A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography
Cryptography is the science and study of protecting data in computer and communication systems from unauthorized disclosure and modification. An ordinary difference equation (a map) can be used in encryption–decryption algorithms. In particular, the Arnold’s cat and the sine-Gordon linear maps can b...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/14/4/124 |
| _version_ | 1797537449703899136 |
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| author | La Zakaria Endah Yuliani Asmiati Asmiati |
| author_facet | La Zakaria Endah Yuliani Asmiati Asmiati |
| author_sort | La Zakaria |
| collection | DOAJ |
| description | Cryptography is the science and study of protecting data in computer and communication systems from unauthorized disclosure and modification. An ordinary difference equation (a map) can be used in encryption–decryption algorithms. In particular, the Arnold’s cat and the sine-Gordon linear maps can be used in cryptographic algorithms for encoding digital images. In this article, a two-dimensional linear mKdV map derived from an ordinary difference mKdV equation will be used in a cryptographic encoding algorithm. The proposed encoding algorithm will be compared with those generated using sine-Gordon and Arnold’s cat maps via the correlations between adjacent pixels in the encrypted image and the uniformity of the pixel distribution. Note that the mKdV map is derived from the partial discrete mKdV equation with Consistency Around the Cube (CAC) properties, whereas the sine-Gordon map is derived from the partial discrete sine-Gordon equation, which does not have CAC properties. |
| first_indexed | 2024-03-10T12:16:17Z |
| format | Article |
| id | doaj.art-4f33cf0f44594c9687de969f8c7d7170 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-10T12:16:17Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-4f33cf0f44594c9687de969f8c7d71702023-11-21T15:49:48ZengMDPI AGAlgorithms1999-48932021-04-0114412410.3390/a14040124A Two-Dimensional mKdV Linear Map and Its Application in Digital Image CryptographyLa Zakaria0Endah Yuliani1Asmiati Asmiati2Department of Mathematics, Universitas Lampung, Bandar Lampung 35145, IndonesiaDepartment of Mathematics, Universitas Lampung, Bandar Lampung 35145, IndonesiaDepartment of Mathematics, Universitas Lampung, Bandar Lampung 35145, IndonesiaCryptography is the science and study of protecting data in computer and communication systems from unauthorized disclosure and modification. An ordinary difference equation (a map) can be used in encryption–decryption algorithms. In particular, the Arnold’s cat and the sine-Gordon linear maps can be used in cryptographic algorithms for encoding digital images. In this article, a two-dimensional linear mKdV map derived from an ordinary difference mKdV equation will be used in a cryptographic encoding algorithm. The proposed encoding algorithm will be compared with those generated using sine-Gordon and Arnold’s cat maps via the correlations between adjacent pixels in the encrypted image and the uniformity of the pixel distribution. Note that the mKdV map is derived from the partial discrete mKdV equation with Consistency Around the Cube (CAC) properties, whereas the sine-Gordon map is derived from the partial discrete sine-Gordon equation, which does not have CAC properties.https://www.mdpi.com/1999-4893/14/4/124cryptographydigital imagelinear mKdV maplinear sine-Gordon mapCAC properties |
| spellingShingle | La Zakaria Endah Yuliani Asmiati Asmiati A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography Algorithms cryptography digital image linear mKdV map linear sine-Gordon map CAC properties |
| title | A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography |
| title_full | A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography |
| title_fullStr | A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography |
| title_full_unstemmed | A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography |
| title_short | A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography |
| title_sort | two dimensional mkdv linear map and its application in digital image cryptography |
| topic | cryptography digital image linear mKdV map linear sine-Gordon map CAC properties |
| url | https://www.mdpi.com/1999-4893/14/4/124 |
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