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Based on best square approximation theory, new feed-forward neural networks are introduced where hidden units activation functions employ Laguerre orthogonal polynomials. Use these neural networks as the identifier model of the chaotic time series. Then, by varying the chaotic initial value and inputting to the networks, can produce new chaotic series, which are close to the theoretical values. We extract a subsequence as same length as the plaintext from the chaotic series and sort it. At last, by permuting the plaintext according to the sorted results of the subsequence, we can achieve the ciphertext. In the encryption system, the security of it depends completely on the complexity and unpredictability of the chaos. Especially, by varying the chaotic initial value, we can implement asynchronous "one-time pad cipher" encryption. The theoretical analysis and encryption instances proved that our arithmetic is useful, simple and high security, and it also has many advantages that a synchronous system can never achieve.