Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant
In this work, a color image encryption and decryption algorithm for digital images is presented. It is based on the modular discrete derivative (MDD), a novel technique to encrypt images and efficiently hide visual information. In addition, Langton’s ant, which is a two-dimensional universal Turing...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/10/2396 |
| _version_ | 1797599218255265792 |
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| author | Ernesto Moya-Albor Andrés Romero-Arellano Jorge Brieva Sandra L. Gomez-Coronel |
| author_facet | Ernesto Moya-Albor Andrés Romero-Arellano Jorge Brieva Sandra L. Gomez-Coronel |
| author_sort | Ernesto Moya-Albor |
| collection | DOAJ |
| description | In this work, a color image encryption and decryption algorithm for digital images is presented. It is based on the modular discrete derivative (MDD), a novel technique to encrypt images and efficiently hide visual information. In addition, Langton’s ant, which is a two-dimensional universal Turing machine with a high key space, is used. Moreover, a deterministic noise technique that adds security to the MDD is utilized. The proposed hybrid scheme exploits the advantages of MDD and Langton’s ant, generating a very secure and reliable encryption algorithm. In this proposal, if the key is known, the original image is recovered without loss. The method has demonstrated high performance through various tests, including statistical analysis (histograms and correlation distributions), entropy, texture analysis, encryption quality, key space assessment, key sensitivity analysis, and robustness to differential attack. The proposed method highlights obtaining chi-square values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>233.951</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>281.687</mn></mrow></semantics></math></inline-formula>, entropy values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>7.9999225223</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>7.9999355791</mn></mrow></semantics></math></inline-formula>, PSNR values (in the original and encrypted images) between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8.134</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9.957</mn></mrow></semantics></math></inline-formula>, the number of pixel change rate (NPCR) values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99.60851796</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99.61054611</mn><mo>%</mo></mrow></semantics></math></inline-formula>, unified average changing intensity (UACI) values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>33.44672377</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>33.47430379</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and a vast range of possible keys <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>></mo><mn>5.8459</mn><mo>×</mo><msup><mn>10</mn><mn>72</mn></msup></mrow></semantics></math></inline-formula>. On the other hand, an analysis of the sensitivity of the key shows that slight changes to the key do not generate any additional information to decrypt the image. In addition, the proposed method shows a competitive performance against recent works found in the literature. |
| first_indexed | 2024-03-11T03:31:37Z |
| format | Article |
| id | doaj.art-bb6d95b076534727ba7ef00b165600aa |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T03:31:37Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bb6d95b076534727ba7ef00b165600aa2023-11-18T02:20:24ZengMDPI AGMathematics2227-73902023-05-011110239610.3390/math11102396Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s AntErnesto Moya-Albor0Andrés Romero-Arellano1Jorge Brieva2Sandra L. Gomez-Coronel3Facultad de Ingeniería, Universidad Panamericana, Augusto Rodin 498, Ciudad de México 03920, MexicoFacultad de Ingeniería, Universidad Panamericana, Augusto Rodin 498, Ciudad de México 03920, MexicoFacultad de Ingeniería, Universidad Panamericana, Augusto Rodin 498, Ciudad de México 03920, MexicoInstituto Politecnico Nacional, UPIITA, Av. IPN No. 2580, Col. La Laguna Ticoman, Ciudad de México 07340, MexicoIn this work, a color image encryption and decryption algorithm for digital images is presented. It is based on the modular discrete derivative (MDD), a novel technique to encrypt images and efficiently hide visual information. In addition, Langton’s ant, which is a two-dimensional universal Turing machine with a high key space, is used. Moreover, a deterministic noise technique that adds security to the MDD is utilized. The proposed hybrid scheme exploits the advantages of MDD and Langton’s ant, generating a very secure and reliable encryption algorithm. In this proposal, if the key is known, the original image is recovered without loss. The method has demonstrated high performance through various tests, including statistical analysis (histograms and correlation distributions), entropy, texture analysis, encryption quality, key space assessment, key sensitivity analysis, and robustness to differential attack. The proposed method highlights obtaining chi-square values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>233.951</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>281.687</mn></mrow></semantics></math></inline-formula>, entropy values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>7.9999225223</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>7.9999355791</mn></mrow></semantics></math></inline-formula>, PSNR values (in the original and encrypted images) between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8.134</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9.957</mn></mrow></semantics></math></inline-formula>, the number of pixel change rate (NPCR) values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99.60851796</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99.61054611</mn><mo>%</mo></mrow></semantics></math></inline-formula>, unified average changing intensity (UACI) values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>33.44672377</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>33.47430379</mn><mo>%</mo></mrow></semantics></math></inline-formula>, and a vast range of possible keys <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>></mo><mn>5.8459</mn><mo>×</mo><msup><mn>10</mn><mn>72</mn></msup></mrow></semantics></math></inline-formula>. On the other hand, an analysis of the sensitivity of the key shows that slight changes to the key do not generate any additional information to decrypt the image. In addition, the proposed method shows a competitive performance against recent works found in the literature.https://www.mdpi.com/2227-7390/11/10/2396image encryption and decryptionmodular discrete derivativecellular automataLangton’s antdeterministic noisechaos theory |
| spellingShingle | Ernesto Moya-Albor Andrés Romero-Arellano Jorge Brieva Sandra L. Gomez-Coronel Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant Mathematics image encryption and decryption modular discrete derivative cellular automata Langton’s ant deterministic noise chaos theory |
| title | Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant |
| title_full | Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant |
| title_fullStr | Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant |
| title_full_unstemmed | Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant |
| title_short | Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant |
| title_sort | color image encryption algorithm based on a chaotic model using the modular discrete derivative and langton s ant |
| topic | image encryption and decryption modular discrete derivative cellular automata Langton’s ant deterministic noise chaos theory |
| url | https://www.mdpi.com/2227-7390/11/10/2396 |
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