Skip to main content
SpringerLink
Log in

Boolean Functions with a Few Walsh Transform Values

  • Conference paper
  • First Online:
Advances in Artificial Intelligence and Security (ICAIS 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1423))

Included in the following conference series:

Abstract

Boolean functions have been extensively studied in coding theory, cryptography, sequence design and graph theory. By adding two products of three linear functions to some known bent functions, in this paper, we construct a class of bent functions and obtain their dual functions. In the meantime, a class of semi-bent functions and some classes of five-valued Walsh spectra are given.

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

Access this chapter

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

References

  1. Canteaut, A., Carlet, C., Charpin, P., Fontaine, C.: On cryptographic properties of the cosets of r(1, m). IEEE Trans. Inf. Theory 47(4), 1494–1513 (2001). https://doi.org/10.1109/18.923730

  2. Carlet, C.: Boolean functions for cryptography and error correcting codes. In: Crama, Y., Hammer, P. (eds.) Chapter of the Monography Boolean Models and Methods in Mathematics, Computer Science, and Engineering, pp. 257–397 (2010)

    Google Scholar 

  3. Carlet, C., Mesnager, S.: On semibent Boolean functions. IEEE Trans. Inf. Theory 58(5), 3287–3292 (2012). https://doi.org/10.1109/TIT.2011.2181330

  4. Charpin, P., Pasalic, E., Tavernier, C.: On bent and semi-bent quadratic Boolean functions. IEEE Trans. Inf. Theory 51(12), 4286–4298 (2005). https://doi.org/10.1109/TIT.2005.858929

  5. Chee, S., Lee, S., Kim, K.: Semi-bent functions. In: Pieprzyk, J., Safavi-Naini, R. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 105–118. Springer, Heidelberg (1995). https://doi.org/10.1007/BFb0000428

    Chapter  Google Scholar 

  6. Khoo, K., Gong, G., Stinson, D.R.: A new characterization of semi-bent and bent functions on finite fields. Des. Codes Cryptogr. 38(2), 279–295 (2006). https://doi.org/10.1007/s10623-005-6345-x

  7. Khoo, K.: Sequence design and construction of cryptographic Boolean functions. Ph. D. Thesis, University Waterloo (Canada) (2004)

    Google Scholar 

  8. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error Correcting Codes. North-Holland, New York (1977)

    Google Scholar 

  9. Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48285-7_33

    Chapter  Google Scholar 

  10. Mesnager, S.: Semi-bent functions from Dillon and Niho exponents, Kloosterman sums, and Dickson polynomials. IEEE Trans. Inf. Theory 57(11), 7443–7458 (2011). https://doi.org/10.1109/TIT.2011.2160039

  11. Mesnager, S.: Several new infinite families of bent functions and their duals. IEEE Trans. Inf. Theory 60(7), 4397–4407 (2014). https://doi.org/10.1109/TIT.2014.2320974

  12. Meier, W., Staffelbach, O.: Fast correlation attacks on stream ciphers. In: Barstow, D., et al. (eds.) EUROCRYPT 1988. LNCS, vol. 330, pp. 301–314. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-45961-8_28

    Chapter  Google Scholar 

  13. Olsen, J., Scholtz, R.A., Welch, L.: Bent-function sequences. IEEE Trans. Inf. Theory 28(6), 858–864 (1982). https://doi.org/10.1109/TIT.1982.1056589

  14. Rothaus, O.S.: On bent functions. J. Comb. Theory Ser. A 20(3), 300–305 (1976). https://doi.org/10.1016/0097-3165(76)90024-8

  15. Wolfmann, J.: Special bent and near-Bent functions. Adv. Math. Commun. 8(1), 21–33 (2014). https://doi.org/10.3934/amc.2014.8.21

  16. Xu, G., Cao, X., Xu, S.: Several classes of Boolean functions with few Walsh transform values. Appl. Algebra Eng. Commun. Comput. 28(2), 155–176 (2016). https://doi.org/10.1007/s00200-016-0298-3

    Article  MathSciNet  MATH  Google Scholar 

  17. Zheng, Y., Zhang, X.-M.: Plateaued functions. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 284–300. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-540-47942-0_24

    Chapter  Google Scholar 

  18. Zheng, Y., Zhang, X.-M.: Relationships between bent functions and complementary plateaued functions. In: Song, J.S. (ed.) ICISC 1999. LNCS, vol. 1787, pp. 60–75. Springer, Heidelberg (2000). https://doi.org/10.1007/10719994_6

    Chapter  Google Scholar 

  19. Zheng, L., Peng, J., Kan, H., Li, Y.: Several new infinite families of bent functions via second order derivatives. Cryptogr. Commun. 12(6), 1143–1160 (2020). https://doi.org/10.1007/s12095-020-00436-0

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, Gansu, People’s Republic of China

    Wengang Jin, Xiaoni Du, Jinxia Hu & Yanzhong Sun

Authors
  1. Wengang Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoni Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jinxia Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanzhong Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Nanjing University of Information Science and Technology, Nanjing, China

    Xingming Sun

  2. Nanjing University of Information Science and Technology, Nanjing, China

    Xiaorui Zhang

  3. Jinan University, Guangzhou, China

    Zhihua Xia

  4. Purdue University, West Lafayette, IN, USA

    Elisa Bertino

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jin, W., Du, X., Hu, J., Sun, Y. (2021). Boolean Functions with a Few Walsh Transform Values. In: Sun, X., Zhang, X., Xia, Z., Bertino, E. (eds) Advances in Artificial Intelligence and Security. ICAIS 2021. Communications in Computer and Information Science, vol 1423. Springer, Cham. https://doi.org/10.1007/978-3-030-78618-2_53

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-78618-2_53

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-78617-5

  • Online ISBN: 978-3-030-78618-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation