High-security floating probabilistic encryption methods based on chain-embedded masking

With the increasing demands for transmission performance and security in optical access networks, this paper proposes a high-security floating probabilistic encryption method based on chain-embedded masking. The constellation points of this chained structure are distributed in a chain-like pattern across concentric circles. A core hexagon is formed by the points on the first layer around the origin. The second layer is then expanded into a star-shaped structure using external triangles, while the remaining points are fixed in the outermost ring. It effectively reduces both the average transmission power and the peak power while maintaining a minimum Euclidean distance of 1, resulting in a constellation figure of merit (CFM) value of 0.444. Based on this structure, a floating chain-embedded encryption scheme is further proposed. A Lorenz chaotic model is employed to generate sequences that dynamically perturb the positions of the outer-ring constellation points within the chain-like structure according to a "0-hold, 1-shift one step, 2-shift two steps" rule. Experimental validation was performed on a seven-core fiber transmission system. The results demonstrate that at a bit error rate of 3.8 × 10^-3, the proposed Hierarchical Triangular-Distorted Hexagonal (HTDH) 16 Quadrature Amplitude Modulation (16QAM) constellation achieves a 0.48 dB improvement in receiver sensitivity compared with conventional 16QAM. The encrypted signals exhibit an additional 0.33 dB sensitivity enhancement over unencrypted signals. This indicates that the encryption mechanism not only enhances security but also synergizes with the energy concentration characteristics of the constellation, ultimately achieving co-optimization of transmission security and system sensitivity.