New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption
Encryption algorithms mostly use key-streams generated from random number generators. Several recent studies have shown that the random number generator used is a chaos function. In this paper, a new chaos function will be developed which can be used as a chaotic random number generator. The develop...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2024-01-01
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| Series: | ITM Web of Conferences |
| Subjects: | |
| Online Access: | https://www.itm-conferences.org/articles/itmconf/pdf/2024/04/itmconf_iscpms2024_01004.pdf |
| _version_ | 1797343618968584192 |
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| author | Mudrika Mudrika Mt Suryadi Madenda Sarifuddin |
| author_facet | Mudrika Mudrika Mt Suryadi Madenda Sarifuddin |
| author_sort | Mudrika Mudrika |
| collection | DOAJ |
| description | Encryption algorithms mostly use key-streams generated from random number generators. Several recent studies have shown that the random number generator used is a chaos function. In this paper, a new chaos function will be developed which can be used as a chaotic random number generator. The development is carried out by forming a new chaos function using the function composition method. The function that is composed is the Gauss Map function against the Dyadic Transformation Map. The results of the new chaos function are chaotic, this is based on the results of the analysis obtained from the results of the bifurcation diagram, the Lyapunov Exponent and the National Institute of Standard Technologies Test (NIST) standard randomness test. The results of the bifurcation diagram show that the density is for the value of α ∈ [−30,0] and has periodic properties to choose the values of β ∈ [−1.02, −0.75], β ∈ [−0.60, −0.30], β ∈ [0.10, 0.25] and β ∈ [0.55, 0.75]. A positive value of Lyapunov Exponential diagram will be employed alpha equal to negative value (α < 0). The results of the NIST standard randomness test with values x0 = 0.9, α = −15 and β = 0.7 resulted in 100 % passing the test (16 tests). |
| first_indexed | 2024-03-08T10:50:24Z |
| format | Article |
| id | doaj.art-76b923c44ff44fe2927180c37cd1c0b5 |
| institution | Directory Open Access Journal |
| issn | 2271-2097 |
| language | English |
| last_indexed | 2024-03-08T10:50:24Z |
| publishDate | 2024-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ITM Web of Conferences |
| spelling | doaj.art-76b923c44ff44fe2927180c37cd1c0b52024-01-26T16:48:07ZengEDP SciencesITM Web of Conferences2271-20972024-01-01610100410.1051/itmconf/20246101004itmconf_iscpms2024_01004New chaos function of composition function Gauss map and dyadic transformation map for digital image encryptionMudrika Mudrika0Mt Suryadi1Madenda Sarifuddin2Department of Information Technology, Faculty of Computer Science and Information Technology (FIKTI), Universitas GunadarmaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas IndonesiaDepartment of Information Technology, Faculty of Computer Science and Information Technology (FIKTI), Universitas GunadarmaEncryption algorithms mostly use key-streams generated from random number generators. Several recent studies have shown that the random number generator used is a chaos function. In this paper, a new chaos function will be developed which can be used as a chaotic random number generator. The development is carried out by forming a new chaos function using the function composition method. The function that is composed is the Gauss Map function against the Dyadic Transformation Map. The results of the new chaos function are chaotic, this is based on the results of the analysis obtained from the results of the bifurcation diagram, the Lyapunov Exponent and the National Institute of Standard Technologies Test (NIST) standard randomness test. The results of the bifurcation diagram show that the density is for the value of α ∈ [−30,0] and has periodic properties to choose the values of β ∈ [−1.02, −0.75], β ∈ [−0.60, −0.30], β ∈ [0.10, 0.25] and β ∈ [0.55, 0.75]. A positive value of Lyapunov Exponential diagram will be employed alpha equal to negative value (α < 0). The results of the NIST standard randomness test with values x0 = 0.9, α = −15 and β = 0.7 resulted in 100 % passing the test (16 tests).https://www.itm-conferences.org/articles/itmconf/pdf/2024/04/itmconf_iscpms2024_01004.pdfnew chaoticcompositionbifurcationlyapunovnist random test |
| spellingShingle | Mudrika Mudrika Mt Suryadi Madenda Sarifuddin New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption ITM Web of Conferences new chaotic composition bifurcation lyapunov nist random test |
| title | New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption |
| title_full | New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption |
| title_fullStr | New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption |
| title_full_unstemmed | New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption |
| title_short | New chaos function of composition function Gauss map and dyadic transformation map for digital image encryption |
| title_sort | new chaos function of composition function gauss map and dyadic transformation map for digital image encryption |
| topic | new chaotic composition bifurcation lyapunov nist random test |
| url | https://www.itm-conferences.org/articles/itmconf/pdf/2024/04/itmconf_iscpms2024_01004.pdf |
| work_keys_str_mv | AT mudrikamudrika newchaosfunctionofcompositionfunctiongaussmapanddyadictransformationmapfordigitalimageencryption AT mtsuryadi newchaosfunctionofcompositionfunctiongaussmapanddyadictransformationmapfordigitalimageencryption AT madendasarifuddin newchaosfunctionofcompositionfunctiongaussmapanddyadictransformationmapfordigitalimageencryption |