A generalized synchronization theorem for discrete-time chaos system with application in data encryption scheme

A constructive theorem of generalized synchronization (GS) for discrete-time chaos system (DTCS) is introduced. Based on the theorem, one can design a GS driven DTCS via a driving chaotic DTCS. As an application, a GS DTCS is constructed based on the Lorenz three-dimensional chaotic map and the Theorem. Using the DTCS designs a encryption scheme with "one-time pad" function. This scheme is able successfully to encrypt and decrypt original information without any loss. The scheme is sensitive to the perturbations of the parameters and initial conditions of the DTCS. Any perturbations which are larger than 10^-15 will make corresponding decryptions become impossible. The key space of the scheme is as large as 10²⁰⁴. The analysis of the key space, sensitivity of key parameters show that this scheme has sound security. Numerical simulations show that our scheme is effective to be used in secure communication.