GANs are different. They may "learn" something plausibly enough, even if they don't know what they are learning. A GAN model could, in theory, generate "plausible" private keys, by learning what private keys are, without knowing anything about their corresponding public keys. Now, from this space of plausible keys that the model generates after we train it, we would just use the results on a subset of the entire Bitcoin network address space, until we find a fit. That's the "brute force" part of it. GANs are coming somehow before that, and they may, because of how they work, shorten the path to a working private key.
I'm not sure I understand this part: "Isn't the whole point of encryption that the fastest way to generate a private key from a public key is to use brute force."
Please educate me but isn't generating plausible private keys rather trivial? But if you want to generate a private key corresponding to any particular public key, there is no choice but to try brute force?
I may have misunderstood some basic things completely.
Generating plausible private keys isn't that trivial. They are derived in a specific process from a part of the public key, and this process involves double hashing.
If by "plausible" you understand correct from a formal point of view (length, allowed chars), this is of course trivial. It's like you would say a person has one nose and two eyes (to continue our GAN example).
But if by "plausible" you understand "with a higher probability to find a fit in a specific set of public keys", then it's different and it's my understanding that GANs can help here. They may create something very close to that, in the same sense they are creating very plausible faces, not just sketchy noses and eyes (have a look at that site).
A very simple explanation of a GAN is that the forger learns specific patterns (nose, eyes, hairlines) by approximating the distance in pixels from them (it's way more complicated than that, obviously). In this sense, if there are patterns in the cryptography generating process, or recognizable groups of letters, etc, a GAN can be closer to a public key than just brute-brute force.
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This I did not know. It cleared up the issue!
Yes, I've read about Generative Adversarial Networks. There are two parts: a generative network that generates possible solutions and an adversarial network that judges them.
But let's get back to plausible private key.
How far from having a plausible keys are you to finding the actual key that corresponds to a public key in general terms?
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That I do not know for sure, but my intuition tells me that we can get closer if we first use GAN, because it may shrink the distribution space. It's just an intuition now, like I said I lack the mathematical skills (or the time) to model properly.
It may even be a question of trial and error until we find which parameters in the learning process affect the validity or the probability of finding a working key.
Sounds cool.