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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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
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