alt Hacker NewsIt's sort of fun to remember the genuine worry in the community around RSA and the (really, really shocking at the time!) progress in factorization leading up to GNFS techniques.
Like, it really looked like everything was going to fall apart. We all rushed to 1024 bit keys, and then to 2048 bit after what felt like a few months. And... maybe even that wouldn't be enough?
And actual history ended up being the boring version: it was absolutely enough, factorization is seemingly settled math at this point, no new techniques have been discovered.
At the end of the day RSA was just fine and no one really needed to bother with ECC and all of its confusing tutorials.
And the ~23 year old 1024 bit key holding my GnuPG box closed is still just fine, cryptographically. (Though the chances of getting hit with a keylogger or other side channel attack over that period are nontrivially high and I suppose I really should rotate it or something).
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the researchers from the RSA-250 record have publicly claimed that factoring 1024-bit RSA keys is within reach of nation states. Your 1024 bit key is only "fine" because you are a small fry, not because cryptographers think it cannot be attacked. This would be true if you used a (non-standard) RSA-768 parameterization as well, which is easier than what we are talking about on this post.
It's also worth mentioning the main concern for RSA is not GNFS, but something stronger. SOTA RSA attacks (such as GNFS) use "index calculus". You can also use index calculus to attack finite field diffie hellman. In the 2010's, there was remarkable progress in index calculus attacks against finite field DH in the small characteristic case. For example, the current record for binary characteristic finite field DH is ~30k bits (and this is by an academic --- a nation state could definitely do more).
It is not known that similar progress is possible in other cases (such as for RSA). But it's very much possible that factoring is much easier than expected. Simultaneously I wouldn't personally bet money on it, and if that breakthrough happened, there were sufficient warning signs that I would feel justified in saying "told you so" to people trusting RSA.
RSA-260 has a 862 bit key. In terms of work, a 1024 bit key is only about 50-100x more work to break than the factorization posted in TFA.
ECC does have the benefit of smaller keys, but yes, RSA seems fine security-wise for the foreseeable future.
You can just send the gnupg box and keys to me, I will hold them securely for you so you don't have to worry about it
but complexity is not known right? like tomorrow someone could come up with a super fast algorithm?
RSA might be fine mathematically but as a production cryptosystem it’s an unmitigated disaster by modern standards.
Compared to elliptic curves, it is comically easy to build an RSA implementation which is catastrophically broken. Both the number of and subtlety of footguns in RSA are extreme.
Even ignoring that, ECC is far more efficient (in part thanks to smaller key sizes and being able to be done with fixed-width arithmetic rather than needing bignums) and far better suited for embedded devices. Migration has been an enormous win even if you think the security of RSA is fine.