The Journal of the Korea institute of electronic communication sciences (한국전자통신학회논문지)

Korea Institute of Electronic Communication Science (한국전자통신학회)
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Synthesis of 90/150 Uniform CA and Computation of Characteristic Polynomial corresponding to uniform CA

90/150 Uniform CA의 합성 및 특성다항식 계산

  • 최언숙 (동명대학교 미디어공학과) ;
  • 조성진 (부경대학교 응용수학과) ;
  • 임지미 (부경대학교 응용수학과)
  • Received : 2009.12.05
  • Accepted : 2010.01.10
  • Published : 2010.02.28
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Abstract

90/150 CA is a CA completely specified by using rule 90 and rule 150. Since 90/150 CA whose minimal and characteristic polynomials are identical has outstanding randomness, this CA is more attractive than LFSR. Sarkar proposed a scheme based on the 90 uniform CA and the 150 uniform CA. That scheme provided authentication by digital signature and other basic security requirements like confidentiality. In this paper we analyze 90 or 150 uniform CA and give a synthesis method of 2n-cell uniform CA and (2n+1)-cell uniform CA using a special n-cell 90/150 CA. And we propose an effective method of computation of characteristic polynomial corresponding to uniform CA.

전이 규칙 90과 150만을 사용하는 90/150 CA는 최소다항식과 특성다항식이 같은 CA로 랜덤성이 우수하여 LFSR의 대안으로 사용되어왔다. 90 Uniform CA와 150 uniform CA는 모든 셀에 동일한 전이규칙이 적용되는 CA로 기밀성과 인증을 제공하는 Sarkar의 암호기법에 사용되었다. 본 논문에서는 전이규칙이 90 또는 150인 uniform CA에 대하여 분석하고 특별한 전이규칙을 갖는 n-셀 90/150 CA를 이용하여 2n-셀 uniform CA와 (2n+1)-셀 uniform CA를 합성하고 대응하는 특성다항식을 계산하는 효율적 방법을 제안한다.

Keywords

References

  1. S. Wolfram, O. Martin and A. M. Odlyzko, "Algebraic properties of cellular automata," Communications in Mathematical Physics, 3, pp. 219-258, 1984.
  2. A.K. Das, "Additive Cellular Automata: Theory and Applications as a Built-In Self-Test Structure," Ph. D. Thesis, I.I.T. Kharagpur, India, 1990.
  3. A.K. Das and P.P. Chaudhuri, "Efficient characterization of cellular automata," Proc. IEE(Part E), Vol. 137, pp. 81-87, 1990.
  4. A.K. Das and P.P. Chaudhuri, "Vector space theoretic analysis of additive cellular automata and its application for pseudo-exhaustive test pattern generation," IEEE Trans. Comput., Vol. 42, pp. 340-352, 1993. https://doi.org/10.1109/12.210176
  5. S. Nandi, B.K. Kar and P.P. Chaudhuri, "Theory and applications of cellular automata in cryptography," IEEE Trans. Computers, Vol. 43, pp. 1346-1357, 1994. https://doi.org/10.1109/12.338094
  6. S. Chakraborty, D.R. Chowdhury, P.P. Chaudhuri, "Theory and application of nongroup cellular automata for synthesis of easily testable finite state machines," IEEE Trans. Computers, Vol. 45, pp. 769-781, 1996. https://doi.org/10.1109/12.508316
  7. S. Nandi and P.P. Chaudhuri, "Analysis of periodic and intermediate boundary 90/150 cellular automata," IEEE Trans. Computers, Vol. 45, pp. 1-12, 1996.
  8. S.J. Cho, U.S. Choi, Y.H. Hwang, Y.S. Pyo, H.D. Kim and S.H. Heo, "Computing Phase Shifts of Maximum-Length 90/150 Cellular Automata Sequences," LNCS, Vol. 3305, pp. 31-39, 2004.
  9. K. Cattell and J. Muzio, "Analysis of one-dimensional linear hybrid cellular automata over GF(q)," IEEE Transactions of Computers, Vol. 45, pp. 782-792, 1996. https://doi.org/10.1109/12.508317
  10. K. Cattell and J. Muzio, "Synthesis of one-dimensional linear hybrid cellular automata," IEEE Transactions on Computer-Aided Design of Integrated Circuit and Systems, Vol. 15, pp. 325-335, 1996. https://doi.org/10.1109/43.489103
  11. S.J. Cho, U.S. Choi, H.D. Kim and Y. H. Hwang, "New synthesis of one-dimensional 90/150 linear hybrid group cellular automata," IEEE Trans. Comput-Aided Des. Integr. Circuits Syst., Vol. 26(9), pp. 1720-1724, 2007. https://doi.org/10.1109/TCAD.2007.895784
  12. S. Chattopadhyay, "Some studies on theory and application of additive cellular automata," PhD thesis, I.I.T., Kharagpur, India, 1995.
  13. S.J. Cho, U.S. Choi, H.D. Kim and Y. H. Hwang, J.G. Kim, "Analysis of 90/150 Two Predecessor Nongroup Cellular Automata," ACRI 2008 LNCS Vol. 5191, pp. 128-135, 2008.
  14. S.K. Sarkar, T. Karmakar, A. Kumar, K. Sharma, P.C. Pradhan and C. Puttamadappa, "A One Dimensional Cellular Automata based Security Sheme providing both Authentication and Confidentiality," IE(I) Journal-CP, Vol. 87, pp. 1-8, 2006.