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Comment by PlasmaPower | Hacker News Reader

The oversight in your thinking is that we have no proofs about how much computation is needed to break cryptography. For all we know, it could be possible to break all modern cryptosystems in under a second on a computer from a decade ago with the right algorithms.

This is how cryptography has been broken in the past: not just advances in the amount of compute we can do, but exponential speedups in the algorithms to break them. While I agree with the author of this post that modern cryptosystems are very secure and LLMs are not currently near breaking them, I don't think it's unreasonable to consider that if LLMs continue to get exponentially smarter they may make strides in cryptanalysis that we had never considered and break cryptography in unexpected ways. After all, many past cryptography breaks have come from previously unknown methods of cryptanalysis.

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Can someone more knowledgeable than me comment on this.

I thought, that Information Theory could mathematically predict the computational challenge of factoring one massive number into its two original primes?

Is that not true? If you have just a random number (aka public key) can you just LLM your way to the private key??!?

It's indeed thought to be really hard to factor multiples of two massive primes, but we don't know that for certain. See https://en.wikipedia.org/wiki/Integer_factorization -- "Unsolved problem in computer science: Can integer factorization be solved in polynomial time on a classical computer?". In fact, we don't even have a proof that this is more complex than multiplying the component primes.

And of course, many cryptosystems are reliant on primitives with much less algebraic structure.

But to be clear, LLMs would presumably break these cryptosystems by building new algorithms and writing code to break them, not by "intuiting" their way to a specific private key.

an LLM would likely just converge on something like a shared prime GCD attack; basically finding private keys somewhere in their training set and then hoping that whatever keygen algo was setup incorrectly and used a shared seed.

There are only two known cryptographic algorithms that are "information-theoretically secure", essentially meaning they are proven impossible to break. Those are one-time-pad encryption, and Shamir's Secret Sharing.

The rest of them rely on more practical considerations. Asymmetric crypto is generally based on some mathematical problem that we don't know how to solve yet (and think we never will) while symmetric crypto is generally based on brute-force-style mixing up the bits so thoroughly they seem impossible to unmix.

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