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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2503.23655 |
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| _version_ | 1866915814933790720 |
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| author | Sun, Jilei Wu, Dianhong |
| author_facet | Sun, Jilei Wu, Dianhong |
| contents | This paper focuses on hyperchaotic-map construction and proposes a 3D-Cascading Crossing Coupling framework (3D-CCC), which cascades, crosses, and couples three one-dimensional chaotic maps to form a three-dimensional hyperchaotic system. The framework avoids modulo-1 operations and introduces bounded-state and denominator safeguards for stable digital implementation. A general 3D-CCC formulation is established, and its derivative/Jacobian structure is analyzed to characterize multidirectional expansion. By instantiating ICMIC, Logistic, and Sine maps, a concrete system (3D-ILS) is derived. Phase portraits, bifurcation behavior, sensitivity tests, and Lyapunov-exponent analysis indicate pronounced ergodicity and hyperchaotic dynamics. As an application of the constructed map, a one-round RGB image-encryption scheme is developed using cross-channel bit mixing with joint permutation-diffusion. Under the reported settings, the cipher reaches near-ideal entropy (average 7.9993), NPCR of 96.61\%, UACI of 33.46\%, and an effective key space of about $2^{309}$. These results support the effectiveness of 3D-CCC as a practical framework for hyperchaotic-system design, with image encryption as one representative application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A 3D-Cascading Crossing Coupling Framework for Hyperchaotic Map Construction and Its Application to Color Image Encryption Sun, Jilei Wu, Dianhong Multimedia This paper focuses on hyperchaotic-map construction and proposes a 3D-Cascading Crossing Coupling framework (3D-CCC), which cascades, crosses, and couples three one-dimensional chaotic maps to form a three-dimensional hyperchaotic system. The framework avoids modulo-1 operations and introduces bounded-state and denominator safeguards for stable digital implementation. A general 3D-CCC formulation is established, and its derivative/Jacobian structure is analyzed to characterize multidirectional expansion. By instantiating ICMIC, Logistic, and Sine maps, a concrete system (3D-ILS) is derived. Phase portraits, bifurcation behavior, sensitivity tests, and Lyapunov-exponent analysis indicate pronounced ergodicity and hyperchaotic dynamics. As an application of the constructed map, a one-round RGB image-encryption scheme is developed using cross-channel bit mixing with joint permutation-diffusion. Under the reported settings, the cipher reaches near-ideal entropy (average 7.9993), NPCR of 96.61\%, UACI of 33.46\%, and an effective key space of about $2^{309}$. These results support the effectiveness of 3D-CCC as a practical framework for hyperchaotic-system design, with image encryption as one representative application. |
| title | A 3D-Cascading Crossing Coupling Framework for Hyperchaotic Map Construction and Its Application to Color Image Encryption |
| topic | Multimedia |
| url | https://arxiv.org/abs/2503.23655 |