具隨機係數之二階混沌映射產生用於高安全性影像加密之複雜混沌序列

Abstract

混沌映射因其複雜性和敏感性而被廣泛應用於圖像加密到關鍵變化。在本篇論文中，我們提出了用最佳化的二階混沌映射隨機係數來產生用於影像加密的混沌序列。利用兩種篩選條件，依據複雜度指數 K 和 SE 找出 300 個候選的混沌映射利用粒子群最佳化演算法來搜尋最優八種不同加權方案下的混沌映射。最優混沌映射可以達到 Np = 2，DKY = 2，CD = 2，K > 0.9，SE > 0.9 且 PE > 0.7。所有關鍵敏感度分析系統參數和初始值證實了最優混沌映射的高安全性。另提出了混合序列生成（HSG）方案以進一步減少影像加密時間。

Chaotic maps have been widely applied on image encryption for their complexity and sensitivity to key variation. In this work, we propose second-order chaotic maps with optimized random coefficients to generate chaotic sequences for image encryption. Two screening conditions are proposed to identify 300 candidate chaotic maps in terms of complexity indices K and SE. A particle swarm optimization algorithm is developed to search for the optimal chaotic maps under eight different weighting schemes. The optimal chaotic maps can achieve Np = 2, DKY = 2, CD= 2, K > 0.9, SE> 0.9 and PE> 0.7. Key sensitivity analysis on all the system parameters and initial values confirms high security of the optimal chaotic maps. A hybrid sequence generation (HSG) scheme is also proposed to further reduce the image encryption time.