Dynamic Wireless Power Transfer (DWPT) can be used for on-demand recharging of Electric Vehicles (EV) while driving. However, DWPT raises numerous security and privacy concerns. Recently, researchers demonstrated that DWPT systems are vulnerable to adversarial attacks. In an EV charging scenario, an attacker can prevent the authorized customer from charging, obtain a free charge by billing a victim user and track a target vehicle. State-of-the-art authentication schemes relying on centralized solutions are either vulnerable to various attacks or have high computational complexity, making them unsuitable for a dynamic scenario. In this paper, we propose Quick Electric Vehicle SEcure Charging (QEVSEC), a novel, secure, and efficient authentication protocol for the dynamic charging of EVs. Our idea for QEVSEC originates from multiple vulnerabilities we found in the state-of-the-art protocol that allows tracking of user activity and is susceptible to replay attacks. Based on these observations, the proposed protocol solves these issues and achieves lower computational complexity by using only primitive cryptographic operations in a very short message exchange. QEVSEC provides scalability and a reduced cost in each iteration, thus lowering the impact on the power needed from the grid.