混沌驱动四元数旋转三维星座加密的WFRFT通信方法

doi:10.12382/bgxb.2023.0393

摘要/Abstract

摘要：

针对现有一维混沌映射序列分布不均和映射参数范围有限的问题,提出一种改进型的一维逻辑正弦混沌映射,在此基础上设计了一种混沌驱动四元数旋转三维星座加密的多参数加权分数傅里叶变换(Chaos driven Quaternion Rotation 3D constellation Encrypted-Multiple Parameters Weighted-type Fractional Fourier Transform, CQR3DE-MPWFRFT)通信方法。Logistic映射和Sine映射耦合,提出L-S混沌映射,将需要传输的信息进行三维星座调制。通过L-S混沌映射产生的混沌密钥驱动生成四元数,对生成的三维星座图进行旋转加密。进行多参数加权分数傅里叶变换(Multiple Parameters Weighted-type Fractional Fourier Transform, MPWFRFT)之后,完成数字调制。仿真结果表明:该混沌映射参数范围更大,随机性更好;所设计的CQR3DE-MPWFRFT方法利用L-S混沌驱动四元数实现了二维星座到三维星座的旋转加密,其星座点与传统调制相比星座空间更大,相较于MPWFRFT方法系统误码率性能有一定的提升,即使窃听方密钥只有10^-15的差异,仍然无法完成窃听,能够提高信息在物理层的传输安全。

关键词: 三维调制, 四元数, 混沌加密, 物理层安全

Abstract:

To address the issues of uneven distribution and limited mapping parameter ranges of existing one-dimensional chaotic mapping sequences, an improved one-dimensional logical sine chaotic mapping is presented. A chaos encrypted multi-parameter weighted-type fractional Fouier transform (MPWFRFT) called chaos driven quaternion rotation three-dimensional (3D) constellation encryption (CQR3DE-MPWFRFT) communication method is proposed to improve the secure transmission performance in the physical layer. Logistic mapping and Sine mapping are coupled together to form a new L-S chaotic mapping. The information that needs to be transmitted is modulated in 3D space. A chaotic key is generated from L-S chaotic mapping to drive quaternions, which rotates and encrypts the generated 3D constellation. The whole digital modulation process is completed after MPWFRFT. The whole system performance is verified through simulation. The simulated results indicate that the proposed L-S chaotic mapping has a larger parameter range and better randomness. The proposed CQR3DE-MPWFRFT method utilizes L-S chaos to drive quaternions, and can achieve the rotational encryption from two-dimensional constellations to 3D constellations which have a larger constellation distance compared to traditional 2D modulation. The bit error rate performance of CQR3DE-MPWFRFT method can be greatly improved. Even if the eavesdropper's key is only 10^-15 different from the correct key, eavesdropping cannot be completed, which helps to improve the transmission security of information in the physical layer.

Key words: three-dimensional modulation, quaternion, chaotic encryption, physical layer security

中图分类号:

TP309.7

于浩洋, 孟庆微, 贠彦直, 王西康. 混沌驱动四元数旋转三维星座加密的WFRFT通信方法[J]. 兵工学报, 2024, 45(8): 2531-2541.

YU Haoyang, MENG Qingwei, YUN Yanzhi, WANG Xikang. Chaos Driven Quaternion Rotation Three-dimensional Constellation Encryption for WFRFT Communication[J]. Acta Armamentarii, 2024, 45(8): 2531-2541.

图/表 14

图1 L-S映射分岔图

Fig.1 Bifurcation diagram of the proposed L-S mapping

图2 Lyapunov指数图谱

Fig.2 Lyapunov exponent graph of the proposed L-S mapping

图3 CQR3DE-MPWFRFT方法系统框图

Fig.3 Block diagram of CQR3DE-MPWFRFT method system

图4 三维空间调制

Fig.4 Three-dimensional space modulation

表1 仿真参数及密钥

Table 1 Simulation parameters and keys

参数	密钥
r₀,k₀,t₀,u₀	0.255,0.448,0.611,0.877
μ,σ,φ,ρ	9.57,15.64,45.79,27.91
m₁,m₂,m₃,m₄	1,3,4,6
n₁,n₂,n₃,n₄	2,3,1,5

表2 四元数旋转三维星座加密

Table 2 Quaternion rotation 3D constellation encryption

表3 图像加密效果

Table 3 Image encryption effect

表4 图像加密效果直方图

Table 4 Image encryption histogram effect

表5 信息熵对比

Table 5 Comparison of information entropies

图像及平均值	原图	本文方法	文献[1]方法	文献[5]方法
cameraman	7.0097	7.9972	7.9973	7.9894
lena	7.4429	7.9971	7.9969	7.9893
peppers	7.5797	7.9977	7.9970	7.9896
平均值	7.3441	7.9973	7.9971	7.9894

表6 相关性对比

Table 6 Correlation comparison

信息熵	加密前	加密后	文献[4]方法
水平方向	0.9213	-0.0020	0.0029
垂直方向	0.9571	-0.0021	-0.0324
对角线方向	0.8951	0.0189	-0.0021
绝对平均值	0.9245	0.0077	0.0125

表7 cameraman图像加密前后相邻像素相关性分析

Table 7 Correlation distribution of adjacent pixels before and after cameraman image encryption

图5 误码率分析

Fig.5 Error rate analysis

图6 误码率对比

Fig.6 Comparison of bit error rates

表8 不同方案的加密图像对比

Table 8 Comparison of encrypted images of different schemes

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