Covert secret-key agreement based on rate-splitting polar code

In order to prevent illegal sensors from detecting the secret-key agreement process in the underwater acoustic channel (UAC), a covert secret-key agreement scheme based on rate-splitting polar code called RSPC is proposed. Firstly, a novel Bhattacharyya parameter is established and calculated by the transmitter for code construction according to the fading process of the UAC. The information set is then selected by sorting the reliability of the polarized sub-channels. Secondly, two independent codewords are obtained by the transmitter through rate-splitting and polar coding. Then, an UAC gain prediction algorithm is designed based on the first-order autoregressive model, Wiener–Khinchin theorem and Karush-Kuhn–Tucker (KKT) condition. Based on the rate-splitting and prediction algorithm, the index set of the polarized sub-channels is divided into a random set and a deterministic set, and the bitwise XOR operation is performed between the very high entropy bits of one codeword and the low entropy bits of the other codeword. This strategy improves the covertness of the codeword transmission in the UAC. According to the sensor-based observation and channel gain, the estimate of the codeword is obtained via successive cancellation decoding and the same secret-key can be extracted by the receiver. Finally, theoretical analyses are conducted on the reliability, covertness, and covert secret-key generation rate of the RSPC scheme. The simulation results show that compared with existing schemes, the RSPC scheme improves the above performance indicators by 21.26%, 47.19%, and 24.71%, respectively. Meanwhile, the secret-key generated by the RSPC scheme successfully passes the NIST randomness detection.