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.

翻译：本文聚焦于超混沌映射的构建，提出了一种三维级联交叉耦合框架（3D-CCC）。该框架通过级联、交叉和耦合三个一维混沌映射，构建出一个三维超混沌系统。该框架避免了模1运算，并引入了有界状态和分母保护机制以确保稳定的数字实现。本文建立了通用的3D-CCC公式，并通过分析其导数/雅可比矩阵结构来表征其多向扩展特性。通过实例化ICMIC、Logistic和Sine映射，推导出一个具体系统（3D-ILS）。相图、分岔行为、敏感性测试和Lyapunov指数分析表明，该系统具有显著的遍历性和超混沌动力学特性。作为所构建映射的一个应用，本文利用跨通道比特混合与联合置乱-扩散技术，开发了一种单轮RGB图像加密方案。在所述设置下，该密码方案达到了接近理想的熵值（平均7.9993）、NPCR为96.61%、UACI为33.46%，以及约$2^{309}$的有效密钥空间。这些结果支持3D-CCC作为超混沌系统设计的实用框架的有效性，图像加密是其代表性应用之一。