Is RSA-signing a given challenge $x$ a zero-knowledge proof of holding the RSA private key, for the modern definition of zero-knowledge proof (which I don't know!)
Assume public and genuine RSA public key $(n,e)$, secret RSA private key $(n,e,d,p,q\ldots)$ with distinct secret primes $p$ and $q$, that the factorization of $n$ can't be found from the public key or from access to a textbook RSA signature oracle, and that the RSA assumption holds.
If necessary, distinguish between
- textbook RSA signature $x\mapsto x^d\bmod n$
- RSA signature with deterministic padding, e.g. RSA-FDH, or RSASSA-PKCS1-v1_5
- RSA signature with random padding, e.g. RSASSA-PSS
Update: I'm reading the answers to a similar question (on signature in general) as no. But I'd like an answer based on a definition of zero-knowledge proof.