Skip to main content

On Immunity Profile of Boolean Functions

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

Abstract

The notion of resilient function has been recently weakened to match more properly the features required for Boolean functions used in stream ciphers. We introduce and we study an alternate notion of almost resilient function. We show that it corresponds more closely to the requirements that make the cipher more resistant to precise attacks.

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

Buying options

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. 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, p. 573. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Carlet, C.: Boolean functions for cryptography and error correcting codes. In: Hammer, P., Crama, Y. (eds.) chapter of the monograph Boolean methods and models, Cambridge University Press, Cambridge (to be published), http://www-rocq.inria.fr/codes/Claude.Carlet/chap-fcts-Bool.pdf

  3. Carlet, C.: On the secondary constructions of resilient and bent functions. In: Workshop on Coding, Cryptography and Combinatorics, pp. 3–28. Birkhäuser, Basel (2004)

    Google Scholar 

  4. Carlet, C.: On bent and highly nonlinear balanced/Resilient functions and their algebraic immunities. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds.) AAECC 2006. LNCS, vol. 3857, pp. 1–28. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Carlet, C., Sarkar, P.: Spectral domain analysis of correlation immune and resilient boolean functions. Finite Fields and their Applications 8, 120–130 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chepyzhov, V.V., Johansson, T., Smeets, B.: A simple algorithm for fast correlation attacks on stream ciphers. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 181–195. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Courtois, N.T.: General principles of algebraic attacks and new design criteria for cipher components. In: Dobbertin, H., Rijmen, V., Sowa, A. (eds.) AES 2005. LNCS, vol. 3373, pp. 67–83. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. 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 

  9. Ke, P.-H., Zhang, J., Wen, Q.-Y.: Further constructions of almost resilient functions. Cryptology ePrint Archive, Report 2005/453 (2005)

    Google Scholar 

  10. Kurosawa, K., Johansson, T., Stinson, D.: Almost k-wise Independent Sample Spaces and Their Cryptologic Applications. Journal of Cryptology 14(4), 301–324 (2001)

    MathSciNet  Google Scholar 

  11. Kurosawa, K., Matsumoto, R.: Almost Security of Cryptographic Boolean Functions. IEEE Transactions on Information Theory 50(11), 2752–2761 (2004)

    Article  MathSciNet  Google Scholar 

  12. MacKay, D.J.C.: Information Theory, Inference, and Learning Algorithms. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  13. Meier, W., Staffelbach, O.: Fast correlation attacks on certain stream ciphers. Journal of Cryptology 1(3), 159–176 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mihaljević, M.J., Fossorier, M.P.C., Imai, H.: A Low-Complexity and High-Performance Algorithm for the Fast Correlation Attack. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 196–210. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. 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 

  16. Siegenthaler, T.: Correlation-immunity of nonlinear combining boolean fucntions for cryptographic applications. IEEE Transactions on Information Theory 30(5), 776–779 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  17. Xiao, G.-Z., Massey, J.L.: A spectral characterization of correlation-immune combining functions. IEEE Transactions on Information Theory 34(3), 569–571 (1988)

    Article  MATH  MathSciNet  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

Carlet, C., Guillot, P., Mesnager, S. (2006). On Immunity Profile of Boolean Functions. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_32

Download citation

  • DOI: https://doi.org/10.1007/11863854_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics