First and foremost: it’s about
block size, not about
key size. Sweet32 itself presents the attack only for 128-bit and 168-bit ciphers (Blowfish, 3DES)
There is a bunch of unspoken assumptions in your post. But I can’t peek in your head, so I may only guess them and respond to my guesses.
The elephant in the room: the assumption about servers breaking connections. This is the easiest one to tackle, because it’s a formal logic error: a failure to properly negate a existential quantification. We can’t use an existential quantification to oppose another existential quantification. The presence of servers breaking connections is irrelevant here.
Further, there is an implication of incompetence for not breaking long-lived connections. That’s unfounded.
Such amounts of data are also routinely observed. To name a few common examples: wireless networks, VPNs, email transfers from/to large operators, continuous monitoring, backups and data dissemination, or database replication.
Then, Sweet32 is not proving vulnerability. The vulnerability was known before Bhargavan and Leurent’s publication. What Sweet32 authors did is showing that vulnerability is exploitable beyond the realm of spherical cows, and they are not even the first to do so. It’s more like the last nail to the coffin, not cutting a tree for one. Such displays are not meant to be reused directly in attacks. They are sounding devices, used to gauge how far the cryptographic ship is from crashing into ground. For a reasonable captain Sweet32 is enough to halt the ship and seek another route. Even if we could still pass this single shoal, we know this entire area is already a catastrophe awaiting.
Finally, the 785 GB mark is not a requirement. The number itself is is a result from this particular experimental setup and may be different in other scenarios. Other attempts are not even mentioning stream size, but deal with time or requests counts. There is a lot of slack coming from what the adversary may know about the plaintext.
But most importantly this is not a fixed value. It’s a probabilistic setup and the authors made a decision to choose number high enough to provide a reasonably high success rate. An actual adversary may accept much worse odds and reduce the amount of data needed.
If you’re interested in the background, among many publications in this very crowd is
McGrew’s 2012 paper “Impossible plaintext cryptanalysis and probable-plaintext collision attacks of 64-bit block cipher modes”. Sweet32 references it too.