Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups
We investigate several cryptographic properties in 8-bit S-boxes obtained by quasigroups of order 4 and 16 with several different algebraic constructions. Additionally, we offer a new construction of $N$-bit S-boxes by using different number of two layers -- the layer of bijectional quasigroup stri...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Vladimir Andrunachievici Institute of Mathematics and Computer Science
2020-12-01
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| Series: | Computer Science Journal of Moldova |
| Subjects: | |
| Online Access: | http://www.math.md/files/csjm/v28-n3/v28-n3-(pp346-372).pdf |
| _version_ | 1818474383965945856 |
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| author | Aleksandra Mileva Aleksandra Stojanova Dusan Bikov Yunqing Xu |
| author_facet | Aleksandra Mileva Aleksandra Stojanova Dusan Bikov Yunqing Xu |
| author_sort | Aleksandra Mileva |
| collection | DOAJ |
| description | We investigate several cryptographic properties in 8-bit S-boxes obtained by quasigroups of order 4 and 16 with several different algebraic constructions. Additionally, we offer a new construction of $N$-bit S-boxes by using different number of two layers -- the layer of bijectional quasigroup string transformations, and the layer of modular addition with $N$-bit constants. The best produced 8-bit S-boxes so far are regular and have algebraic degree 7, nonlinearity 98 (linearity 60), differential uniformity 8, and autocorrelation 88. Additionally we obtained 8-bit S-boxes with nonlinearity 100 (linearity 56), differential uniformity 10, autocorrelation 88, and minimal algebraic degree 6. Relatively small set of performed experiments compared with the extremly large set of possible experiments suggests that these results can be improved in the future. |
| first_indexed | 2024-04-14T04:36:14Z |
| format | Article |
| id | doaj.art-7ecc1b9ff0aa464998507bd56ee6c529 |
| institution | Directory Open Access Journal |
| issn | 1561-4042 |
| language | English |
| last_indexed | 2024-04-14T04:36:14Z |
| publishDate | 2020-12-01 |
| publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| record_format | Article |
| series | Computer Science Journal of Moldova |
| spelling | doaj.art-7ecc1b9ff0aa464998507bd56ee6c5292022-12-22T02:11:51ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422020-12-01283(84)346372Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by QuasigroupsAleksandra Mileva0Aleksandra Stojanova1Dusan Bikov2Yunqing Xu3Faculty of Computer Science, University "Goce Delcev" Stip, Republic of N. MacedoniaFaculty of Computer Science, University "Goce Delcev" Stip, Republic of N. MacedoniaFaculty of Computer Science, University "Goce Delcev" Stip, Republic of N. MacedoniaNingbo University, Peoples Republic of China, Ningbo, Peoples Republic of ChinaWe investigate several cryptographic properties in 8-bit S-boxes obtained by quasigroups of order 4 and 16 with several different algebraic constructions. Additionally, we offer a new construction of $N$-bit S-boxes by using different number of two layers -- the layer of bijectional quasigroup string transformations, and the layer of modular addition with $N$-bit constants. The best produced 8-bit S-boxes so far are regular and have algebraic degree 7, nonlinearity 98 (linearity 60), differential uniformity 8, and autocorrelation 88. Additionally we obtained 8-bit S-boxes with nonlinearity 100 (linearity 56), differential uniformity 10, autocorrelation 88, and minimal algebraic degree 6. Relatively small set of performed experiments compared with the extremly large set of possible experiments suggests that these results can be improved in the future.http://www.math.md/files/csjm/v28-n3/v28-n3-(pp346-372).pdf8-bit s-boxesnonlinearitydifferential uniformityautocorrelation |
| spellingShingle | Aleksandra Mileva Aleksandra Stojanova Dusan Bikov Yunqing Xu Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups Computer Science Journal of Moldova 8-bit s-boxes nonlinearity differential uniformity autocorrelation |
| title | Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups |
| title_full | Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups |
| title_fullStr | Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups |
| title_full_unstemmed | Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups |
| title_short | Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups |
| title_sort | investigation of some cryptographic properties of the 8x8 s boxes created by quasigroups |
| topic | 8-bit s-boxes nonlinearity differential uniformity autocorrelation |
| url | http://www.math.md/files/csjm/v28-n3/v28-n3-(pp346-372).pdf |
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