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Broadcast-style downlinks (e.g., PONs and satellites) expose physical waveforms despite transport-layer cryptography, motivating physical-layer encryption (PLE). Digital chaotic encryption is appealing for its noise-like spectra, sensitivity, and DSP-friendly implementation, but in low-CSPR KK-SSB systems, common embeddings disrupt minimum-phase requirements and raise PAPR/SSBI near 1 dB CSPR, while finite-precision effects can leak correlation after KK reconstruction. We bridge this gap by integrating 3D Lorenz-based PLE into our low-CSPR KK-SSB receiver. A KK-compatible embedding applies a Lorenz-driven XOR mapping to I/Q bitstreams before PAM4-to-16QAM modulation, preserving the minimum phase and avoiding spectral zeros. Co-design of chaotic strength and subband usage with the KK SSBI-suppression method maintains SSBI mitigation with negligible PAPR growth. We further adopt digitization settings and fractional-digit-parity-based key derivation to suppress short periods and remove key-revealing synchronization cues. Experiments demonstrate a 1091 key space without degrading transmission quality, enabling secure, key-concealed operation on shared downlinks and offering a practical path for chaotic PLE in near-minimum-CSPR SSB systems.
