We present a cyber-attack on packet-based time synchronization protocols (PBTSP) with high-accuracy requirements. The cyber-attack is undetectable from the PBTSP's perspective and exploits a vulnerability that is in the nature of all PBTSPs. It can be successfully performed regardless of the cryptographic protocol that the PBTSP is protected with and it is undetectable by the clock-servo algorithm inside the target slave clock. To perform this cyber-attack, we built a "Delay Box" capable of advancing or delaying a slave clock by introducing a malicious offset of a few microseconds. We run experimental tests to the delay box to prove the magnitude of the attack and to confirm undetectability. We discuss possible countermeasures for this type of attack.