Authors: Dimitrova, Vesna
Bakeva, Verica
Popovska-Mitrovikj, Aleksandra
Krapež, Aleksandar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Cryptographic properties of parastrophic quasigroup transformation
Journal: Advances in Intelligent Systems and Computing
Volume: 207 AISC
First page: 235
Last page: 243
Conference: 4th ICT Innovations Conference on Secure and Intelligent Systems; Ohrid; North Macedonia; 12 September 2012 through 15 September 2012
Issue Date: 1-Jan-2013
ISBN: 978-3-642-37168-4
ISSN: 2194-5357
DOI: 10.1007/978-3-642-37169-1_23
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.
Keywords: cryptographic properties | experimental mathematics | parastrophic quasigroup transformations | quasigroup
Publisher: Springer Link

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