A method to efficiently factor large numbers will also break the ECDSA.

CamperBob2 · 2025-08-31T19:26:50 1756668410

No, ECDSA relies on the hardness of the discrete logarithm problem. Nothing to do with factoring, at least not in the classical sense.

On a quantum computer, my understanding is that Shor's algorithm could potentially target both problems, though.

cyberax · 2025-08-31T20:19:00 1756671540

Both systems are an example of a hidden Abelian subgroup problem. That is also why Shor's algorithm equally applies to both: https://en.m.wikipedia.org/wiki/Shor%27s_algorithm#Shor's_al...

So a hypothetical classic algorithm that breaks the RSA is also highly likely to break the ECDSA.