Skip to main content
SpringerLink
Log in
Book cover

International Conference on Sequences and Their Applications

SETA 2006: Sequences and Their Applications – SETA 2006 pp 402–416Cite as

Partially Perfect Nonlinear Functions and a Construction of Cryptographic Boolean Functions

  • Conference paper

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

Abstract

In this paper the concept of partially perfect nonlinear (PPN) function is introduced as an extension of binary partially Bent function and is used to construct a new class of Boolean functions with good cryptographic properties. The construction is a composition of a PPN function and a Boolean function. The nonlinearity, correlation immunity, propagation criterion, and other cryptographic properties of the constructed functions are analyzed. In particular, new plateaued functions can be obtained by the proposed method and the construction of Khoo and Gong in [1] is improved.

This work is supported in part by the National Science Foundation of China (NSFC) under Grants No.60373041 and No.90104034, and in part by the open foundation of the State Key Laboratory of Information Security.

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. Khoo, K., Gong, G.: New Constructions for Resilient and Highly Nonlinear Boolean Functions. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 498–509. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Matsui, M.: Linear Cryptanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)

    Google Scholar 

  3. Rueppel, R.: Analysis and Design of Stream Ciphers. Springer, Heidelberg (1986)

    MATH  Google Scholar 

  4. Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. J. Cryptology 4, 3–72 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  5. Rothaus, O.: On Bent Functions. J. Combinatorial Theory 20, 300–305 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  6. Carlet, C.: Partially-Bent Functions. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 280–291. Springer, Heidelberg (1993)

    Google Scholar 

  7. Lidl, R., Niederreiter, H.: Finite Fields. In: Encyclopedia of Mathematics and Its Applications, vol. 20. Addison-Wesley, Reading (1983)

    Google Scholar 

  8. McWilliams, F., Solane, N.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)

    Google Scholar 

  9. Zheng, Y., Zhang, X.: Plateaued Functions. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 284–300. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  10. Carlet, C., Ding, C.: Highly Nonlinear Mappings. J. Complexity 20, 205–244 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Siegenthaler, T.: Correlation Immunity of Nonlinear Combining Functions for Cryptographic Applications. IEEE Trans. Inform. Theory 30, 776–780 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  12. Xiao, G., Massey, J.: A Spectral Characterization of Correlation Immune Combining Functions. IEEE Trans. Inform. Theory 34, 569–571 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  13. Camion, P., Carlet, C., Charpin, P., Sendrier, N.: On Correlation-Immune Functions. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 86–100. Springer, Heidelberg (1992)

    Google Scholar 

  14. 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 

  15. Webster, A.F., Tavares, S.: On the Design of S-boxes. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 523–534. Springer, Heidelberg (1986)

    Google Scholar 

  16. Courtois, N., Meier, W.: Algebriac Attack on Stream Ciphers with Linear Feeback. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 345–359. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  17. 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 

  18. Dalai, D.K., Gupta, K.C., 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)

    Chapter  Google Scholar 

  19. Batten, L.M.: Algebraic Attacks over GF(q). In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 84–91. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Chinese Academy of Sciences, State Key Laboratory of Information Security, Beijing, 100049, P.R. China

    Lei Hu & Xiangyong Zeng

  2. The Faculty of Mathematics and Computer Science, Hubei University, Xueyuan Road 11, Wuhan, 430062, P.R. China

    Xiangyong Zeng

Authors
  1. Lei Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiangyong Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Guang Gong

  2. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

  3. Department of Electrical and Electronic Engineering, Yonsei University, 121-749, Seoul, Korea

    Hong-Yeop Song

  4. Dept. of Electronics and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 790-784, Pohang, Kyungbuk, Korea

    Kyeongcheol Yang

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hu, L., Zeng, X. (2006). Partially Perfect Nonlinear Functions and a Construction of Cryptographic 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_35

Download citation

  • DOI: https://doi.org/10.1007/11863854_35

  • 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

Search

Navigation