Multiple Parameters Weighted-type FRactional Fourier Transform Secure Communication Method Based on Cosine Power-Activation Discrete Hyperchaotic Encryption
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摘要: 为提高物理层安全传输性能，该文提出一种新的基于2维余幂-激活(2D-CPA)离散超混沌加密的多参数加权分数傅里叶变换(MP-WFRFT)安全通信方法。首先，将激活函数和余弦函数作为非线性因子引入1维立方(cubic)混沌映射，构造2维混沌映射。非线性因子可对原始cubic混沌映射的迭代过程进行扰动，从而获得更加饱满的相轨。利用分岔图、相图、Lyapunov指数谱等对提出的2维混沌映射动力学特性进行了验证。结果表明，构造的2维混沌序列随机性良好，可进入超混沌状态。然后，利用余幂-激活离散超混沌序列分别构建幅度变换矩阵、相位旋转矩阵和MP-WFRFT参数池，完成对星座幅相加密，以及MP-WFRFT动态变换加密过程，进一步消除数据统计特征，同时提升MP-WFRFT变换的抗参数扫描性能。数值仿真结果表明，加密数据的星座图呈类高斯分布，且传输系统对密钥的敏感性良好。
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关键词:
- 2维离散超混沌 /
- 星座加密 /
- 多参数加权分数傅里叶变换 /
- Lyapunov指数
Abstract: To improve the secure transmission performance of physical layer, a novel Multiple Parameters Weighted-type FRactional Fourier Transform (MP-WFRFT) secure communication method based on Two-Dimensional Cosine Power-Activation (2D-CPA) discrete hyperchaotic encryption is proposed. Firstly, the activation function and cosine function are introduced into the one-dimensional cubic chaos map as nonlinear factors to construct the 2D chaos map. The nonlinear factor can perturb the iterative process of the original cubic chaotic map so as to obtain a fuller phase orbit. The dynamic characteristics of the proposed two-dimensional chaotic mapping are verified by using bifurcation diagram, phase diagram and Lyapunov exponential spectrum. The results show that the constructed 2D chaotic sequence has good randomness and can enter hyperchaotic state. Then, the amplitude transformation matrix, phase rotation matrix and MP-WFRFT parameter pool are constructed by using 2D-CPA hyperchaotic sequence respectively to complete the constellation amplitude phase encryption and MP-WFRFT dynamic transformation encryption process, the statistical characteristics of data are further eliminated and the anti-parameter scanning performance of MP-WFRFT transform is improved. Numerical simulation results show that the constellation diagram of the encrypted data is Gaussian-like and that the transmission system is well sensitive to the key. -
表 1 两类混沌映射的Lyapunov指数、ApEn和PE
混沌映射 最大Lyapunov指数 ApEn PE cubic 0.6512 0.6403 0.9290 2D-CPA 0.8054 0.9689 0.9955 
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