To enhance the anti-breaking performance of privacy information, this article proposes a new encryption method utilizing the leaping peculiarity of the periodic orbits of chaos systems. This method maps the secret sequence to several chaos periodic orbits, and a short sequence obtained by evolving the system parameters of the periodic orbits in another nonlinear system will be the key to reconstruct these periodic orbits. In the decryption end, the shadowing method of chaos trajectory based on the modified Newton-Raphson algorithm is adopted to restore these system parameters. Through deciding which orbit each pair coordinate falls on, the original digital sequence can be decrypted.