IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-59435-9_22.html
   My bibliography  Save this book chapter

Differential and Linear Distributions of Substitution Boxes for Symmetric-Key Cryptosystems

In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas

Author

Listed:
  • Peter Roelse

    (Eindhoven University of Technology, Department of Mathematics and Computer Science)

Abstract

In many secret-key cryptosystems substitution boxes are the only nonlinear component, and provide resistance against both differential and linear cryptanalyis. In this paper the notions of differential and linear distribution of the mapping defined by a substitution box are introduced. These distributions contain considerable information about its resistance against linear and differential cryptanalysis. With a computer search the differential and linear distribution of four-bit permutations with an optimal resistance against the attacks mentioned above were determined. In particular, this shows that Almost Perfect Nonlinear (APN) permutations on four bits do not exist. The substitution-boxes used in the AES finalist Serpent and the construction used for the S-box of AES are compared with these optimal four-bit permutations. In addition, identities on the elements of the differential and linear distribution of a mapping are presented. These relations are used to explain the close connection between the optimal distributions of four-bit permutations that were found by the computer search.

Suggested Citation

  • Peter Roelse, 2002. "Differential and Linear Distributions of Substitution Boxes for Symmetric-Key Cryptosystems," Springer Books, in: Gary L. Mullen & Henning Stichtenoth & Horacio Tapia-Recillas (ed.), Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pages 270-285, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59435-9_22
    DOI: 10.1007/978-3-642-59435-9_22
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-59435-9_22. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.