Is there any proof for ECDSA signature algorithm?

Question

Related: Is there an interactive version of ECDSA signature protocol like the Schnorr identification protocol?

Answer 1

As pointed out by @SEJPM, you can read more about security proofs for DSA/ECDSA family on this thread.

As for whether there exists an interactive protocol corresponding to DSA/ECDSA à la Schnorr identification/Schnorr signature, not that I am aware of. I would add that this is unlikely for two reasons:

1. The (unfortunate) reason for coming up with DSA/ECDSA was to bypass the patent on Schnorr signatures. Therefore its design was supposed be different enough from Schnorr.
2. If there were some kind of a sigma protocol then it is very likely that this would lead to a security proof (at least in the random-oracle model) as there exist standard methods to construct signatures from identification. Since we don't know a proof, one could say that there probably isn't an interactive protocol either (but this argument is very hand-wavy).