Skip to main content

Generating Expander Graphs Using Cellular Automata

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7495)

Abstract

The paper characterizes a special class of Cellular Automaton (CA) called Two Predecessor Single Attractor CA (TPSA-CA). We show that the transition graphs of the TPSA-CA can be used to realize pseudo-random regular graphs with good expansion properties. The elegance of the scheme lies in the fact that the storage required to capture the graph is O(log N), where N is the total number of vertices in the graph.

Keywords

  • expander graphs
  • Cellular Automata (CA)
  • Two-Predecessor Single Attractor CA (TPSA-CA)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Goldreich, O.: Candidate One-Way Functions Based on Expander Graphs. Cryptology ePrint Archive, Report 2000/063 (2000)

    Google Scholar 

  2. Charles, D.X., Lauter, K.E., Goren, E.Z.: Cryptographic Hash Functions from Expander Graphs. Journal of Cryptology (2007)

    Google Scholar 

  3. Chaudhuri, P.P., Chowdhury, D.R., Nandi, S., Chattopadhyay, S.: Additive Cellular Automata Theory and its Application, vol. 1. IEEE Computer Society Press (1997)

    Google Scholar 

  4. Linial, N., Wigderson, A.: Expander graphs and their applications, (2003), http://www.math.ias.edu/boaz/ExpanderCourse/

  5. Lubotzky, A., Phillips, R., Sarnak, P.: Ramanujan graphs. Combinatorica 8(3), 261–277 (1988)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Margulis, G.A.: Explicit constructions of expanders. Problemy Peredači Informacii 9(4), 71–80 (1973)

    MathSciNet  MATH  Google Scholar 

  7. Margulis, G.A.: Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators. Problemy Peredachi Informatsii 24(1), 51–60 (1988)

    MathSciNet  Google Scholar 

  8. Panjwani, S.K.: An Experimental Evaluation of Goldreich’s One-Way Function, Cryptology ePrint Archive, Report 2000/063 (2001)

    Google Scholar 

  9. Alon, N.: Eigen Values, Geometric Expanders, Sorting in Rounds and Ramsey Theorem. Combinatorica 6, 207–219 (1986)

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mukhopadhyay, D. (2012). Generating Expander Graphs Using Cellular Automata. In: Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2012. Lecture Notes in Computer Science, vol 7495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33350-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33350-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33349-1

  • Online ISBN: 978-3-642-33350-7

  • eBook Packages: Computer ScienceComputer Science (R0)