Can anyone ELI-CS graduate this vulnerability? My understanding from reading the page is that modern processors process certain data with higher frequency, and

Can anyone ELI-CS graduate this vulnerability? My understanding from reading the page is that modern processors process certain data with higher frequency, and somehow that allows an attacker to know guess private keys. However, I don't understand the connection between those two things. How would an attacker trigger a lot of almost-identical CPU runs without hitting some rate limit somewhere? And how is this different than just guessing the password?