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The RCL Shunted-Josephson Junction (RCLSJJ) circuit models are complex. They show chaotic behaviour due to internal and external perturbations such as environmental noise, high operational frequencies, parameter variations, and external device forces. The RCLSJJ chaotic behaviour has applications in secure information communication systems (SICS). SICS require synchronization to recover the original signals. This research article proposes a novel adaptive robust control strategy for synchronizing two identical RCLSJJ chaotic systems exposed to bounded unknown exogenous disturbances and un-modelled dynamics. The proposed control strategy achieves faster and smoother convergence of the synchronization error vector to zero. This controller synthesis the control signals without eliminating the nonlinear terms in the closed-loop and is independent of the system’s parameters. These characteristics make the closed-loop performance robust, ensuring smooth state-variable trajectories. The proposed controller uses estimates of unknown model uncertainties and bounds to compensate for unknown exogenous disturbances. Proofs of mathematical analysis are based on the Lyapunov second theorem of stability. Theoretical findings get verified through computer simulations showing that the proposed control technique quickly compels the error vector to the origin with less active oscillations for all signals. Comparative computer simulations confirm that the performance of the designed controller is better than the other state-of-the-art feedback controllers. The proposed strategy is applied to encrypt and decrypt one-dimensional and two-dimensional messages in secure communication systems.