Breaking RSA, given a special kind of oracle that decrypts related ciphertexts for us Let $c=E^{RSA}_{e}(w)$ be the ciphertext belonging to the plaintext $w$ if an $RSA$ system is used. Assume that the public exponent $e$ satisfies $e \le 10$. Furthermore, assume there is an oracle that, on input $r&gt;0$, responds with the value $c_{r}= E^{RSA}_{e} (w + r)$.

Can the plaintext be decrypted efficiently, given this oracle?
Hint 1: what's the binomial expansion of $E_e^{RSA}(w+r)$?  That is, how can that be expressed as a polynomial in variables $w$ and $r$?  What degree are those polynomials, in terms of $w$?

Hint 2: suppose we ask for $E_e^{RSA}(w+r)$ for $0 &lt; r &lt; e$ (and we also know $E_e^{RSA}(w)$); what can we do with the corresponding $e$ polynomials?