Integrated Circuits (IC) are increasingly present in our daily lives through various everyday objects. Many third-party companies are involved during the manufacturing process. It introduces many threats to the ICs manufacturing, such as IP piracy and Hardware Trojans. Strong Logic Locking methodology is generally used to protect from IC piracy, such as counterfeiting or reverse engineering, and against Hardware Trojans insertion; however, the lack of automated tools fully integrated into a CAD flow limits the integration of countermeasures. This paper proposes mathematical models on the Strong Logic Locking method to optimize the security and an automatic security design inserted in an open CAD flow. We implemented an exact algorithm to maximize the security measure while implementing a strategy to minimize the impact of delay and area on the circuit. This algorithm is a custom branch and bound based on the mathematical model developed in this paper. In addition, we propose a strategy to limit the impact of countermeasures on the delay. Furthermore, our approach takes place inside a standard open CAD flow after logic synthesis to be as generic as possible. The experiments carried out that security can be added in a standard open CAD flow with a reasonable computation time and a limited impact on the circuit. Our security measure is more precise than the previous one, with a limited area overhead defined by a user. The increase of the critical path is less than 7% for large benches with a limit of 10% area overhead.