MUCCHI L , JAYOUSI S , CAPUTO S , et al . Physical-layer security in 6G networks [J ] . IEEE Open Journal of the Communications Society , 2021 , 2 : 1901 - 1914 . DOI: 10.1109/OJCOMS.2021.3103735 http://doi.org/10.1109/OJCOMS.2021.3103735 https://ieeexplore.ieee.org/document/9509581/ https://ieeexplore.ieee.org/document/9509581/

王颖 , 张晓忠 , 曾娟 , 等 . 基于二级混沌映射的OFDM安全传输方案 [J ] . 通信学报 , 2016 , 37 ( 7 ): 132 - 139 . DOI: 10.11959/j.issn.1000-436x.2016141 http://doi.org/10.11959/j.issn.1000-436x.2016141 基于OFDM技术，结合混沌序列的伪随机特性和初值敏感性，提出了一种数据相位混沌旋转和子载波混沌映射的安全传输方案。仿真结果和分析表明，该方案能够有效地对信息进行混沌安全传输，增强输出信号的随机特性，窃听方无法通过信号的统计特性估计出发送信息，从而保证通信的安全性。与常用的安全措施，如AES（高级加密标准）、多天线随机化传输矩阵等方法相比，所述方案能够达到较好的计算安全性。

WANG Y , ZHANG X Z , ZENG J , et al . A secure OFDM transmission scheme based on two-level chaotic mapping [J ] . Journal of Communication , 2016 , 37 ( 7 ): 132 - 139 . (in Chinese)

倪磊 , 达新宇 , 胡航 , 等 . 基于改进Logistic相位扰码的抗截获通信 [J ] . 华中科技大学学报 , 2019 , 47 ( 6 ): 35 - 40 .

NI L , DA X Y , HU H , et al . Anti-interception communication based on improved logistic phase scrambling code [J ] . Journal of Huazhong University of Science and Technology , 2019 , 47 ( 6 ): 35 - 40 . (in Chinese)

HU Z Y , CHAN C K . A 7-D hyperchaotic system-based encryption scheme for secure fast-OFDM-PON [J ] . Journal of Lightwave Technology , 2018 , 36 ( 16 ): 3373 - 3381 . DOI: 10.1109/JLT.2018.2841042 http://doi.org/10.1109/JLT.2018.2841042 https://ieeexplore.ieee.org/document/8367792/ https://ieeexplore.ieee.org/document/8367792/

SULTAN A , YANG X L , HAJOMER A , et al . Chaotic distribution of QAM symbols for secure OFDM signal transmission [J ] . Optical Fiber Technology , 2019 , 47 : 61 - 65 . DOI: 10.1016/j.yofte.2018.11.022 http://doi.org/10.1016/j.yofte.2018.11.022 This paper proposes and demonstrates a novel dynamic quadrature amplitude modulation (QAM) mapping scheme to provide a secure physical-layer transmission in orthogonal frequency division multiplexing passive optical network (OFDM-PON). In the proposed scheme, permutated QAM symbols are independently and randomly mapped onto chaotically selected new locations on the complex plane. With the proposed encryption scheme these new locations are within the dimensions of a conventional QAM. A hyper digital chaos is applied to perform a multi-fold encryption in the proposed scheme which involves dynamic QAM mapping as well as time domain and frequency domain permutations on QAM symbols. As a result, a noise-like constellation with a key space of similar to 10(310) is achieved to enhance the high-level security in physical-layer transmission. A successful transmission experiment of 9.4-Gb/s encrypted 16-QAM OFDM signals is demonstrated over 25-km standard single mode fiber (SSMF), where the robust security and transmission performances are validated.

牛莹 , 张勋才 . 基于变步长约瑟夫遍历和DNA动态编码的图像加密算法 [J ] . 电子与信息学报 , 2020 , 42 ( 6 ): 1383 - 1391 .

NIU Y , ZHANG X C . Image encryption algorithm based on variable-step Joseph traversal and DNA dynamic coding [J ] . Journal of Electronics and Information , 2020 , 42 ( 6 ): 1383 - 1391 . (in Chinese)

张勋才 , 刘奕杉 , 崔光照 . 基于DNA编码和超混沌系统的图像加密算法 [J ] . 计算机应用研究 , 2019 , 36 ( 4 ): 1139 - 1143 .

ZHANG X C , LIU Y S , CUI G Z . An image encryption algorithm based on DNA coding and hyperchaotic systems [J ] . Computer Application Research , 2019 , 36 ( 4 ): 1139 - 1143 . (in Chinese)

李锦青 , 刘泽飞 , 满振龙 . 基于生成对抗网络的密钥生成方法及其在微光图像加密中的应用 [J ] . 兵工学报 , 2022 , 43 ( 2 ): 337 - 344 .

LI J Q , LIU Z F , MAN Z L . Key generation method based on generative adversarial network and its application in low-light-level image encryption [J ] . Acta Armamentarii , 2022 , 43 ( 2 ): 337 - 344 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2022.02.011 http://doi.org/10.3969/j.issn.1000-1093.2022.02.011 Generative adversarial network (GAN) is a deep learning model, which is one of the most promising methods for unsupervised learning in complex distributed environment in recent years. The random numbers generated by GAN and chaotic systems have many similar advantages, such as randomness and sensitivity. But at the same time,the random numbers generated by GAN have the features that the random numbers generated by chaotic systems do not have, such as non-reproducibility.The random number generated by GAN training shows its rapidity and higher security in the encryption of low-light-level images with low signal-to-noise ratio and few gray levels. GAN is introduced into the random key generation. The pseudo-random number generated by quantum cellular neural network (QCNN) system is used as the training set of GAN, and a completely random key pool is obtained through GAN to learn and train the random key generated by hyperchaotic system. For the application of the proposed key generation method in low-light-level image encryption, a new low-light-level image encryption algorithm is proposed, which uses a 2D-pointer related to the plaintext to randomly select two phase masks in the key pool to achieve the security of low-light-level images. The results show that the encryption key generated by the learning key generation scheme can pass all the random tests of The National Institute of Standards and Technology, and the scheme can resist differential attacks by cryptanalysts, known/chosen plaintext attacks, and various statistical analyses. The performance comparison with other similar algorithms also shows the superiority of the proposed cryptosystem.

梁源 , 达新宇 . 基于多参数加权分数阶傅里叶变换的星座预编码系统研究与实现 [J ] . 电子与信息学报 , 2018 , 40 ( 4 ): 825 - 831 .

LIANG Y , DA X Y . Research and implementation of a constellation precoding system based on multi-parameter weighted fractional-order Fourier transform [J ] . Journal of Electronics and Information , 2018 , 40 ( 4 ): 825 - 831 . (in Chinese)

ZHANG N , FANG X J , WANG Y , et al . Physical-layer authentication for internet of things via WFRFT-based Gaussian tag embedding [J ] . IEEE Internet of Things , 2020 , 7 ( 9 ): 9001 - 9010 .

桑之昂 , 刘亚南 , 刘子威 , 等 . 基于WFRFT的卫星信号掩盖方法研究 [J ] . 电子与信息学报 , 2022 , 44 ( 1 ): 339 - 345 .

SANG Z A , LIU Y N , LIU Z W , et al . Research on satellite signal masking method based on WFRFT [J ] . Journal of Electronics and Information , 2022 , 44 ( 1 ): 339 - 345 . (in Chinese)

张笑宇 , 冯永新 . 一种基于时分数据调制的加权分数阶傅里叶变换通信方法 [J ] . 兵工学报 , 2020 , 41 ( 7 ): 1360 - 1367 . DOI: 10.3969/j.issn.1000-1093.2020.07.013 http://doi.org/10.3969/j.issn.1000-1093.2020.07.013 加权分数阶傅里叶变换是一种新型物理层保密通信方式，可极大地提高通信系统的抗调制方式识别能力。针对单参数加权分数阶傅里叶变换易被破解的不足，提出一种基于时分数据调制的加权分数阶傅里叶变换通信方法。该方法采用奇偶位不同调制的策略，充分利用旋转因子动态加密，进行时分数据加权分数阶傅里叶变换调制，减弱信道中噪声对信号的影响，从而提高加权分数阶傅里叶变换调制信号的可靠性和安全性。仿真结果表明：基于时分数据调制的加权分数阶傅里叶变换调制信号，能够提高传统加权分数阶傅里叶变换信号的可靠性，显著降低窃听方的破译能力，可进一步增强信息传输的保密性能。

ZHANG X Y , FENG Y X . A communication method based on time division modulation weighted fractional Fourier transform [J ] . Acta Armamentarii , 2020 , 41 ( 7 ): 1360 - 1367 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.07.013 http://doi.org/10.3969/j.issn.1000-1093.2020.07.013 The weighted fractional Fourier transform (4-WFRFT) is a new physical layer secret communication method, which can greatly improve the anti-modulation identification of the communication system. For the deficiencies of single-parameter weighted fractional Fourier transform, a time division modulation weighted fractional Fourier transform (TM-WFRFT) communication method is proposed. The proposed method adopts the strategy of different parity modulation and makes full use of the rotation factor to encrypt dynamically, so the security of the 4-WFRFT signal can be improved by time-division data weighted fractional Fourier modulation. The simulated results show that TM-WFRFT can significantly improve the 4-WFRFT reliability and significantly reduce the ability of the eavesdropper to decipher, thus improving the effectiveness of signal transmission and further enhancing the confidentiality of information transmission. Key

徐瑞阳 , 达新宇 , 梁源 , 等 . 基于跳频的改进加权分数阶傅里叶变换 [J ] . 华中科技大学学报(自然科学版) , 2019 , 47 ( 2 ): 30 - 35 .

XU R Y , DA X Y , LIANG Y , et al . Improved weighted fraction Fourier transform based on frequency hopping [J ] . Journal of Huazhong University of Science & Technology (Nature Science Edition) , 2019 , 47 ( 2 ): 30 - 35 . (in Chinese)

杨振鑫 . WFRFT信号参数识别方法研究 [D ] . 哈尔滨 : 哈尔滨工业大学 , 2020 .

YANG Z X . Studies on the methods of parameters identification of WFRFT signal [D ] . Harbin : Harbin Institute of Technology , 2020 . (in Chinese)

LIU F . A cross-hierarchical scanning method based SP-4-WFRFT for digital communication signals [J ] . Mathematical Problems in Engineering , 2018 , 2018 : 6580146 .

张笑宇 , 宋碧雪 , 王洋 , 等 . 基于循环相关的加权分数阶傅里叶变换信号旋转因子估计方法 [J ] . 兵工学报 , 2022 , 43 ( 7 ): 1646 - 1654 . DOI: 10.12382/bgxb.2021.0412 http://doi.org/10.12382/bgxb.2021.0412 加权分数阶傅里叶变换（WFRFT）信号具有很强的抗截获和抗调制方式识别能力，广泛应用于保密通信，WFRFT信号的旋转因子估计可为后续信号处理提供重要依据。通过分析WFRFT信号的特性，统计分析不同旋转因子归一化相关值的峰值及其位置，提出一种未知信号参数下WFRFT信号旋转因子的估计方法。为缩短估计时间，引入循环相关法实现WFRFT信号的快速旋转因子估计。仿真结果表明，基于循环相关的参数估计方法可有效地估计旋转因子，且有效缩短旋转因子估计时间，为WFRFT通信对抗提供重要的依据。

ZHANG X Y , SONG B X , WANG Y , et al . An estimation method for rotation factor of weighted fractional Fourier transform signals based on cyclic correlation [J ] . Acta Armamentarii , 2022 , 43 ( 7 ): 1646 - 1654 . (in Chinese)

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HU Z Y , CHAN C K . A 7-D hyperchaotic system-based encryption scheme for secure fast-OFDM-PON [J ] . Journal of Lightwave Technology , 2018 , 36 ( 16 ): 3373 - 3381 . DOI: 10.1109/JLT.2018.2841042 http://doi.org/10.1109/JLT.2018.2841042 https://ieeexplore.ieee.org/document/8367792/ https://ieeexplore.ieee.org/document/8367792/

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肖成龙 , 孙颖 , 林邦姜 , 等 . 基于神经网络与复合离散混沌系统的双重加密方法 [J ] . 电子与信息学报 , 2020 , 42 ( 3 ): 687 - 694 .

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