IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-540-79409-7_26.html
   My bibliography  Save this book chapter

A Deterministic Optimization Approach for Generating Highly Nonlinear Balanced Boolean Functions in Cryptography

In: Modeling, Simulation and Optimization of Complex Processes

Author

Listed:
  • Le Hoai Minh

    (University of Paul Verlaine – Metz, Laboratory of Theoretical and Applied Computer Science (LITA EA 3097))

  • Le Thi Hoai An

    (University of Paul Verlaine – Metz, Laboratory of Theoretical and Applied Computer Science (LITA EA 3097))

  • Pham Dinh Tao

    (National Institute for Applied Sciences-Rouen, Laboratory of Modelling, Optimization & Operations Research)

  • Pascal Bouvry

    (University of Luxembourg, Computer Science Research Unit)

Abstract

We propose in this work a deterministic continuous approach for constructing highly nonlinear balanced Boolean functions, which is an interesting and open question in Cryptography. Our approach is based on DC (Difference of Convex functions) programming and DCA (DC optimization Algorithms). We first formulate the problem in the form of a combinatorial optimization problem, more precisely a mixed 0–1 linear program. By using exact penalty technique in DC programming, this problem is reformulated as polyhedral DC program. We next investigate DC programming and DCA for solving this latter problem. Preliminary numerical results show that the proposed algorithm is promising and more efficient than somes heuristic algorithms.

Suggested Citation

  • Le Hoai Minh & Le Thi Hoai An & Pham Dinh Tao & Pascal Bouvry, 2008. "A Deterministic Optimization Approach for Generating Highly Nonlinear Balanced Boolean Functions in Cryptography," Springer Books, in: Hans Georg Bock & Ekaterina Kostina & Hoang Xuan Phu & Rolf Rannacher (ed.), Modeling, Simulation and Optimization of Complex Processes, pages 381-391, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-79409-7_26
    DOI: 10.1007/978-3-540-79409-7_26
    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:978-3-540-79409-7_26. 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.