This question relates to the underlying RSA assumption. Forgetting about the fact that Textbook RSA is deterministic, I am curious about the assumed strength of the RSA problem.
Does RSA hide all bits of the message, or are there some bits that can be easily revealed. Concretely,
$$m^e \space \bmod \space N$$
Can any part of $m$ be learned(with significant probability) without learning the secret key, and if so how?