Authentication protocols are often used in smart grids to deliver the necessary level of security. A huge number of clients in such a system, however, provides the attacker with the ability to clone them, for example. Device fingerprints, or Physically Unclonable Functions (PUF), have been investigated as an authentication feature to thwart such attacks. In order to accomplish the necessary security in smart grid neighborhood area network communications and to prevent unwanted physical access to smart meters, a former study designed a lightweight authentication system in this way. The suggested protocol uses PUFs to reduce physical attacks. As a consequence, the server/meter impersonation attack is one of the many assaults that this protocol is thought to be secure against. On the other hand, it is generally acknowledged that no security solution should be trusted unless its security has been verified by independent researchers. As a result, this paper assesses the security of this protocol against a typical adversary who has access to or influences over the messages carried over the public channel. This study demonstrates that the attacker is simply capable of impersonating the server for the meter and vice versa. In addition, the suggested attacks desynchronize them, making the adversary the only one capable of interacting with the meter in the role of the legal server rather than the latter. Each of the proposed attacks is extremely effective, and their success probability is almost 1. Finally, a modification is suggested that successfully fixes the protocol’s security weaknesses. The security proof of the improved protocol has been done through the Scyther tool. The computational cost comparison shows that the overhead of the proposed protocol compared to the former scheme is 4.85%, while it withstands various attacks, including traceability, desynchronization, impersonation, man-in-the-middle, and secret disclosure attacks.