Physical layer security is a crucial step towards fully secure communications systems. The flexibility and ubiquity of digital signal processors in modern wireless and optical communication systems open up a clear path for the development of discrete-signals encryption techniques, which can be implemented relatively cheap. In this paper, we show the fundamental role of amplitude and phase encoding in the security and practical implementation of linear discrete signal cryptography (DSC). We focus on the spectral implementation of these encoding schemes and consider the equivalence between spectral amplitude encoding (SAE) and spectral scrambling (SS). Numerical simulation results show that 16-quadrature amplitude modulation (16-QAM) signals encrypted by SS and spectral phase encoding (SPE) can be recovered only if eavesdroppers know the exact position of $\sim ~95$ % of the scrambled samples with a maximum phase error of $\pm ~7^{\circ }$ for all samples. The number of brute force attacks to break such encrypted signals far exceeds the one provided by the widely deployed data ciphering algorithm Advanced Encryption Standard (AES). Physical layer results reveal that the bit error ratio (BER) associated with the encrypted signals is 0.50 regardless of the deployed signal format and DSC scheme. The BER vs. signal-to-noise ratio performance of the encrypted/ decrypted signal is the same as that of signals not encrypted. Finally, the paper proposes the adoption of pseudo-random dynamic keys (PRDKs) to promote encryption randomness, diffusion, and confusion to the encrypted signals. A new numerical methodology shows this strategy outperforms AES diffusion and confusion properties.

中文翻译：

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使用伪随机动态密钥的单载波信号离散频谱加密

物理层安全是实现完全安全的通信系统的关键一步。现代无线和光通信系统中数字信号处理器的灵活性和普遍性为离散信号加密技术的发展开辟了一条清晰的道路，而且该技术的实施成本相对较低。在本文中，我们展示了幅度和相位编码在线性离散信号加密（DSC）的安全性和实际实现中的基本作用。我们重点关注这些编码方案的频谱实现，并考虑频谱幅度编码（SAE）和频谱加扰（SS）之间的等效性。数值仿真结果表明，只有窃听者知道SS和频谱相位编码（SPE）加密的16正交幅度调制（16-QAM）信号的确切位置才能恢复。 $\sim ~95$ 最大相位误差为的加扰样本的百分比 $\pm ~7^{\circ }$对于所有样品。破解此类加密信号的暴力攻击次数远远超过了广泛部署的数据加密算法高级加密标准 (AES) 所提供的次数。物理层结果表明，无论部署的信号格式和 DSC 方案如何，与加密信号相关的误码率 (BER) 均为 0.50。加密/解密信号的 BER 与信噪比性能与未加密信号相同。最后，本文提出采用伪随机动态密钥（PRDK）来提高加密信号的加密随机性、扩散性和混淆性。一种新的数值方法表明该策略优于 AES 扩散和混淆特性。