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

한국전자통신학회 (Korea Institute of Electronic Communication Science)
권호 표지
DOI QR코드

DOI QR Code

대칭 1차원 5-이웃 CA 기반의 키 수열 생성기 설계

Design of Key Sequence Generators Based on Symmetric 1-D 5-Neighborhood CA

  • 투고 : 2021.04.06
  • 심사 : 2021.06.17
  • 발행 : 2021.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

시스템의 성능을 평가하기 위하여 1차원 3-이웃 셀룰라 오토마타(Cellular Automata, 이하 CA) 기반의 의사 난수 생성기가 여러 분야에서 많이 응용되고 있다. 보다 더 효과적인 키 수열 생성을 위해 2차원 CA와 1차원 5-이웃 CA가 응용되었으나, 주어진 특성 다항식에 대응하는 대칭 1차원 5-이웃 CA를 설계하는 것은 매우 어려운 문제이다. 이를 해결하기 위해 특성 다항식의 점화식을 이용한 합성 방법, Krylov 행렬을 이용한 합성 방법과 같이 1차원 5-이웃 CA 합성에 관한 연구들이 진행되었다. 그러나 여전히 비선형 방정식을 풀어야 하는 문제점이 있었다. 이러한 문제점을 해결하기 위해, 최근 90/150 CA의 전이 행렬과 블록행렬을 이용한 1차원 5-이웃 CA 합성 방법이 제안되었다. 본 논문에서는 제안된 알고리즘의 이론적인 과정을 상세히 기술하고 그 알고리즘을 이용하여 높은 차수의 원시 다항식에 대응하는 대칭 1차원 5-이웃 CA를 구한다.

To evaluate the performance of a system, one-dimensional 3-neighborhood cellular automata(CA) based pseudo-random generators are widely used in many fields. Although two-dimensional CA and one-dimensional 5-neighborhood CA have been applied for more effective key sequence generation, designing symmetric one-dimensional 5-neighborhood CA corresponding to a given primitive polynomial is a very challenging problem. To solve this problem, studies on one-dimensional 5-neighborhood CA synthesis, such as synthesis method using recurrence relation of characteristic polynomials and synthesis method using Krylov matrix, were conducted. However, there was still a problem with solving nonlinear equations. To solve this problem, a symmetric one-dimensional 5-neighborhood CA synthesis method using a transition matrix of 90/150 CA and a block matrix has recently been proposed. In this paper, we detail the theoretical process of the proposed algorithm and use it to obtain symmetric one-dimensional 5-neighborhood CA corresponding to high-order primitive polynomials.

키워드

과제정보

본 논문은 2019학년도 인제대학교 학술연구조성비 보조에 의한 것임.

참고문헌

  1. J. Von 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. Los Alamitos: 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. 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
  5. S. Cho, H. Kim, U. Choi, and S. Kang, "Synthesis of symmetric 1-D 5-neighborhood CA using Krylov matrix," J. of the Korea Institute of Electronic Communication Sciences, vol. 15, no. 6, Dec. 2020, pp. 1105-1111. https://doi.org/10.13067/JKIECS.2020.15.6.1105
  6. U. Choi, S. Cho, and S. Kang, "1-D symmetric 5-neighbor MLCA based color image encryption," 2021 IEEE the 6th Int. Conf. on Computer and Communication Systems, Chengdu, China, vol. 1, Apr. 2021. pp. 1-6.
  7. 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
  8. 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.
  9. H. M. Ghadirli, A. Nodehi, and R. Enayatifar, "An overview of encryption algorithms in color images," Signal Processing, vol. 164, Nov. 2019, pp. 163-185. https://doi.org/10.1016/j.sigpro.2019.06.010
  10. Z. Mehmahad and A. Latif, "A novel image encryption scheme based on reversible cellular automata and chaos," I. J. Information Technology and Computer Science, vol. 11, no. 1, Apr. 2019, pp. 15-23.
  11. 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.
  12. 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
  13. S. Maiti and D. R. Chowdhury, "Study of five-neighborhood linear hybrid cellular automata and their synthesis," ICMC 2017, CCIS 655, Apr. 2017, pp. 68-83.
  14. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge : Cambridge Univ. Press, 1985.