Decoding of signal from phase modulated unstable periodic orbit

In the method of secure communication suggested by Abarbanel and Linsay, a binary message is encoded by phase modulation of an unstable periodic orbit (UPO) of a chaotic system. It is demonstrated that the encoded message can be decoded from the transmitted signal alone without the knowledge of chaotic system, its orbit, and encoding scheme. The decoding method is based on the fact that errors in single step prediction for models which reconstruct the state space using the local linear approximation are relatively large for the points on UPO in the transmitted signal. This enables us to extract the UPO from the transmitted signal. The identification of UPO is then used to recover the original message.