I worked at Apple, and they told me when I left I could not put anything about my work on LinkedIn. I didn't work on anything that would be considered remotely classified to any other companies. Apple treats EVERYTHING as super secret. It sort of worked for me, because when my current company asked what I worked on I just said "sorry I can't talk about it ;)" instead of "I was paid almost 200k a year to make one spreadsheet look like another"
"Bob worked at GCHQ between month/year and month/year".
Lots of places understand that there are strict confidentiality agreements (whether those are by convention, contract like NDA, or law like Official Secrets) and they often welcome this.
Not sure if this is a reference to Charles Stross's Laundry series (whose protagonist is named Bob and works at GCHQ as an occult computer scientist) or if just a coincidence.
This is also the case for folks that work on classified projects such at the NSA. There’s more to working than bragging about it to others.