Movatterモバイル変換

[0]ホーム
URL:

Skip to main content

Advertisement

Springer Nature Link
Log in

Results on Rotation Symmetric Bent and Correlation Immune Boolean Functions

  • Conference paper

Part of the book series:Lecture Notes in Computer Science ((LNCS,volume 3017))

Included in the following conference series:

  • 2536Accesses

Abstract

Recent research shows that the class of Rotation Symmetric Boolean Functions (RSBFs), i.e., the class of Boolean functions that are invariant under circular translation of indices, is potentially rich in functions of cryptographic significance. Here we present new results regarding the Rotation Symmetric (rots) correlation immune (CI) and bent functions. We present important data structures for efficient search strategy of rots bent and CI functions. Further, we prove the nonexistence of homogeneous rots bent functions of degree ≥ 3 on a single cycle.

Similar content being viewed by others

Keywords

References

  1. Clark, J., Jacob, J., Stepney, S., Maitra, S., Millan, W.: Evolving Boolean Functions Satisfying Multiple Criteria. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 246–259. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Clark, J., Jacob, J., Maitra, S., Stanica, P.: Almost Boolean Functions: The Design of Boolean Functions by Spectral Inversion. In: The proceedings, CEC 2003, the 2003 Congress on Evolutionary Computation, Canberra, Australia, December 8–12, vol. 3. IEEE Press, Los Alamitos (2003)

    Google Scholar 

  3. Cusick, T.W., Stănică, P.: Fast Evaluation, Weights and Nonlinearity of Rotation-Symmetric Functions. Discrete Mathematics 258(1-3), 289–301 (2002)

    Article MATH MathSciNet  Google Scholar 

  4. Filiol, E., Fontaine, C.: Highly nonlinear balanced Boolean functions with a good correlation-immunity. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 475–488. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

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

    Article MATH  Google Scholar 

  6. Lidl, R., Niederreiter, H.: Introduction to finite fields and their applications. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  7. Maitra, S., Pasalic, E.: Further constructions of resilient Boolean functions with very high nonlinearity. IEEE Transactions on Information Theory 48(7), 1825–1834 (2002)

    Article MATH MathSciNet  Google Scholar 

  8. Maitra, S., Sarkar, P.: Cryptographically significant Boolean functions with five-valued walsh spectra. Theoretical Computer Science 276(1–2), 133–146 (2002)

    Article MATH MathSciNet  Google Scholar 

  9. Maity, S., Johansson, T.: Construction of Cryptographically Important Boolean Functions. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 234–245. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Pasalic, E., Maitra, S., Johansson, T., Sarkar, P.: New constructions of resilient and correlation immune Boolean functions achieving upper bound on nonlinearity. In: Workshop on Coding and Cryptography - WCC 2001, Paris, January 8–12. Electronic Notes in Discrete Mathematics, vol. 6. Elsevier Science, Amsterdam (2001)

    Google Scholar 

  11. Pieprzyk, J., Qu, C.X.: Fast Hashing and Rotation-Symmetric Functions. Journal of Universal Computer Science 5(1), 20–31 (1999)

    MathSciNet  Google Scholar 

  12. 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 

  13. Sarkar, P., Maitra, S.: Construction of nonlinear Boolean functions with important cryptographic properties. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 485–506. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Sarkar, P., Maitra, S.: Nonlinearity bounds and constuction of resilient Boolean functions. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 515–532. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  15. Stănică, P., Maitra, S.: Rotation Symmetric Boolean Functions – Count and Cryptographic Properties. In: R.C. Bose Centenary Symposium on Discrete Mathematics and Applications, December 2002. Electronic Notes in Discrete Mathematics, vol. 15. Elsevier, Amsterdam (2002)

    Google Scholar 

  16. Stănică, P., Maitra, S.: A constructive count of Rotation Symmetric functions. Information Processing Letters 88, 299–304 (2003)

    Article MATH MathSciNet  Google Scholar 

  17. Xia, T., Seberry, J., Pieprzyk, J., Charnes, C.: Homogeneous bent functions of degree n in 2n variables do not exist for n > 3. Discrete Mathematics (to appear)

    Google Scholar 

  18. Zhang, X.-M., Zheng, Y.: GAC – the criterion for global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science 1(5), 316–333 (1995)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Auburn University Montgomery, Montgomery, AL, 36124-4023, USA

    Pantelimon Stănică

  2. Applied Statistics Unit, Indian Statistical Institute, 203, B T Road, Kolkata, 700 108, INDIA

    Subhamoy Maitra

  3. Department of Computer Science, University of York, York, YO10 3EE, England

    John A. Clark

Authors
  1. Pantelimon Stănică

    You can also search for this author inPubMed Google Scholar

  2. Subhamoy Maitra

    You can also search for this author inPubMed Google Scholar

  3. John A. Clark

    You can also search for this author inPubMed Google Scholar

Editor information

Editors and Affiliations

  1. Indian Statistical Institute, Applied Statistics Unit, 203 B T Road, 700 108, Kolkata, India

    Bimal Roy

  2. FHNW, Windisch, Switzerland

    Willi Meier

Rights and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stănică, P., Maitra, S., Clark, J.A. (2004). Results on Rotation Symmetric Bent and Correlation Immune Boolean Functions. In: Roy, B., Meier, W. (eds) Fast Software Encryption. FSE 2004. Lecture Notes in Computer Science, vol 3017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25937-4_11

Download citation

Publish with us

[8]ページ先頭
©2009-2025 Movatter.jp