Provable Security - This paper studies provable security guarantees for cyber-physical systems (CPS) under actuator attacks. Specifically, we consider safety for CPS and propose a new attack-detection mechanism based on a zeroing control barrier function (ZCBF) condition. To reduce the conservatism in its implementation, we design an adaptive recovery mechanism based on how close the state is to violating safety. We show that the attack-detection mechanism is sound, i.e., there are no false negatives for adversarial attacks. Finally, we use a Quadratic Programming (QP) approach for online recovery (and nominal) control synthesis. We demonstrate the effectiveness of the proposed method in a case study involving a quadrotor with an attack on its motors.