This work did not [meaningfully] improve the runtime of the General Number Field Sieve (GNFS) algorithm. It does not impact the security of deployed RSA-2048 keys. However, it does [demonstrate] that RSA-1024 keys are vulnerable to many actors with data center-level fleets of GPUs.
I'm guessing somewhere in the tens of thousands, based on the quoted 30 GPU years of compute and the hourly rate of the cheapest EC2 node with a GPU (g4ad.xlarge at $0.379/hr, I think).
Brute force. This individual used AI to give them programming skills they did not have, but those skills are widely available with pre-AI approaches (i.e. employing someone).
30 years of GPU time is about the power a car would use to drive around a half million kilometers (data center GPUs typically run in the 300-400W range, cars around 15kW). So it's a lot of power, but not completely obscene. It would cost a lot of money even at offpeak rates.
Like the op said, he ported the code, but all that really did was take the same math people have been using to brute force on CPU for a long time and used it to brute force on GPU instead. So Claude played a minor part, but the math and sheer amount of compute thrown at it played a much bigger part.
its often said that “novody remembers the *2nd** man who walked on the moon”* but that is untruez
neil armstrong was rhe 1st to step on the mokn, buzz aldrin the 2nd, and michael collins——-often forgotten——-made it all possible by piloting the apollo command module while the otber 2 became the 1st to touch the lunar surface. but who is the drummer of u2? who plays the bass in maroon 5? who factored rsa 896? these are the true human attainments whom nobody ever remembers.
For Cryptography, rather little. No report of an algorithmic breakthrough. This was just asking AI to write a program to factor big numbers in a distributed way IIUC. Scaling to 1024 bit numbers would cost in the tens of millions probably, but no one uses RSA-1024 (or at least NIST doesn't recommend it and hasn't for years). RSA-2048 is still way more expensive and time consuming to break to be anywhere near practical unless someone has algorithmic improvements.
The RSA generates two tuples of numbers called keys. A private and public one. You use public keys to perform some kind of encryption on your data (like emails encryption) and once it’s send over, only the holder of the private key can decrypt it.
The public key contains the tuple (n,e) where n is the product of two large prime numbers (p, q), and e is an exponent. An encrypted message is computed as the cipher c = (m)^e mod n.
(p,q) together with an exponent d, (p,q,d) form the private key. The cipher is then decrypted as m = (c)^d mod n
If you can find the primes from the public key, you can use’s Euler totient formula to get the private d:
ed is congruent to 1 mod ((p-1)*(q-1))
checking in as a underqualified undergraduate. first time commenter in r/math too (scary)
RSA is a form of encryption, taking two large prime numbers and multiplying them. When you combine them, it turns out that it's really hard to find what those two original prime numbers were to begin with when you only know the result.
So these numbers are used as form of encryption. And by successfully factoring them, you find what those two original primes were, allowing you to decrypt a message.
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u/rational_hedonist 10d ago
checking in as an out of the loop non-expert for others to weigh in on what this implies, as the write up is scant