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A Diffie-Hellman public-key cryptography based on chaotic attractors of neural networks is described in the paper. There is a one-way function between chaotic attractors and initial states in an Overstoraged Hopfield Neural Networks (OHNN). If the synaptic matrix of OHNN is changed, each attractor and its corresponding domain of initial state attraction will be changed. Then, we regard the neural synaptic matrix as a trap door, and change it with commutative random permutation matrix. A new Diffie-Hellman public-key cryptosystem can be implemented, namely keeping the random permutation operation of the neural synaptic matrix as the secret key, and the neural synaptic matrix after permutation as public-key. In order to explain the practicability of the encryption scheme, Security and encryption efficient of the scheme are discussed. The scheme of application for Internet secure communications is implemented by using Java program. The experimental results show that the proposed cryptography is feasible, and has a good performance of encryption and decryption speed to ensure the real time of IPng secure communications. [ABSTRACT FROM AUTHOR]