Recently (2023), the default of GnuPG has been changed: a new key generated will be no longer RSA but ECC. Elliptic (25519) is a way to go: keys are much shorter than say RSA4096. Migrating to elliptic is convenient and perhaps safer, even though RSA may be still safe too.
Realistically 2048 is about 600-digit. Factorization of a 100-400 digit number is more or less possible now. 600 is still hard, but maybe not totally impossible in the near future.
25519 was designed by D. J. Bernstein, who tenaciously fought a long legal battle against the US cryptography export regulations. He’s also strongly criticized various sabotages (backdoor) in NIST standardized cryptography algorithms, such as the random bit generation in Dual EC. That’s why people tend to like 25519, over RSA etc.
Nerdy footnotes 😅
multiplying two different large prime numbers
Technically, the two numbers are usually not proven primes (not a big deal: they’re most probably primes, just not mathematically proven…).
brute-force cracking a strong key would require an enormous amount of time
Obviously, one wouldn’t do a naive brute-force, like trial division. There are some number theoretic, sophisticated algorithms, and they’re getting stronger and stronger, both algorithm-wise and machine power-wise… Not too long ago, people were saying RSA512 was strong enough!
Looked into my key ring and found only a few RSA2048 keys (used by old Proton users). Apparently most devs use Ed or RSA4096 to sign today. Even Thunderbird (its OpenPGP is convenience first, security second, in a sense that your sec key is not passphrase-protected) generates at least RSA3072, RSA2048 is not even an option!
Though this news might be a joke, it’s totally possible that RSA2048 (or RSA itself) becomes eventually obsolete. Which doesn’t mean cryptography in general will be broken, of course. There are different kinds of "one-way" problems, like Ed, already widely used, based on elliptic curves.
If a faster factorization algorithm is found (though that may be proved to be impossible after all), it’s essentially great news. Even Gauss said, “the dignity of the science itself seems to require that every possible means be explored for the solution” (of primality test and factorization), meaning “We must try everything to find a better way to factor a big number!” (which also implies “a more effective attack against RSA!”).
Though no one wants broken cryptography, factorization is something number theorists would love to do quickly too, if possible at all.
See also [not directly related]: https://en.wikipedia.org/wiki/Logjam_(computer_security)