<p>In this paper, problem of secure message (signal and image) transmission is studied. The message is encrypted by masking it with a chaotic system state and then transmitted to receiver-side via a communication channel. It is assumed that the communication channel may be prone to a cyber-attack. The transmission system dynamics in presence of the cyber-attack in the communication channel is modeled by a singular dynamical system. Then, at the receiver-side, a novel observer is designed to recover the message together with the cyber-attack signal. Estimation of the cyber-attack is crucial for monitoring the communication channel and enable a network supervisor to mitigate the adverse consequences and make an appropriate strategy. It is assumed neither restrictions on the message nor on the cyber-attack signals. This makes the proposed scheme, the best solution in the real applications. Moreover, comparing to the existing methods which two public and private channels are required, only one communication channel is used in this paper for transmission the encrypted signal which results in a cheaper solution. Solving the optimization problem can be easily performed with the help of the existing toolboxes such as YALMIP and CVX software in MATLAB. Finally, numerical simulations for signal and image transmission are presented to justify the applicability and superior performance of the proposed scheme.</p>