RSA-896

…but super-polynomial.

I misspoke and corrected down thread.

A sufficiently motivated person with a good thermal camera and a cessna 172, entirely within the bounds of the law, could probably make an estimate of the waste heat from this, and then calculate backwards for how much compute power it is.

https://en.wikipedia.org/wiki/Utah_Data_Center

> How long would it take for NSA to crack them if they had say the equivalent of a million GPU's? (either GPU's or crypto tuned ASICs)

Something I've often wondered is where the curve between "shit encryption / nation state cracking" crosses.

How much CPU would you need to be Annoyingly Difficult to crack?

I reckon with elliptic curves you could be quite annoying within about a minute on a 1980s-level CPU, to the extent that you could send a fairly ephemeral message quite quickly that would take disproportionately long to crack. Certainly long enough for the thing you have communicated to be no longer worth the effort to know.

You could probably do 256-bit Curve25519 key generation in under ten minutes on an Apple II or Commodore 64, because the 6502's maths is terribly limited, but something like the Tandy Color or Dragon 32 with its 6809 processor (or hey why not the Ensoniq Mirage sampler?) could do that in probably a minute or so because it has a MUL opcode that's quite fast.

I reckon that would keep even a fairly interested nation state chewing away long after your message had been read, understood, and acted upon.

    > 1024 bit keys with recordings of not too old data can probably be found

I think GitHub might turn into a scary vector of supply chain attacks in the foreseeable future. There is a five digit number of users still running around with 1024 bit RSA keys.

Hard to judge. The bottleneck is the phase of the algorithm where a really big linear system needs to be solved. That takes a lot of communication between nodes. The breakthrough in using GPUs is that there is good communication between nodes[1]. At the scale of 1024 bit RSA the communication might become a bottleneck again.

[1] https://cognition.com/blog/factoring-rsa-260

The author works at Anthropic, so probably idle capacity in Anthropic's datacenters.

If you look at the numbers, he managed about 50% utilization of those 2048 GPUs over 10 days, so he was probably sneaking in factoring work between training runs.

but we have AI now so it doesnt matter what people know about computers :'). we got plenty of rainforest to burn afterall have you seen Brazil?

~so then how does one even understand this post? you have a person who appears to have done some sort of expert-level thing; however, their approach doesn't even make sense...?~

edit: GPU discussed here https://cognition.com/blog/factoring-rsa-260

I don't get your argument. The GPU effectiveness derives from massive parallelism. Has nothing to do with integer vs floating point. You just can't cram 20,000 CPU cores in the same space a GPU puts the same number of SIMTs. You'll never crack it on CPUs.

34 bits of key growth resulted in resource usage growth slightly more than 2 (30 GPU-years vs 13.5 GPU-years).

Thus, it appears, that ~585 GPU years can factor 1024 bit RSA. 2.2^((1024-896)/34)=19.5, expected growth of resources' usage compared to 896 bits factorization, multiplying it by 30 GPU years for 896 bits gives about 585 GPU-years.

This will cost about $20M with Cognition AI setup.

Yep, they ran on some newer GPUs so were able to use fewer. Their implementation was faster than mine on RSA-260. For RSA-896, mine improved the performance a bit and selected a good polynomial.

I’ll post more details once I get a chance. I wanted to publish as soon as I had the factors because I was beat by 48 hours last time.

But Anthropic isn't paying for the electricity and cooling. They don't run their own data centers, they rent compute from providers who cover those costs.

That's entirely why they can blow compute on the fun projects like this. If they had to pay extra for the electricity, they wouldn't do it.

Most of the GPU cost is in the GPUs themselves (and in the space and maintenance costs of the building). Electricity is a small fraction, and it's not like datacenters are just going to shut down their servers when they're not in use.

There is cost, but the cost is mostly the opportunity cost of not being able to do something else.

wouldn't even cover the cost of power and cooling otherwise everyone would still be doin it

You missed the part where they have already pre-paid for the GPU-hours and they pay the same regardless of he electricity used.

Also, even if they were paying for electricity, they would lose less money mining crypto than factoring RSA numbers.

Someone allocated those GPUs.

Yeah it's a bit ambiguous, but in any case I'd think simply using that idle capacity to generate tokens would be more valuable than finding a basically meaningless number.

True, I forgot about that! It's more fun when the inputs are printable ascii, though :P

It should also be easy to beat with just a few GPU weeks.

30 years of busy GPUs instead of idling GPUs converts to a lot of pee in the shower. I’m not sure I will live long enough.

There's about 900 BTC remaining for anyone who breaks these keys:

https://privatekeys.pw/puzzles/bitcoin-puzzle-tx

If you break one though be careful when redeeming it, there are bots set up to pounce and steal the coins when they are transacted because the reduced entropy makes that possible. You need to submit the transaction to a mining pool that will not broadcast it until it is mined.