The triple data encryption standard (3DES) has played a key role in the field of data encryption over the past few decades. However, the ciphertext’s security is decreased by the meet-in-the-middle attack. Accordingly, we propose a systematic design methodology combining chaotic synchronization with 3DES to conduct double encryption. The encryption method not only increases the strength of the communications system but also effectively protects the encrypted message (ciphertext). The conventional genetic algorithm (GA) has flaws in premature convergence and local search. While the methods of improving the GA performance have been explored, we adopted an improved genetic algorithm (IGA) in this work due to its better performance in the light of globalization and convergence rate. The IGA-based observer not only realizes the exponential synchronization but also minimizes the disturbance attenuation level to get optimal $H^{\infty }$ performance simultaneously. In the end, an example with numerical simulations is provided to demonstrate the effectiveness of this study.