[Taps on the forehead] You wouldn't get cache timing attacks for speculative accesses, if your CPU does not have nanosecond-scale timing measurement instructions. Or a cache. Or speculation. Or memory reads. Easy!
This is true, but to mitigate you need to shut off access to time entirely, or cleverly falsify it, not just reduce resolution.
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That was not-so-obvious joke, because you can always model time, with e.g. timed events, timeouts, heck even just something that monotonically increments a global counter. Timing measurement is extremely hard to restrict access to...
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Pure-functional code obviously has no access to time, but yes, its a very restrictive assumption.
End of conversation
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