K., Chaudhuri, P.P.: Theory and applications of cellular automata in cryptography. IEEE Trans. Computers 43, 1346–1357 (1994)
Paul, K.: Theory and application of GF(2p) cellular automata, Ph. D. Thesis, B.E. College (Deemed University), Howrah, India (2002)
Chattopadhyay, C.: Some studies on theory and applications of additive cellular automata, Ph. D. Thesis, I.I.T., Kharagpur, India (2002)
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)
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)
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)
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)
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)
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)
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Cho, SJ., Choi, US., Hwang, YH., Kim, HD., Choi, HH. (2006). Behaviors of Single Attractor Cellular Automata over Galois Field GF(2p). In: El Yacoubi, S., Chopard, B., Bandini, S. (eds) Cellular Automata. ACRI 2006. Lecture Notes in Computer Science, vol 4173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861201_28
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DOI: https://doi.org/10.1007/11861201_28
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