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

Korea Institute of Electronic Communication Science (한국전자통신학회)
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Synthesis of Symmetric 1-D 5-neighborhood CA using Krylov Matrix

Krylov 행렬을 이용한 대칭 1차원 5-이웃 CA의 합성

  • 조성진 (부경대학교 응용수학과) ;
  • 김한두 (인제대학교 컴퓨터공학부) ;
  • 최언숙 (동명대학교 정보통신공학과) ;
  • 강성원 (부경대학교 정보보호학과)
  • Received : 2020.09.08
  • Accepted : 2020.12.15
  • Published : 2020.12.31
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Abstract

One-dimensional 3-neighborhood Cellular Automata (CA)-based pseudo-random number generators are widely applied in generating test patterns to evaluate system performance and generating key sequence generators in cryptographic systems. In this paper, in order to design a CA-based key sequence generator that can generate more complex and confusing sequences, we study a one-dimensional symmetric 5-neighborhood CA that expands to five neighbors affecting the state transition of each cell. In particular, we propose an n-cell one-dimensional symmetric 5-neighborhood CA synthesis algorithm using the algebraic method that uses the Krylov matrix and the one-dimensional 90/150 CA synthesis algorithm proposed by Cho et al. [6].

1차원 3-이웃 셀룰라 오토마타(Cellular Automata, 이하 CA) 기반의 의사난수 생성기는 시스템의 성능을 평가하기 위한 테스트 패턴 생성과 암호 시스템의 키수열 생성기 등에 많이 응용되고 있다. 본 논문에서는 더 복잡하고 혼돈스러운 수열을 생성할 수 있는 CA기반의 키 수열 생성기를 설계하기 위해 각 셀의 상태전이에 영향을 주는 이웃을 5개로 확장한 1차원 대칭 5-이웃 CA에 대해 연구한다. 특히 대칭 5-이웃 CA를 합성하기 위해 Krylov 행렬을 이용하는 대수적인 방법과 Cho et al.의 알고리즘을 기반으로 한 1차원 n셀 대칭 5-이웃 CA 합성 알고리즘을 제안한다.

Keywords

References

  1. J. V. Neumann, Theory of self-reproducing automata. Urbana and London: University of Illinois Press, 1966.
  2. P. P. Chaudhuri, D. R. Chowdhury, S. Nandi, and S. Chattopadhyay, Additive cellular automata, Theory and applications, vol. 1. Los Alamitos, California: IEEE Computer Society Press, 1997.
  3. H. Kim, S. Cho, U. Choi, M. Kwon, and G. Kong, "Synthesis of uniform CA and 90/150 hybrid CA," J. of the Korea Institute of Electronic Communication Sciences, vol. 11, no. 3, Mar. 2016, pp. 293-302. https://doi.org/10.13067/JKIECS.2016.11.3.293
  4. U. Choi and S. Cho, "Analysis of Pseudorandom Sequences Generated by Maximum Length Complemented Cellular Automata," J. of the Korea Institute of Electronic Communication Sciences, vol. 14, no. 5, 2019, pp. 1001-1008.
  5. U. Choi, S. Cho, H. Kim and S. Kang, "Design and Analysis of Pseudorandom Number Generators Based on Programmable Maximum Length CA," J. of the Korea Institute of Electronic Communication Sciences, vol. 15, no. 2, 2020, pp. 319-326. https://doi.org/10.13067/JKIECS.2020.15.2.319
  6. S. Cho, U. Choi, H. Kim, Y. Hwang, J. Kim, and S. Heo, "New synthesis of one-dimensional 90/150 linear hybrid group cellular automata," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, vol. 26, no. 9, Sept. 2007, pp. 1720-1724. https://doi.org/10.1109/TCAD.2007.895784
  7. U. Choi, S. Cho, H. Kim, and J. Kim, "90/150 CA corresponding to polynomial of maximum weight," J. of Cellular Automata, vol. 13, no. 4, 2018, pp. 347-358.
  8. U. Choi, S. Cho, H. Kim, and M. Kwon, "Analysis of 90/150 CA corresponding to the power of irreducible polynomials," J. of Cellular Automata, vol. 14, no. 5-6, 2019, pp. 417-433.
  9. H. Jeong, S. Cho, and S. Kim, "Medical image encryption based on C-MLCA and 1D CAT," J. of the Korea Institute of Electronic Communication Sciences, vol. 14, no. 2, Apr. 2019, pp. 439-446. https://doi.org/10.13067/JKIECS.2019.14.2.439
  10. J. Jose and D. R. Chowdhury, "Four neighborhood cellular automata as better cryptographic primitives," IACR Cryptology ePrint Archive 2015, vol. 700, 2015, pp. 74-82.
  11. S. Maiti and D. R. Chowdhury, "Study of five-neighborhood linear hybrid cellular automata and their synthesis," International Conference on Mathematics and Computing, vol. 655, 2017, pp. 68-83.
  12. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U. K.: Cambridge Univ. Press, 1985.
  13. M. Serra and T. Slater, "A Lanczos algorithm in a finite field and its application," J. Comb. Math. Comput., vol. 7, 1990, pp. 11-32.