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Comment by sghiassy | Hacker News Reader

A next-word-in-the-sentence prediction engine can’t predict the factor of two insanely large prime numbers… tell me more

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I think the thing most of us missed in dismissing GPT 2-3 as 'next word in sentence predictors' was that recursively this allows something resembling thinking, 'reasoning'.

LLMs are capable not just of calculating the most likely next word from a prompt according to a corpus of training text, but of doing so & feeding back into themselves, the most likely word now based not only on the corpus but on the basic prediction, a second (nth) stage of thought.

Yes it's all still token prediction, but it's predicting conversation between let's say not experts but capable speakers with all the information at hand. Undergraduates if you like. And such conversation can yield real results.

I’m with ya

I’ve even heard arguments that prediction is consciousness.

But using a Language-Model to break cryptography is still a stretch for me.

From the little I know, cryptography uses information theory to make sure that reversing the equation (aka finding the passowrd) is predictably impossible, given current compute standards for the foreseeable future (disregard quantum computer here though :) they’re not LLMs)

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.

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.

I think you misunderstand. The idea is not that one feeds a cryptographic text to LLMs and they crack it. The idea is that one feeds a cryptographic algorithm to an LLM and they break it somehow. Bear in mind that cryptographers consider a "break" anything that reduces the strength of an algorithm, but that doesn't mean that it is practical to use the given "break" to obtain even one plaintext, let alone obtain them all.

Many crypto algorithms have formal proofs that they are reductions of hard problems like factorization. Those problems may not be solvable, only brute forcible. Some could be eventually solved, but the likelihood of every single one being solvable is unlikely.

RSA is asymmetric crypto. This article is about symmetric cryptography. I expect LLMs will advance state of the art in factoring algorithms, considerably.

Why?

Thank you

I guess I only know asymmetric cryptography. I should learn more about symmetric…

Anyone care to boil it down for me :)

Edit: Isn’t this just advanced static analysis of any code base?

Very, very briefly, most symmetric algorithms are block ciphers, meaning that their input are blocks of a fixed length in bits (plus a key), and their output is another block of the same length. Ideally, a block cipher with its key produces a random permutation of the input space into the output space, thus diluting the information and dramatically increasing (ideally maximizing) the entropy; what that means is that whether the input is just zeroes and ones in ASCII or fully random, after encryption it should be indistinguishable.

Thank you

I wish I knew more in this domain.

It almost sounds like hashing with a salt

It pretty much is, except it's reversible. At the block level it meets the cascading requirement, and you can set it up to expand the output arbitrarily by padding the input with zeroes (thus also turning it into a PRNG).

A symmetric cipher is: ciphertext = data XOR key. XOR is reversible: plaintext = ciphertext XOR key.

If the key is a set of truly random numbers the same size as the ciphertext, then this is a one-time pad, and it is truly secure in the information theory sense. Nothing other than knowing the original randomly selected key values can decode the ciphertext.

But of course, it's hard to come up with terabytes of random numbers at the drop of a hat, and to share them securely with the other party. So symmetric ciphers use pseudo-random generation techniques, to iterate through many pseudo-random keys based on one original key. With PRNGs the "randomness" may have patterns and that is the opening for a break in the crypto.

There is already a mathematically secure algorithm for securing a message: One Time Pad. The problem is that OTP requires that the length of the key and the length of message must be the same, which is inconvenient for large amounts of data.

So the solution is to find algos that let you use a smaller key, but the side effect is that by pigeonhole principle, your keyspace is smaller than the message space, so it MUST be insecure. The trick is to make it so that it's only insecure enough that it's infeasible to break.

It's inconvenient for any amount of data, because it essentially begs the question; if you can securely transmit N bytes of key pad to a counterparty, just use that mechanism to transmit N bytes of plaintext instead.

It has the advantage that the key can be sent before the message is known. Think military battlefield. Your commander goes out to war with a CD, and then he can transmit messages like "we encountered the enemy". It would do no good to transmit "we encountered the enemy" before the war started.

Perhaps, but it’s still trivially easy to increase the difficulty of factorization problems on classical computers, We need a machine that can run Shor’s algorithm before integer factorization is practical and we’re still a long way out f M that.

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