Abstract: Aiming at the problem that underwater acoustic channel is vulnerable to various threats and attacks due to the uncertainty of marine environment,a key agreement scheme based on ocean acoustic channel is proposed.Firstly,the uncertainty of marine environment is modeled,and the expressions of calculated noise,multipath and Doppler parameter expressions are constructed,and the concept of interference factor of underwater acoustic channel based on Rényi entropy is proposed.Secondly,a Hash function based on Twisted Edwards elliptic curve equation is constructed for conducting identity authentication and extracting the initial key.Then,the typical sequence of piecewise initial keys is used as initial seed to generate piecewise Toeplitz matrix,and the matrix multiplication of Toeplitz matrix and the initial key are used to generate the label by piecewise operation,and securely transfer the initial key.Finally,the initial key is hashed again for privacy amplification and a final secure key generated.The correctness,robustness and confidentiality of the scheme are proved by the information theory,and the upper bound of the probabi-lity of success of the active attack is obtained.Simulation results demonstrate that when the initial information amount is 50 000 bit,the upper bound of the success rate of adversary’s active attack is 4.3×10^－23,and the key generation rate is 631 bit/s.Compared with existing schemes,the proposed scheme has obvious advantages in key generation rate and bit error rate.

Key words: Active attack, Key agreement, Privacy amplification, Toeplitz matrix, Underwater acoustic channel