The folks that invented high-assurance security (TCSEC A1-class) were eliminating storage and timing channels best they could. An early reference was in VAX Security Kernel that tried to assess and mitigate timing channels.

http://ix.cs.uoregon.edu/~butler/teaching/10F/cis607/papers/...

http://ieeexplore.ieee.org/document/213271/

Mainstream security professionals have always ignored such work dismissing it as red tape with no value or too costly. The early work preempted most problems, though, back in the 1980's-1990's by focusing on root causes. The same crowd that ignores them keep rediscovering the lessons in new forms while continuing to ignore them. (There are exceptions who pay attention.) Far as covert channels, the first technique I saw to systematically examine was Kemmerer's in 1983. It was one that made it into the first criteria for security certification. As in, it was mandatory to look for covert/side channels the best you could.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.462...

https://fas.org/irp/nsa/rainbow/tg030.htm

So, the basic concepts have been known for decades under covert, channel analysis. The analysis technique established long ago was to identify every shared resource between two things in the system. If they could read/write to it, it was a potential, storage channel. It was a timing channel if they can manipulate its activity with a way to time that. Those are basic ones. So, you can just list everything, categorize them, and do the analysis by brute force. They'd have found the caching stuff quickly. Here's an example that should've happened a long time ago:

https://eprint.iacr.org/2016/613.pdf