Skip to main content
SpringerLink
Log in
Book cover

Australasian Conference on Information Security and Privacy

ACISP 2007: Information Security and Privacy pp 11–28Cite as

On the Security of the LILI Family of Stream Ciphers Against Algebraic Attacks

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4586))

Abstract

In this paper, we present an algebraic analysis of the LILI family of stream ciphers, and in particular LILI-II, and investigate the security provided against both standard and fast algebraic attacks. We show that the size of the two registers used, the difference between their lengths, the maximum number of times a register is clocked and the degree of the filter function all play important roles in providing resistance against algebraic attacks. Further, we show that the degree 10 filter function used in LILI-II has an algebraic immunity (AI) of 4. Using this, a fast algebraic attack can be performed on LILI-II that significantly reduces the attack complexity, although not to such a degree that it is more efficient than exhaustive key search. These algebraic attacks recover the internal state of the cipher rather than the key bits. We investigate the role of the initialization process in providing resistance to algebraic attacks aimed at key recovery. The investigation shows that, generally, for the LILI family of stream ciphers, the complexity of recovering key bits using algebraic attacks is much worse than exhaustive key search because of the very high degree equations generated during the initialization process.

This is a preview of subscription content, 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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alhinai, S., Batten, L., Colbert, B., Wong, K.: Algebraic attacks on clock controlled stream ciphers. In: Batten, L.M., Safavi-Naini, R. (eds.) ACISP 2006. LNCS, vol. 4058, pp. 1–16. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Armknecht, F.: Improving fast algebraic attacks. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 65–82. Springer, Heidelberg (2004)

    Google Scholar 

  3. Armknecht, F., Krause, M.: Algebraic attacks on combiners with memory. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 162–175. Springer, Heidelberg (2003)

    Google Scholar 

  4. Armknecht, F., Carlet, C., Gaborit, P., Kunzli, S., Meier, W., Ruatta, O.: Efficient Computation of Algebraic Immunity for Algebraic and Fast Algebraic Attacks. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 147–164. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Batten, L., Canteaut, A., Viswanathan, K.: INDOCRYPT 2004. LNCS, vol. 3348, pp. 84–91. Springer, Heidelberg (2004)

    Google Scholar 

  6. Berger, T., Minier, M.: Two Algebraic Attacks Against the F-FCSRs Using the IV Mode. In: Maitra, S., Madhavan, C.E.V., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 143–154. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Clark, A., Ed Dawson, J., Fuller, J., Golić, J., Lee, H-J., Millan, W., Moon, S-J., Simpson, L.: LILI-II Keystream Generator. In: ACISP 2002. LNCS, vol. 2384, pp. 25–39. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Cho, J., Pieprzyk, J.: Algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 49–64. Springer, Heidelberg (2004)

    Google Scholar 

  9. Courtois, N.: Cryptanalysis of Sfinks. In: Won, D.H., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 261–269. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Courtois, N.: Fast algebraic attacks on stream ciphers with linear feedback. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 176–194. Springer, Heidelberg (2003)

    Google Scholar 

  11. Courtois, N., Meier, W.: Algebraic attacks on stream ciphers with linear feedback. In: Biham, E. (ed.) Advances in Cryptology – EUROCRPYT 2003. LNCS, vol. 2656, pp. 346–359. Springer, Heidelberg (2003)

    Google Scholar 

  12. Courtois, N., Pieprzyk, J.: Cryptanalysis of block ciphers with overdefined systems of equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267–287. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Dawson, E., Golić, J., Millan, W., Simpson, L.: Response to Initial Report on LILI-128.NESSIE submission, available at http://www.cryptonessie.org

  14. Dawson, E., Clark, A., Golić, J., Millan, W., Penna, L., Simpson, L.: The LILI-128 keystream generator.NESSIE submission. In: The proceedings of the First Open NESSIE Workshop (Leuven, November 2000), available at http://www.cryptonessie.org

  15. Dalai, D., Gupta, K., Maitra, S.: Results on Algebraic Immunity for Cryptographically Significant Boolean Functions. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 92–106. Springer, Heidelberg (2004)

    Google Scholar 

  16. Didier, F.: Using Wiedemanna Algorithm to Compute the Immunity Against Algebraic and Fast Algebraic Attacks. In: Barua, R., Lange, T. (eds.) INDOCRYPT 2006. LNCS, vol. 4329, pp. 236–250. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Lee, D., Kim, J., Hong, J., Han, J., Moon, D.: Algebraic Attacks on Summation Generators. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 34–48. Springer, Heidelberg (2004)

    Google Scholar 

  18. Hawkes, P., Rose, G.: Rewriting Variables: The Complexity of Fast Algebraic Attacks on Stream Ciphers. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 390–406. Springer, Heidelberg (2004)

    Google Scholar 

  19. Meier, W., Pasalic, E., Carlet, C.: Algebraic attacks and decomposition of Boolean functions. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 474–491. Springer, Heidelberg (2004)

    Google Scholar 

  20. Molland, H., Helleseth, T.: An Improved Correlation Attack Against Irregular Clocked and Filtered Keystream Generators. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 373–389. Springer, Heidelberg (2004)

    Google Scholar 

  21. Molland, H.: Improved linear consistency attack on irregular clocked keystream generators. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 109–126. Springer, Heidelberg (2004)

    Google Scholar 

  22. Saarinen, M.: A Time-Memory Tradeoff Attack Against LILI-128. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 231–236. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Simpson, L., Dawson, E., Golić, J., Millan, W.: LILI Keystream Generator. In: Stinson, D.R., Tavares, S. (eds.) SAC 2000. LNCS, vol. 2012, pp. 248–261. Springer, Heidelberg (2001)

    Google Scholar 

  24. Strassen, V.: Gaussian Elimination is Not Optimal. Numerische Mathematik 13, 354–356 (1969)

    Article  MATH  Google Scholar 

  25. Sugimoto, K., Chikaraishi, T., Morizumi, T.: Design criteria and security evaluations on certain stream ciphers. IEICE Technical Report, ISEC2000-69 (September 2000)

    Google Scholar 

  26. Wong, K., Colbert, B., Batten, L., Alhinai, S.: Algebraic attacks on clock controlled cascade ciphers. In: Barua, R., Lange, T. (eds.) INDOCRYPT 2006. LNCS, vol. 4329, pp. 32–47. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  27. Zhang, X., Pieprzyk, J., Zheng, Y.: On Algebraic Immunity and Annihilators. In: Rhee, M.S., Lee, B. (eds.) ICISC 2006. LNCS, vol. 4296, pp. 65–80. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information Security Institute (ISI), Queensland University of Technology (QUT), Australia

    Sultan Zayid Al-Hinai, Ed Dawson & Leonie Simpson

  2. Institute for Infocomm Research, Singapore

    Matt Henricksen

Authors
  1. Sultan Zayid Al-Hinai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ed Dawson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matt Henricksen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Leonie Simpson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Josef Pieprzyk Hossein Ghodosi Ed Dawson

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Al-Hinai, S.Z., Dawson, E., Henricksen, M., Simpson, L. (2007). On the Security of the LILI Family of Stream Ciphers Against Algebraic Attacks. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds) Information Security and Privacy. ACISP 2007. Lecture Notes in Computer Science, vol 4586. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73458-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73458-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73457-4

  • Online ISBN: 978-3-540-73458-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation