IDEAS home Printed from https://ideas.repec.org/a/hin/complx/2108014.html
   My bibliography  Save this article

Binomial Representation of Cryptographic Binary Sequences and Its Relation to Cellular Automata

Author

Listed:
  • Sara D. Cardell
  • Amparo Fúster-Sabater

Abstract

The binomial sequences are binary sequences that correspond to the diagonals of the binary Sierpinski’s triangle. They have fancy properties such that all the sequences with period equal to a power of 2 can be represented as the sum of a finite set of binomial sequences. Other structural properties of these sequences (period, linear complexity, construction rules, or relations among the different binomial sequences) have been analyzed in detail. Furthermore, this work enhances the close relation between the binomial sequences and a kind of Boolean networks, known as linear cellular automata. In this sense, the binomial sequences exhibit the same behavior as that of particular Boolean networks. Consequently, the binomial sequences can be considered as primary tools for generating other more complex Boolean networks with applications in communication systems and cryptography.

Suggested Citation

  • Sara D. Cardell & Amparo Fúster-Sabater, 2019. "Binomial Representation of Cryptographic Binary Sequences and Its Relation to Cellular Automata," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    • Handle: RePEc:hin:complx:2108014
    DOI: 10.1155/2019/2108014
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/2108014.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/2108014.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/2108014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Juan A. Aledo & Silvia Martinez & Jose C. Valverde, 2015. "Parallel Dynamical Systems over Graphs and Related Topics: A Survey," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-14, March.
    2. Desheng Zheng & Guowu Yang & Xiaoyu Li & Zhicai Wang & Feng Liu & Lei He, 2013. "An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-7, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Amparo Fúster-Sabater & Verónica Requena & Sara D. Cardell, 2022. "An Efficient Algorithm to Compute the Linear Complexity of Binary Sequences," Mathematics, MDPI, vol. 10(5), pages 1-23, March.
    2. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2020. "Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    3. Jose Luis Martin-Navarro & Amparo Fúster-Sabater, 2021. "Review of the Lineal Complexity Calculation through Binomial Decomposition-Based Algorithms," Mathematics, MDPI, vol. 9(5), pages 1-22, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2019. "Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems," Complexity, Hindawi, vol. 2019, pages 1-10, March.
    2. Mauro Mezzini & Fernando L. Pelayo, 2020. "An Algorithm for Counting the Fixed Point Orbits of an AND-OR Dynamical System with Symmetric Positive Dependency Graph," Mathematics, MDPI, vol. 8(9), pages 1-9, September.
    3. Pedro J. Rivera Torres & E. I. Serrano Mercado & Luis Anido Rifón, 2018. "Probabilistic Boolean network modeling of an industrial machine," Journal of Intelligent Manufacturing, Springer, vol. 29(4), pages 875-890, April.
    4. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Solution to the predecessors and Gardens-of-Eden problems for synchronous systems over directed graphs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 22-28.
    5. Aledo, Juan A. & Diaz, Luis G. & Martinez, Silvia & Valverde, Jose C., 2019. "Dynamical attraction in parallel network models," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 874-888.
    6. Changki Hong & Jeewon Hwang & Kwang-Hyun Cho & Insik Shin, 2015. "An Efficient Steady-State Analysis Method for Large Boolean Networks with High Maximum Node Connectivity," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-19, December.
    7. Juan A. Aledo & Luis G. Diaz & Silvia Martinez & Jose C. Valverde, 2017. "On the Periods of Parallel Dynamical Systems," Complexity, Hindawi, vol. 2017, pages 1-6, January.
    8. Luboš Brim & Samuel Pastva & David Šafránek & Eva Šmijáková, 2021. "Parallel One-Step Control of Parametrised Boolean Networks," Mathematics, MDPI, vol. 9(5), pages 1-16, March.

    More about this item

    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:hin:complx:2108014. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.