Low order chaotic maps has many distinct physiognomies, such as strong sensitiveness to initial conditions, parameters, better unpredictability, distinct random like complex temporal behavior and so on. This results the demand of new generators for chaotic systems with complicated dynamics but simple designs. In this work, a 4D mixed chaotic map with hyper-chaotic properties and high randomness behavior has been constructed by using the 1D Sine map and the 2D Thinker bell map. Furthermore, by using the proposed chaotic system and symmetric group S₈ permutation, a novel image encryption scheme is introduced to explore the applications of the proposed chaotic system. The action of symmetric group S₈ increases the key size by a factor of (8!)⁶⁵⁵³⁶ for an image of size 256 × 256 which results a strong encryption structure to resists the well-known attacks. Simulation results on different images and extensive security analysis demonstrate that the proposed approach has adequate properties in image encryption.

低阶混沌图具有许多独特的面貌，如对初始条件、参数的敏感性强，更好的不可预测性，像复杂的时间行为那样明显的随机性等。这导致对具有复杂动力学但设计简单的混沌系统的新生成器的需求。在这项工作中，使用一维正弦图和二维 Thinker 钟形图构建了具有超混沌特性和高随机行为的 4D 混合混沌图。此外，通过使用所提出的混沌系统和对称群S ₈ 置换，引入了一种新的图像加密方案来探索所提出的混沌系统的应用。对称群S ₈的作用使密钥大小增加了 (8!) ⁶⁵⁵³⁶倍对于大小为 256 × 256 的图像，这会产生强大的加密结构以抵抗众所周知的攻击。不同图像的仿真结果和广泛的安全分析表明，所提出的方法在图像加密方面具有足够的特性。