You are confusing authentication and encryption. Authenticated time protects against MITM attacks. You can obtain authenticated time synch from many national labs, such as NIST[1] or CRC[2].
Well, my thought was that you might be able to determine local clock drift by snooping. But as then mentioned, that's of near zero use, I suspect (as anything that uses time sync for authentication or otherwise is not likely to be that tightly bound to accuracy).
I do not understand the need for confidentiality.
[1]: http://www.nist.gov/pml/div688/grp40/auth-ntp.cfm
[2]: https://www.nrc-cnrc.gc.ca/eng/solutions/advisory/calibratio...