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International Conference on Hybrid Artificial Intelligence Systems

HAIS 2012: Hybrid Artificial Intelligent Systems pp 97–104Cite as

Cryptographic Applications of 3x3 Block Upper Triangular Matrices

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7209))

Abstract

In this paper we describe a special group of block upper triangular matrices with 3 ×3 blocks and elements in a finite field. We also verify that, with properly chosen parameters, the cardinality of the subgroup generated by one matrix of this group can be as large as required. Then we introduce two examples of this group of matrices employed in cryptography among the many available: a key exchange scheme and a pseudorandom generator.

Partially supported by University of Alicante grants GRE09-02 and GRE10-34 and Generalitat Valenciana grant GV/2011/01.

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References

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Author information

Authors and Affiliations

  1. Dpto. de Ciencia de la Computación e Inteligencia Artificial, Universidad de Alicante, (Campus de San Vicente) Ap. Correos 99, E–03080, Alicante, Spain

    Rafael Álvarez, Francisco Martínez, José-Francisco Vicent & Antonio Zamora

Authors
  1. Rafael Álvarez
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  2. Francisco Martínez
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  3. José-Francisco Vicent
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  4. Antonio Zamora
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Editor information

Editors and Affiliations

  1. Universidad de Salamanca, Plaza de la Merced S/N, 37008, Salamanca, Spain

    Emilio Corchado

  2. VŠB-TU Ostrava 17, Listopadu 15, 70833, Ostrava, Czech Republic

    Václav Snášel

  3. Machine Intelligence Research Labs Machine Intelligence Research Labs(MIR Labs),, Scientific Network for Innovation and Research Excellence, P.O. Box 2259, 98071, Auburn, Washington, USA

    Ajith Abraham

  4. Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370, Wroclaw, Poland

    Michał Woźniak

  5. University of the Basque Country, Pº Manuel Lardizabal 1, 20018, San Sebastian, Spain

    Manuel Graña

  6. Yonsei University, 134 Shinchon-dong, 120-749, Sudaemoon-ku, Seoul, Korea

    Sung-Bae Cho

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© 2012 Springer-Verlag Berlin Heidelberg

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Álvarez, R., Martínez, F., Vicent, JF., Zamora, A. (2012). Cryptographic Applications of 3x3 Block Upper Triangular Matrices. In: Corchado, E., Snášel, V., Abraham, A., Woźniak, M., Graña, M., Cho, SB. (eds) Hybrid Artificial Intelligent Systems. HAIS 2012. Lecture Notes in Computer Science(), vol 7209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28931-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-28931-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28930-9

  • Online ISBN: 978-3-642-28931-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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