Chaos Driven Quaternion Rotation Three-dimensional Constellation Encryption for WFRFT Communication

doi:10.12382/bgxb.2023.0393

Abstract

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

CLC Number:

TP309.7

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.

Figures/Tables 14

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

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

Fig.3 Block diagram of CQR3DE-MPWFRFT method system

Fig.4 Three-dimensional space modulation

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

Table 2 Quaternion rotation 3D constellation encryption

Table 3 Image encryption effect

Table 4 Image encryption histogram effect

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

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

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

Fig.5 Error rate analysis

Fig.6 Comparison of bit error rates

Table 8 Comparison of encrypted images of different schemes

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