IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i6p996-d775015.html
   My bibliography  Save this article

Security and Efficiency of Linear Feedback Shift Registers in GF (2 n ) Using n -Bit Grouped Operations

Author

Listed:
  • Javier Espinosa García

    (Institute of Physical and Information Technologies (ITEFI), Spanish National Research Council (CSIC), 28006 Madrid, Spain)

  • Guillermo Cotrina

    (Escuela Técnica Superior de Ingeniería de Telecomunicación, Universidad de Málaga, 29071 Málaga, Spain)

  • Alberto Peinado

    (Escuela Técnica Superior de Ingeniería de Telecomunicación, Universidad de Málaga, 29071 Málaga, Spain)

  • Andrés Ortiz

    (Escuela Técnica Superior de Ingeniería de Telecomunicación, Universidad de Málaga, 29071 Málaga, Spain)

Abstract

Many stream ciphers employ linear feedback shift registers (LFSRs) to generate pseudorandom sequences. Many recent LFSRs are defined in G F ( 2 n ) to take advantage of the n -bit processors, instead of using the classic binary field. In this way, the bit generation rate increases at the expense of a higher complexity in computations. For this reason, only certain primitive polynomials in G F ( 2 n ) are used as feedback polynomials in real ciphers. In this article, we present an efficient implementation of the LFSRs defined in G F ( 2 n ) . The efficiency is achieved by using equivalent binary LFSRs in combination with binary n -bit grouped operations, n being the processor word’s length. This improvement affects the general considerations about the security of cryptographic systems that uses LFSR. The model also allows the development of a faster method to test the primitiveness of polynomials in G F ( 2 n ) .

Suggested Citation

  • Javier Espinosa García & Guillermo Cotrina & Alberto Peinado & Andrés Ortiz, 2022. "Security and Efficiency of Linear Feedback Shift Registers in GF (2 n ) Using n -Bit Grouped Operations," Mathematics, MDPI, vol. 10(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:996-:d:775015
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/6/996/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/6/996/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:10:y:2022:i:6:p:996-:d:775015. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.