Skip to main content
SpringerLink
Log in

Achieving Better Security Using Nonlinear Cellular Automata as a Cryptographic Primitive

  • Conference paper
  • First Online:
Mathematics and Computing (ICMC 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 834))

Included in the following conference series:

Abstract

Nonlinear functions are essential in different crypto-primitives as they play an important role on the security of a cipher design. Wolfram identified Rule 30 as a powerful nonlinear function for cryptographic applications. However, Meier and Staffelbach mounted an attack (MS attack) against Rule 30 Cellular Automata (CA). MS attack is a real threat on a CA based system. Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide better cryptographic primitives and they are also secure against MS attack.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. NIST SP 800-22: A statistical test suite for random and pseudorandom number generators for cryptographic applications. U.S. Department of Commerce (2010)

    Google Scholar 

  2. Bardell, P.: Analysis of cellular automata used as pseudorandom pattern generators. In: Proceedings of the IEEE International Test Conference 1990, Washington, D.C., 10–14 September 1990, pp. 762–768 (1990)

    Google Scholar 

  3. Cattell, K., Muzio, J.C.: Synthesis of one-dimensional linear hybrid cellular automata. IEEE Trans. CAD Integr. Circuits Syst. 15(3), 325–335 (1996)

    Article  Google Scholar 

  4. Chaudhuri, P.P., Roy Chowdhury, D., Nandi, S., Chattopadhyay, S.: Additive Cellular Automata: Theory and Applications. IEEE Computer Socity Press, New York (1997)

    MATH  Google Scholar 

  5. Formenti, E., Imai, K., Martin, B., Yunès, J.-B.: Advances on random sequence generation by uniform cellular automata. In: Calude, C.S., Freivalds, R., Kazuo, I. (eds.) Computing with New Resources. LNCS, vol. 8808, pp. 56–70. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13350-8_5

    Chapter  Google Scholar 

  6. Ghosh, S., Sengupta, A., Saha, D., Roy Chowdhury, D.: A scalable method for constructing non-linear cellular automata with period \(2^n - 1\). In: Cellular Automata: Proceedings of the 11th International Conference on Cellular Automata for Research and Industry, ACRI 2014, Krakow, Poland, 22–25 September 2014, pp. 65–74 (2014)

    Google Scholar 

  7. Jose, J., Roy Chowdhury, D.: Four neighbourhood cellular automata as better cryptographic primitives. IACR Cryptology ePrint Archive 2015, 700 (2015)

    Google Scholar 

  8. Lacharme, P., Martin, B., Sole, P.: Pseudo-random sequences, Boolean functions and cellular automata. In: Proceedings of Boolean Functions and Cryptographic Applications, pp. 80–95 (2008)

    Google Scholar 

  9. Leporati, A., Mariot, L.: 1-resiliency of bipermutive cellular automata rules. In: Kari, J., Kutrib, M., Malcher, A. (eds.) AUTOMATA 2013. LNCS, vol. 8155, pp. 110–123. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40867-0_8

    Chapter  MATH  Google Scholar 

  10. Maiti, S., Ghosh, S., Roy Chowdhury, D.: On the security of designing a cellular automata based stream cipher. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017, Part II. LNCS, vol. 10343, pp. 406–413. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59870-3_25

    Chapter  MATH  Google Scholar 

  11. Martin, B.: A Walsh exploration of elementary CA rules. Cell. Autom. 3(2), 145–156 (2008)

    MathSciNet  MATH  Google Scholar 

  12. Meier, W., Staffelbach, O.: Analysis of pseudo random sequences generated by cellular automata. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 186–199. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_17

    Chapter  Google Scholar 

  13. Neumann, J.V.: The Theory of Self-reproducing Automata. (Edited by A.W. Burks) University of Illinois Press, Urbana (1966)

    Google Scholar 

  14. Serra, M., Slater, T., Muzio, J.C., Miller, D.M.: The analysis of one-dimensional linear cellular automata and their aliasing properties. IEEE Trans. CAD Integr. Circuits Syst. 9(7), 767–778 (1990)

    Article  Google Scholar 

  15. Wolfram, S.: Cryptography with cellular automata. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 429–432. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-39799-X_32

    Chapter  Google Scholar 

  16. Wolfram, S.: Random sequence generation by cellular automata. In: Advances in Applied Mathematics, vol. 7, pp. 123–169 (1986)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indian Institute of Technology Kharagpur, Kharagpur, India

    Swapan Maiti & Dipanwita Roy Chowdhury

Authors
  1. Swapan Maiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dipanwita Roy Chowdhury
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Swapan Maiti or Dipanwita Roy Chowdhury .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology BHU, Varanasi, Uttar Pradesh, India

    Debdas Ghosh

  2. Haldia Institute of Technology, Haldia, India

    Debasis Giri

  3. University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  4. Istanbul Commerce University, Istanbul, Turkey

    Ekrem Savas

  5. Kyushu University, Fukuoka, Japan

    Kouichi Sakurai

  6. Indian Institute of Technology (BHU), Varanasi, India

    L. P. Singh

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Maiti, S., Roy Chowdhury, D. (2018). Achieving Better Security Using Nonlinear Cellular Automata as a Cryptographic Primitive. In: Ghosh, D., Giri, D., Mohapatra, R., Savas, E., Sakurai, K., Singh, L. (eds) Mathematics and Computing. ICMC 2018. Communications in Computer and Information Science, vol 834. Springer, Singapore. https://doi.org/10.1007/978-981-13-0023-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-0023-3_1

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0022-6

  • Online ISBN: 978-981-13-0023-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation