Skip to main content
SpringerLink
Log in
Book cover

IMA International Conference on Cryptography and Coding

Cryptography and Coding 2005: Cryptography and Coding pp 290–303Cite as

Probabilistic Algebraic Attacks

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3796))

Abstract

This paper investigates a probabilistic algebraic attack on LFSR-based stream ciphers. We consider two scenarios (S3a and S3b) proposed by Meier et al. at Eurocrypt 2004. In order to derive the probability in this new algebraic attack, we quantify the distance between a Boolean function and a function with annihilator of a certain degree. We show that in some cases the approximations can improve the algebraic attacks. Moreover, this distance leads to other theoretical results such as the weights of the subfunctions and the distance to normal functions; it also provides information on the Walsh spectrum of the function.

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. Bailey, D.H., Lee, K., Simon, H.D.: Using Strassen’s algorithm to accelerate the solution of linear systems. Journal of Supercomputing 4, 357–371 (1990)

    Article  Google Scholar 

  2. Canteaut, A., Charpin, P.: Decomposing bent functions. IEEE Transactions on Information Theory IT-49(8), 2004–2019 (2003)

    Article  MathSciNet  Google Scholar 

  3. Canteaut, A., Trabbia, M.: Improved fast correlation attacks using parity-check equations of weight 4 and 5. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 573–588. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  4. Canteaut, A., Videau, M.: Degree of composition of highly nonlinear functions and applications to higher order differential cryptanalysis. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 518–533. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  5. Courtois, N., Meier, W.: Algebraic attacks on stream ciphers with linear feedback. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 345–359. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  6. Courtois, N.T.: Higher order correlation attacks, XL algorithm, and cryptanalysis of Toyocrypt. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 182–199. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Daemen, J.: Cipher and Hash Function Design. PhD thesis, Katholieke Universiteit Leuven (1995)

    Google Scholar 

  8. Dillon, J.: A survey of bent functions. Technical report, NSA Technical Journal, 191–215 (1972) unclassified

    Google Scholar 

  9. Dubuc, S.: Etude des proprietes de degenerescene et de normalite des fonctions booleennes et construction des fonctions q-aires parfaitement non-lineaires. PhD thesis, Universite de Caen (2001)

    Google Scholar 

  10. Faug’ere, J.-C., Sugita, M., Kawazoe, M., Imai, H.: Comparison between XL and Grobner basis algorithms. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 338–353. Springer, Heidelberg (2004), ISBN 3-540-00171-9

    Google Scholar 

  11. Faug’ere, J.-C.: A new efficient algorithm for computing Grobner bases without reduction to zero (F5). In: International Symposium on Symbolic and Algebraic Computation — ISSAC 2002, pp. 75–83. ACM Press, New York (2002)

    Chapter  Google Scholar 

  12. Guo-Zhen, X., Massey, J.: A spectral characterization of correlation-immune combining functions. IEEE Transactions on Information Theory IT-34(3), 569–571 (1988)

    Google Scholar 

  13. Johansson, T., Jonsson, F.: Fast correlation attacks based on Turbo Code techniques. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 181–197. Springer, Heidelberg (1999)

    Google Scholar 

  14. Koholosha, A.: Investigation in the Design and Analysis of Key-Stream Generators. PhD thesis, Technische Universiteit Eindhoven (2003)

    Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. Meier, W., Staffelbach, O.: Fast correlation attacks on certain stream ciphers. Journal of Cryptology 1(3), 67–86 (1992)

    Google Scholar 

  17. Mihaljevic, M.J., Imai, H.: Cryptanalysis of Toyocrypt-HS1 stream cipher. IEICE Transactions on Fundamentals E85-A, 66–73 (2002)

    Google Scholar 

  18. Preneel, B., Van Leekwijck, W., Van Linden, L., Govaerts, R., Vandewalle, J.: Propagation characteristics of Boolean functions. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 161–173. Springer, Heidelberg (1991)

    Google Scholar 

  19. Quisquater, M.: Applications of Character Theory and The Moobius Inversion Principle to the Study of Cryptographic Properties of Boolean Functions. PhD thesis, Katholieke Universiteit Leuven (2004)

    Google Scholar 

  20. Siegenthaler, T.: Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Transactions on Information Theory IT-30(5), 776–780 (1984)

    Article  MathSciNet  Google Scholar 

  21. Siegenthaler, T.: Decrypting a class of stream ciphers using ciphertext only. IEEE Transactions on Computers C-34(1), 81–85 (1985)

    Article  Google Scholar 

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

    Chapter  Google Scholar 

  23. Zheng, Y., Zhang, X.M.: Plateaud functions. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 284–300. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  24. Zheng, Y., Zhang, X.M.: Relationships between bent functions and complementary plateaud functions. In: Song, J.S. (ed.) ICISC 1999. LNCS, vol. 1787, pp. 60–75. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Katholieke Universiteit Leuven, Dept. Elect. Eng.-ESAT/SCD-COSIC, Kasteelpark Arenberg 10, 3001, Heverlee, Belgium

    An Braeken & Bart Preneel

Authors
  1. An Braeken
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bart Preneel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. Computer Science, University of Bristol, Woodland Road, BS8 1UB, Bristol, United Kingdom

    Nigel P. Smart

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Braeken, A., Preneel, B. (2005). Probabilistic Algebraic Attacks. In: Smart, N.P. (eds) Cryptography and Coding. Cryptography and Coding 2005. Lecture Notes in Computer Science, vol 3796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11586821_20

Download citation

  • DOI: https://doi.org/10.1007/11586821_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30276-6

  • Online ISBN: 978-3-540-32418-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation