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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