textbook RSA signature scheme security Are textbook RSA signatures secure if an Adversary does not have access to ask signing oracle queries?
No, plain RSA signatures are existentially forgeable under a key only attack. This is because of the following attack strategy:

Given a verification key $(e,N)$, set the message to $m=s^e \bmod{N}$ for an arbitrary $s$ in the message space and set the corresponding signature to $s$. Output the message signature pair $(m,s)$ as a forgery.

It is easy to verify that this pair passes the verification equation.