Time Distribution Networks (TDNs) evolve as new technologies occur to ensure more accurate, reliable, and secure timing information. These networks typically exploit several distributed time servers, organized in a master-slave architecture, that communicate via dedicated timing protocols. From the security perspective, timing data must be protected since its modification or filtering can lead to grave consequences in different time-based contexts, such as health, energy, finance, or transportation. Thus, adequate countermeasures must be employed in all the stages and systems handling timing data from its calculation until it reaches the final users. We consider a TDN offering highly accurate (nanosecond level) time synchronization through specific time unit devices that exploit terrestrial atomic or rubidium clocks and Global Navigation Satellite Systems (GNSS) receivers. Such devices are appealing targets for attackers, who might exploit various attack vectors to compromise their functionality. We individuate three possible software integrity attacks against time devices, and we propose a solution to counter them by exploiting the cryptographic Trusted Platform Module (TPM), defined and supported by the Trusted Computing Group. We used remote attestation software for cloud environments, namely the Keylime framework, to verify (periodically) the software daemons running on the time devices (or their configuration) from a trusted node. Experiments performed on a dedicated testbed set up in the ROOT project with customized time unit devices from Seven Solutions (currently Orolia Spain) allow us to demonstrate that exploiting TPMs and remote attestation in the TDNs is not only helpful but is fundamental for discovering some attacks that would remain otherwise undetected. Our work helps thus TDN operators build more robust, accurate, and secure time synchronization services.INDEX TERMS Software attacks, time distribution networks, GNSS, trusted computing, remote attestation, keylime.