Is it proven that breaking RSA signature is as hard as breaking the RSA encryption, considering the same key size?
I know that they both are based on the RSA function, but I believe that, as always with cryptography, the answer can't be that simple.
First, technically, RSA signing and RSA encryption use different exponents: the former uses a private exponent, and the latter uses a public exponent (which is typically smaller).
Second, padding schemes do matter - but I'm assuming in my question that a "good" padding scheme is used - for instance, for signatures it's RSA-PSS or RSASSA-PKCS1-v1_5 (the latter is non provably correct, but it's still widely deployed and not actually cracked yet).
Third, does the answer depend on the allowed usages of the RSA keys in question? I.e. comparing situations: a) having two keys, one restricted to only Digital signature, and another to only Key/Data encipherment, b) having a single key, with both usages allowed.
Any references to books/standards/conference presentations will be appreciated. Thanks!