Abstract: With the continuous development of wireless networks, the security of physical layer has gradually become the focus of widespread concern. Concerning the problem of how to extract a highly confidential key from the source information when legitimate nodes have more uncertainty than that of eavesdropping node under the circumstances of multipath and Doppler effects in underwater acoustic channel, a time-varying underwater acoustic channel based physical layer secret key generation scheme is proposed. For the first time, the α order Rényi entropy with multipath and Doppler effects is accurately depicted, and the uncertainty of the source sequence from the legitimate nodes and the eavesdropping node is also obtained. On this basis, a key agreement protocol with strong security is proposed, which uses Hash function to construct one-variable high-order polynomial to complete identity authentication for both sides of communication and to realize secure transmission of index sequence and preselected key under the public channel. Moreover, a privacy amplification protocol against active attacks is designed using bilinear mapping, which does not depend on the length and randomness of the random seed. The robustness, confidentiality and correctness of the scheme are proved by the information theory. The simulation results show that the upper bound of key leakage rate is 3.74×10\+\{-6\} and the upper bound of active attack success rate is 5.468×10\+\{-20\} when the amount of the source information is 50 000 b, which verifies the feasibility of the proposed scheme.

Key words: underwater acoustic channel, physical layer, Rényi entropy, key agreement, privacy amplification