Large key space and efficient hierarchical chaotic encryption for secure transmission of 65536-QAM via delta sigma modulation

Radio over fiber (RoF) links support high-capacity transmission for next generation mobile fronthaul but remain vulnerable to security threats. For RoF systems operating at high data rates, physical-layer encryption should provide enhanced security without imposing substantial processing overhead on the signal path. This paper proposes and experimentally validates a hierarchical chaotic encryption scheme for delta sigma modulation (DSM) systems. The proposed rule-constructed chaotic sequence (RCCS) generation uses a logistic sequence to dynamically select state variables from the Lorenz and Halvorsen systems, thereby generating three composite chaotic outputs. This design expands the effective key space through multiple secret key parameters while applying only three perturbation sequences to the transmitted signal. A Chaotic Sorting Stride Permutation (CSSP) algorithm is proposed to enhance permutation variability by introducing a dynamic starting position and a cyclic access stride. Secure transmission of a 3 GHz 65536-ary quadrature amplitude modulation (65536-QAM) discrete multitone (DMT) signal at 42.2 Gb/s over 2 km of standard single-mode fiber is experimentally demonstrated using an intensity modulation direct detection system with two cascaded fourth-order 1-bit DSMs. The RCCS provides an effective key space of approximately 10²⁰⁸. At 50 and 60 Gbaud, the authorized receiver shows bit error rata (BER) performance comparable to the unencrypted system, with receiver sensitivities of approximately -5.0 and -4.6 dBm at the 7% hard-decision forward-error correction (HD-FEC) threshold after 2 km transmission. In contrast, the unauthorized receiver maintains a BER near 0.5 and fails to recover the transmitted information. These results demonstrate enhanced physical-layer security with negligible transmission penalty.