Forging 1024-bit RSA signatures in nearly SNFS time

[Ibrahim_Mihai]

This repository contains a paper (eprint 2026/XXXX) and code implementing a variant of the number field sieve (NFS) algorithm. It shows that an attacker can use temporary access to a raw, unpadded RSA signing/decryption oracle to gain the permanent ability to forge signatures / decrypt ciphertexts.
The algorithm only works if a raw signing oracle is available. Most RSA usage in practice (that is, RSA signatures using PKCS#1v1.5 or RSA-PSS padding) do not expose such an oracle, and thus this attack does not pose a practical risk. Examples of RSA use that do expose such a signing oracle would include blind RSA signatures (e.g. Privacy Pass) or HSM APIs.

https://github.com/ucsd-hacc/NSNFSSSFSFN/

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[chants]

I found the most interesting part to be the authors tweet indicating why RSA2048 is out of reach for now:

https://x.com/miro_haller/status/2102094654724608460

And the preprint

https://eprint.iacr.org/2026/2131

[jonwil]

There is a reason so many people say to avoid RSA-1024 in 2026.

[chants]

I agree RSA1024 is moving towards limited shelf life. Too much happening now with NFS methods that are practical at 896 bits for someone with GPU resources