A more TLDR article about this: https://www.extremetech.com/defense/173108-researchers-crack-the-worlds-toughest-encryption-by-listening-to-the-tiny-sounds-made-by-your-computers-cpu
FAQs from the researchers: https://web.archive.org/web/20230130225254/http://www.cs.tau.ac.il/~tromer/acoustic/
This paper is a bullshit. Authors claim they are able to extract an RSA 4096 decryption key within an hour using a prepared cyphertext, but this cannot work for PGP. PGP uses an asymmetric cypher (i.e. RSA) only to encrypt a symmetric cypher key (e.g. AES) that is used to encrypt/decrypt the text itself. So RSA does not work for hours, it takes only few milliseconds to decrypt a key that is 256 bit maximum.
Even if this method worked, it would be very hardware dependant. They would need to tune their algorithm for each laptop being attacked. So if you don't give your laptop to attacker for several weeks, he won't be able to steal your key.
I don't know that much about audio sidechannels so I don't know how realistic this would be, but my immediate thought is whether this can be extended to extract not just a single key but other data as well. For example, if you had a phone next to a computer that was reading and displaying a text file that contained confidential information, or perhaps reading values from a database, could it be possible to leak the actual data this way?
I also wonder how many videos and audio recordings made near computers have encryption keys and other sensitive data hidden in them, just waiting to be decoded. Or whether a video recorded by a smartphone can reveal what the phone is doing in the background. A terrifying prospect.