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 ~95% of the scrambled samples with a maximum phase error of ± 7° 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 encrypt signals. The paper also investigates the use 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.