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Due to the rapid development of mobile communication and hardware technologies, several mobile‐based web applications have gained popularity among mobile users. Mobile users can utilize these devices to access numerous services over the Internet. To ensure secure communication, different key exchange and authentication (KEA) protocols are proposed and frequently used. However, due to the advent of quantum computers, numerous quantum‐safe KEA protocols are also developed using various complex mathematical problems in ideal lattices. As it is an emerging and developing area, we analyze the security of recently suggested ring learning with error based KEA protocols. The goal of this study is to gain a comprehensive understanding of quantum‐safe KEA mechanisms. For our study, we have considered Dharminder's LWE‐based KEA mechanism and Dharminder and Chandran's LWE‐based KEA mechanism. These protocols enable effective communication and provide a better means for safely transmitting messages between user and server. However, we have discovered that a fundamental security weakness in these methods makes them vulnerable to signal leakage attacks (SLA). Based on our analysis, we demonstrated security weakness against SLA and provide the road‐map for secure construction.