A smart brute-force double random-phase encoding attack is presented that takes advantage of an unreported vulnerability: the smoothness of mean squared error (MSE) and correlation coefficient (CC) curves in a key-sensitivity analysis. The vulnerability reported here is made visible in a key-sensitivity analysis. It is shown that a modular arithmetic pre-coding provides significant robustness against this form of attack because the pre-coding creates a highly nonlinear, highly oscillatory MSE and CC curve in the key space. Knowledge of this new vulnerability and how to prevent this in the first place provides a better understanding of the robustness of various double random-phase encoding designs.