Skip to main content

A General Formulation of Algebraic and Fast Correlation Attacks Based on Dedicated Sample Decimation

  • Conference paper
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2006)

Abstract

This paper proposes a novel approach for cryptanalysis of certain cryptographic pseudorandom sequence (keystream) generators consisting of the composition of a linear finite state machine (LFSM) and nonlinear mapping. The proposed approach includes a dedicated decimation of the sample for cryptanalysis based on the following: Suppose certain B bits of the LFSM initial state as known and identify time instances where certain arguments of the nonlinear function depend only on these B bits and are equal to zero. As opposed to previously reported methods, the proposed one also identifies and uses certain characteristics of the LFSM state-transition matrix in order to reduce the nonlinearity of the system of overdefined equations employed in an algebraic attack scenario, or to reduce the noise introduced by the linearization of the nonlinear function which corrupts the linear equations employed in a correlation attack scenario.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Chapter  Google Scholar 

  2. Braeken, A., Nikov, V., Nikova, S., Preneel, B.: On Boolean functions with generalized cryptographic properties. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 120–135. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Chose, P., Joux, A., Mitton, M.: Fast Correlation Attacks: An Algorithmic Point of View. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 209–221. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. 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 

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

    Chapter  Google Scholar 

  7. Fossorier, M.P.C., Mihaljević, M.J., Imai, H.: A Unified Analysis on Block Decoding Approaches for the Fast Correlation attack. In: 2005 IEEE Int. Symp. Inform. Theory - ISIT 2005, Proceedings, Adelaide, Australia, September 2005, 4 p. (2005) (accepted for publication)

    Google Scholar 

  8. 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 

  9. Johansson, T., Jonsson, F.: Theoretical Analysis of a Correlation Attack Based on Convolutional Codes. IEEE Trans. Information Theory 48, 2173–2181 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lu, P.: A new correlation attack on LFSR sequences with high error tolerance. In: Feng, K., Niederreiter, H., Xing, C. (eds.) Coding, Cryptography and Combinatorics, May 2004. Birkhauser Verlag AG, Basel (2004)

    Google Scholar 

  11. Menezes, A., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Roton (1997)

    MATH  Google Scholar 

  12. Meier, W., Staffelbach, O.: Fast correlation attacks on certain stream ciphers. Journal of Cryptology 1, 159–176 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  13. 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 

  14. Mihaljević, M.J., Fossorier, M.P.C., Imai, H.: On decoding techniques for cryptanalysis of certain encryption algorithms. IEICE Trans. Fundamentals E84-A, 919–930 (2001)

    Google Scholar 

  15. Mihaljević, M.J., Golić, J.D.: A method for convergence analysis of iterative probabilistic decoding. IEEE Trans. Inform. Theory 46, 2206–2211 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mihaljević, M.J., Fossorier, M.P.C., Imai, H.: Fast Correlation Attack Algorithm with List Decoding and an Application. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 196–210. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

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

    Google Scholar 

  18. Mihaljević, M.J., Kohno, R.: Cryptanalysis of fast encryption algorithm for multimedia FEA-M. IEEE Commun. Lett. 6, 382–384 (2002)

    Article  Google Scholar 

  19. Mihaljević, M.J., Imai, H.: The decimated sample based improved algebraic attacks on the nonlinear filters. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 310–323. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Mihaljević, M.J., Fossorier, M.P.C., Imai, H.: Cryptanalysis of keystream generator by decimated sample based algebraic and fast correlation attacks. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 155–168. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Molland, H., Mathiassen, J.E., Helleseth, T.: Improved Fast Correlation Attack using Low Rate Codes. In: Paterson, K.G. (ed.) Cryptography and Coding 2003. LNCS, vol. 2898, pp. 67–81. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  22. Siegenthaler, T.: Decrypting a class of stream ciphers using ciphertext only. IEEE Trans. Comput. C-34, 81–85 (1985)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mihaljević, M.J., Fossorier, M.P.C., Imai, H. (2006). A General Formulation of Algebraic and Fast Correlation Attacks Based on Dedicated Sample Decimation. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2006. Lecture Notes in Computer Science, vol 3857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617983_20

Download citation

  • DOI: https://doi.org/10.1007/11617983_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31423-3

  • Online ISBN: 978-3-540-31424-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics