Security-Enhanced 16QAM-OFDM Scheme via 3D Hexagonal Shaping and 4D Hyperchaotic Encryption

This work proposes a coherent optical orthogonal frequency-division multiplexing (OFDM) scheme combining three-dimensional (3D) geometric shaping with four-dimensional (4D) hyperchaotic phase encryption. The 3D-Hexagon-16 constellation achieves a constellation figure of merit (CFM) of 0.6956 at a unit minimum Euclidean distance (MED), compared with 0.4726 for 3D-Cube-16. Two 3D points are packed into three complex-valued OFDM data positions. HKDF, an extract-and-expand key derivation function based on a hash-based message authentication code, uses the 256-bit Secure Hash Algorithm (SHA-256) to derive frame-dependent initial-state offsets for the hyperchaotic generator, which produces unit-modulus phase masks. Numerical evaluation over 80 km of standard single-mode fiber (SSMF) shows a receiver sensitivity improvement of approximately 0.7 dB over 3D-Cube-16 at a bit error rate (BER) of 10−4. The payload rate is 59.58 Gb/s, with a payload spectral efficiency of 1.986 bit/s/Hz after accounting for the evaluated frame overheads. At an optical signal-to-noise ratio of 23 dB referenced to 0.1 nm, the tested 64-candidate key search and same-frame known-plaintext attack each yield a BER of approximately 0.41 on the unknown suffix. Distinct frame contexts increase the cross-frame attacker BER from approximately 0.06 with mask reuse to 0.41, reducing the usefulness of previously recovered masks for decrypting subsequent frames. However, amplitude-based MAP detection yields an overall BER of approximately 0.31 and a first-label-bit BER of approximately 0.02. The preserved magnitudes therefore leak substantial label information, and the phase-only mechanism does not protect all payload bits. These security results apply only to the evaluated attack models and budgets.