Skip to main content
SpringerLink
Log in

Inclusion Relations of Boolean Functions Satisfying PC(l) of Order k

  • Conference paper
Sequences and their Applications

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

  • 355 Accesses

Abstract

PC(l) of order k is an important cryptographic criterion of Boolean functions. Denote by PC n,(l, k ) the set of Boolean functions satisfying PC(l) of order k with n input bits. Recently, Carlet and Hirose proved that PC n,(l 1, k 1) = PC n,(l 2, k 2) for some class of l 1, k1, l2 and k 2. In this paper, we prove that PC n(l 1,k 1≠ PC n(l 2, k 2) for a large class of l 1, k 1, l 2 and k 2. Our result can be considered as a complement of their results.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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. C. Carlet. On the propagation criterion of degree 1 and order k. In Advances in Cryptology — EUROCRYPT ‘88 Proceedings, Lecture Notes in Computer Science 1403, pages 462–474. Springer-Verlag, 1998.

    Google Scholar 

  2. J.F. Dillon. Elementary Hadamard difference sets. Ph. D. Thesis. Univ. of Maryland. 1974.

    Google Scholar 

  3. R. Forré. The strict avalanche criterion: spectral properties of Boolean functions and an extend definition. In Advances in Cryptology — CRYPTO ‘88 Proceedings, Lecture Notes in Computer Science 403, pages 450–468. Springer-Verlag, 1990.

    Google Scholar 

  4. S. Hirose. Boolean functions related to cryptography and their complexity. Doctoral dissertation. Kyoto Univ. Japan. February 1995.

    Google Scholar 

  5. K. Kurosawa and T. Satoh. Design of SAC/PC(1) of order k Boolean functions and three other cryptographic criteria. In Advances in Cryptology — EUROCRYPT ‘87 Proceedings, Lecture Notes in Computer Science 1233, pages 434–449. Springer-Verlag, 1997.

    Google Scholar 

  6. W. Meier and O. Staffelbach. Nonlinearity criteria for cryptographic functions. In Advances in Cryptology — EUROCRYPT ‘89 Proceedings, Lecture Notes in Computer Science 434, pages 549–562. Springer-Verlag, 1990.

    Google Scholar 

  7. B. Preneel, W. van Leekwijck, L. van Linden, R. Govaerts, and J. Vandewalle. Propagation characteristics of Boolean functions. In Advances in Cryptology — EUROCRYPT ‘80 Proceedings, Lecture Notes in Computer Science 473, pages 161–173. Springer-Verlag, 1991.

    Google Scholar 

  8. J. Seberry, X. Zhang and Y. Zheng. Nonlinearity and propagation characteristics of Boolean functions. In Information and Computation, vol. 119, No. 1, pages 1–13, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  9. A.F. Webster and S.E. Tavares. On the design of S-boxes. In Advances in Cryptology — CRYPTO ‘85 Proceedings, Lecture Notes in Computer Science 218, pages 523–534. Springer-Verlag, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Electronic Engineering Faculty of Engineering, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo, 152-8552, Japan

    Tetsu Iwata & Kaoru Kurosawa

Authors
  1. Tetsu Iwata
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kaoru Kurosawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, School of Computing, National University of Singapore, Lower Kent Ridge Road, Singapore, 119260

    C. Ding

  2. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    T. Helleseth

  3. Institute of Information Processing, Austrian Academy of Sciences, Sonnenfelsgasse 19, A01010, Vienna, Austria

    H. Niederreiter

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag London

About this paper

Cite this paper

Iwata, T., Kurosawa, K. (1999). Inclusion Relations of Boolean Functions Satisfying PC(l) of Order k . In: Ding, C., Helleseth, T., Niederreiter, H. (eds) Sequences and their Applications. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0551-0_19

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0551-0_19

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-196-2

  • Online ISBN: 978-1-4471-0551-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation