Cryptanalysis of a family of 1D unimodal maps
In this paper, we proposed a topologically conjugate map,equivalent to the well known logistic map. This constructed map is defined on the integer domain [0, 2n) with a view to be used as a random number generator (RNG) based on an integer domain as is the required in classical cryptography. The maps...
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| Format: | Article |
| Language: | English |
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Springer Verlag
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/61262/ http://psasir.upm.edu.my/id/eprint/61262/1/CRYP.pdf |
| _version_ | 1848854377053290496 |
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| author | Md Said, Mohamad Rushdan Hina, Aliyu Danladi Banerjee, Santo |
| author_facet | Md Said, Mohamad Rushdan Hina, Aliyu Danladi Banerjee, Santo |
| author_sort | Md Said, Mohamad Rushdan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we proposed a topologically conjugate map,equivalent to the well known logistic map. This constructed map is defined on the integer domain [0, 2n) with a view to be used as a random number generator (RNG) based on an integer domain as is the required in classical cryptography. The maps were found to have a one to one correspondence between points in their respective defining intervals defined on an n-bits precision. The dynamics of the proposed map similar with that of the logistic map, in terms of the Lyapunov exponents with the control parameter. This similarity between the curves indicates topological conjugacy between the maps. With a view to be applied in cryptography as a Pseudo-Random number genera-tor (PRNG), the complexity of the constructed map as a source of randomness is determined using both the permutation entropy (PE)and the Lempel-Ziv (LZ-76) complexity measures, and the results are compared with numerical simulations. |
| first_indexed | 2025-11-15T11:08:54Z |
| format | Article |
| id | upm-61262 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:08:54Z |
| publishDate | 2017 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-612622021-07-16T09:47:43Z http://psasir.upm.edu.my/id/eprint/61262/ Cryptanalysis of a family of 1D unimodal maps Md Said, Mohamad Rushdan Hina, Aliyu Danladi Banerjee, Santo In this paper, we proposed a topologically conjugate map,equivalent to the well known logistic map. This constructed map is defined on the integer domain [0, 2n) with a view to be used as a random number generator (RNG) based on an integer domain as is the required in classical cryptography. The maps were found to have a one to one correspondence between points in their respective defining intervals defined on an n-bits precision. The dynamics of the proposed map similar with that of the logistic map, in terms of the Lyapunov exponents with the control parameter. This similarity between the curves indicates topological conjugacy between the maps. With a view to be applied in cryptography as a Pseudo-Random number genera-tor (PRNG), the complexity of the constructed map as a source of randomness is determined using both the permutation entropy (PE)and the Lempel-Ziv (LZ-76) complexity measures, and the results are compared with numerical simulations. Springer Verlag 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/61262/1/CRYP.pdf Md Said, Mohamad Rushdan and Hina, Aliyu Danladi and Banerjee, Santo (2017) Cryptanalysis of a family of 1D unimodal maps. European Physical Journal: Special Topics, 226 (10). pp. 2281-2297. ISSN 1951-6355; ESSN: 1951-6401 https://link.springer.com/article/10.1140/epjst/e2017-70011-y#citeas 10.1140/epjst/e2017-70011-y |
| spellingShingle | Md Said, Mohamad Rushdan Hina, Aliyu Danladi Banerjee, Santo Cryptanalysis of a family of 1D unimodal maps |
| title | Cryptanalysis of a family of 1D unimodal maps |
| title_full | Cryptanalysis of a family of 1D unimodal maps |
| title_fullStr | Cryptanalysis of a family of 1D unimodal maps |
| title_full_unstemmed | Cryptanalysis of a family of 1D unimodal maps |
| title_short | Cryptanalysis of a family of 1D unimodal maps |
| title_sort | cryptanalysis of a family of 1d unimodal maps |
| url | http://psasir.upm.edu.my/id/eprint/61262/ http://psasir.upm.edu.my/id/eprint/61262/ http://psasir.upm.edu.my/id/eprint/61262/ http://psasir.upm.edu.my/id/eprint/61262/1/CRYP.pdf |