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Cryptographic Properties of Parastrophic Quasigroup Transformation

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ICT Innovations 2012 (ICT Innovations 2012)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 207))

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Abstract

We consider cryptographic properties of parastrophic quasigroup transformation defined elsewhere. Using this transformation we classify the quasigroups of order 4 into three classes: 1) parastrophic fractal; 2) fractal and parastrophic non-fractal; and 3) non-fractal. We investigate the algebraic properties of above classes and present a relationship between fractal and algebraic properties of quasigroups of order 4. We also find a number of different parastrophes of each quasigroup of order 4 and use it to divide the set of all quasigroups of order 4 into four classes. Using these classifications the number of quasigroups of order 4 which are suitable for designing of cryptographic primitives is increased compared to the case where parastrophes are not used.

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References

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Authors and Affiliations

  1. Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University, Skopje, Macedonia

    Vesna Dimitrova, Verica Bakeva & Aleksandra Popovska-Mitrovikj

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Aleksandar Krapež

Authors
  1. Vesna Dimitrova
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  2. Verica Bakeva
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  3. Aleksandra Popovska-Mitrovikj
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  4. Aleksandar Krapež
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Corresponding author

Correspondence to Vesna Dimitrova .

Editor information

Editors and Affiliations

  1. , Faculty of Computer Science, Ss Cyrill and Methodius University, Ruger Boskovic 16, POBox 393, Skopje, 1000, Macedonia

    Smile Markovski

  2. , Faculty of Information Sciences, Ss Cyrill and Methodius University, Ruger Boskovic 16, Skopje, 1000, Macedonia

    Marjan Gusev

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Dimitrova, V., Bakeva, V., Popovska-Mitrovikj, A., Krapež, A. (2013). Cryptographic Properties of Parastrophic Quasigroup Transformation. In: Markovski, S., Gusev, M. (eds) ICT Innovations 2012. ICT Innovations 2012. Advances in Intelligent Systems and Computing, vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37169-1_23

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  • DOI: https://doi.org/10.1007/978-3-642-37169-1_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37168-4

  • Online ISBN: 978-3-642-37169-1

  • eBook Packages: EngineeringEngineering (R0)

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