Man-in-the-middle attack on text-book RSA PKE
I see four ways how to attack this scheme

1) RSA malleability
Suggested in comments

2) If $e=3$ then
Trivial attack exists. Hint: What is the minimal possible size of $N$?

3) If the attack is active(MiTM)
Cheaper attack exists. Hint: Treat the task as a set of Oracles:


$Oracle0: n \mapsto E(n)$ - If you know $(e,N)$, you can encrypt any $n$.
$Oracle1: \epsilon \mapsto E(R_1)$
$Oracle2: E(n) \mapsto E(R_2*2^{28}+n)$
$Oracle3: E(n) \mapsto E(n*2^{156}+R_3)$ - Are you sure? 


4) You treat it as a blackbox
Your solution