Claude reveals ECDSA curve origins

As unsurprised as I am by this, and as much as I suspect a lot of people could have guessed it, having Claude confirm it is still fascinating, but.

Somehow, I find these results fascinating, but also quite sad, because we used a machine to solve it at all. I feel like some half drunk motivated graduate level humans could have figured it out too.

Then again, once you know the answer, perhaps you have an obligation to share it, keeping it to yourself might be unfair to everyone else.

Honestly I’m not entirely sure how I feel about all this. I would gladly welcome any groundbreaking work Claude might do to solve hard problems and move the world forward by decades or even centuries.

But these sorts of fun problems feel like things we should avoid pointing LLMs at. They remind me of those weird programming puzzles that are difficult to solve but incredibly fun to work through.

My concern is that if Claude ends up solving all the fun problems, will humans be left with nothing but the hard, headache-inducing ones? Tao had raised a similar concern, problems that graduate students would have been expected to solve and learn the process, are now things you can simply point an LLM at.

I’m still not sure how I will ever reconcile with this feeling, about any of this. I just find it genuinely sad that we might be automating away not only the difficult work, but also the joy of figuring things out for ourselves.

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Stochastic parrot truthers in shambles.

What proof is it that it is really the origin of the curves? That looks credible like most hallucinated output of LLM but it might easily be a coincidence similar to a collision attack, no?

Especially finding the solution that is based on using a random number generator.

It's like people seeing proof that the future was written in Harry Potter books by reading the first letter of the top of the page of a weird set of pages.

>“seed” parameter

>provided by the NSA with no explanation or justification.

Really? Nobody is concerned about the NSA just cheerfully dictating that? Smells very rainbow-table-y

Computers can search information space exhaustively.

This is not very exciting

I’d be interested in a Bayesian analysis of how they arrive at the degree of certainty that their hypothesized solution is in fact the correct one. Like even if it’s 99.999999% likely or some such, I’d still like to see the math at how they arrive at that. Edit: Since in crypto solutions there’s always this question of hamming distance. PS. Amazing I can get downvoted already, minutes in, for posing a show-me type comment, (presumably just for making noise in face of big crypto brand names like Anthropic & NSA), without substantiation for the downvote; thanks HN community for displaying your spots. Even if a Bayesian analysis would be trivial in the case at hand, the effort would be helpful at informing similar efforts entailing comparatively greater uncertainty.

> This is not a cryptographic break, new attack, or weakness in the ECDSA curves. In fact, this makes us more confident the curves were chosen without any backdoors or intentional weaknesses.

Uh… did you talk to any cryptographers? This is EXACTLY what a weak curve would look like. Imagine that 1 in a thousand, or one in a million keys, selected at random, are vulnerable to some withheld attack. This approach lets you vary the timestamp or number of iterations until a weak key is found, then have plausible deniability afterward. This is why modern systems choose constants in a way with no free choice of parameters (e.g. sqrt of 2 for first constant, cube root for second constant, etc.).

They even note later in the article that viable curves in the generator sequence seem to have been skipped.

They are so desperate for claude to be good at maths, like chatgpt. But claude is optimized for quick, pragmatic results and chatgpt is trained to be careful. There is a reason the best anthropic could do was an organized search - not real mathematics.

I have strong doubt on this claim.

It claims that NIST member feed UNIX time of certain points in 1997-1998 to srand() and draw 20 bytes for n times, then use the last 20 bytes for the SEEDS.

Why NIST staff in 1999 used default rand() implementation of libc(or languages which rely on libc) at that time? Linear congruential generator was infamous for its poor quality even in 1990s.

NIST published recommended SEED value in 1999, July. Why did they use UNIX time from 1997-1998?

Why the exact date of that UNIX times are so sparse? 1 in 1997 May, 3 in 1997 Auguest, 1 in 1998 April? If they did srand(time(NULL)), it should be more closer.

The number of n'th 20 bytes thrown out is also doesn't make sense. n=139 for P-192, n=7026 for P-224 and so on. Why did they choose this numbers in particular? Why P-192 was odd and 3 digits while rest of 4 were even and 4 digits?

It seems to me, Claude simply hit a jackpot of coincidentally matching 20 bytes.