I am attempting to solve the following problem:
I know the following:
3 messages are being sent between Alice and Bob, all messages are encrypted with the known public key $(d,N)$:
- Alice sends Bob: $m_1=E(R_1);$ $R_1$ is a 28-bit number.
Bob sends Alice: $m_2=E(R_2,R_1);$ $R_2$ is a 28-bit number and $R_1$ follows (i.e, $p_2 = (2^{28} * R_2 + R_1)$ if i am not mistaken)
Alice sends Bob: $m_3=E(R_2,R_1,R_3);$ $R_3$ is a 156-bit number known in advance.
The goal is to alter $R_3$'s value which is about to be sent to Bob to a new value (first 7 bits only).
The best I could come up with is to precompute all possible 28-bit number encryptions which will allow me to know $R_1$'s value when sent by Alice -> then easily figure out $R_2$'s value -> send my desired $R_3$ value to Bob.
Is there a neater (and more feasible) way to do so?