IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-59435-9_12.html

VHDL Specification of a FPGA to Divide and Multiply in GF(2 m )

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

Author

Listed:
  • Mario Alberto García-Martínez

    (Instituto Tecnológico de Orizaba, Departamento de Ingeniería Eléctrica-Electrónica)

  • Guillermo Morales-Luna

    (Instituto Mexicano del Petróleo, Programa de Ingeniería Molecular
    Computer Science Section)

Abstract

Some FPGA’s are designed to compute division and multiplication on Galois fields. FPGA’s are quite cheap programmable logic devices used in digital circuits with the important characteristic of being reprogrammable. Any FPGA can be specified within VHDL which at present is a standard language in the design of digital systems. We describe in VHDL the divider and multiplier basic cells and their whole integration. The structures have scalable systolic architectures. The circuits operate by pipelining; the divider in GF (2 m ) requires 5m − 1 clock cycles while the multiplier 3m − 1. The divider proceeds by the Gaussian triangulation algorithm and is uniform with respect to the irreducible polynomial generating the field. The codes, some simulations and performance measurements are provided.

Suggested Citation

  • Mario Alberto García-Martínez & Guillermo Morales-Luna, 2002. "VHDL Specification of a FPGA to Divide and Multiply in GF(2 m )," Springer Books, in: Gary L. Mullen & Henning Stichtenoth & Horacio Tapia-Recillas (ed.), Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pages 164-176, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59435-9_12
    DOI: 10.1007/978-3-642-59435-9_12
    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_12. 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.