I can't tell if you are serious at this point. I literally say, twice, that I'm not talking about a language model. And I also say the model would predict the key...not the plaintext.
If you were in a place to debate this, you would have known the above (or something similar) is what I was suggesting when i said train on plaintext, cipertext -> key, and you'd have some deep mathematical insight as to why no architecture known is likely to work. And you would also know I wouldn't be here talking to you about it if I really had a solid idea of an architecture that is likely to work.
I think it would make sense to explain how a theoretical model could do better than SAT. Otherwise, is the idea here just "magic is possible"?
Current SOTA language and vision models, or models used to predict protein shapes are magic by the standards of 2016. As for why could it be better than a SAT? Why couldn't it be? Models are better than deterministic, logically written software for lots of situations. You can create infinite training data for this problem. The number of humans that work on encryption is tiny. The idea that because humans haven't figured out how to break some encryption schemes it can't be done is kind of absurd.
You can build and train a model in about 15 lines of pytorch. And you can build and break your own 8 bit xor cipher in about 10 lines of python.
Hacker news is full of software engineers. You are unlikely to find one that hasn't built a model using pytorch these days, and an xor cipher is a common university lab exercise.
For any NN to learn, the function it is approximating must structured enough to admit small set of parameters (i.e., not exponential), otherwise it will take exponentially many nodes to do anything. AES is not differentiable, as are all secure hash and encryption functions. This is a basic test that is used to attack everything.
So you'd get a NN that must be big enough to simply memorize all plaintext, key, output triplets, which is simply a lookup table. With around 2^768 nodes. Good luck.