Modern side channel attacks are really frustrating. There are so many things to think about.
Although, this one seems easier to patch: Especially modern hardware has dedicated hardware/trustlets to generate keys. If firmware makes them always clock at the same frequency for always the same time when generating keys, there should be no attack vector left.
I haven't read through the preprint yet but I'm also sceptical of the real world applicability of this...
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Maybe it's only a concern for PCs under more or less ideal conditions. In a realistic production server with multiple workloads, the CPU scaling is going to be governed by too many external factors to realistically learn any secrets from it I think