Let $p$ be a large public prime. Alice holds a private key $(e_1,d_1) \in Z_{p-1}^*$ such that $e_1 d_1 = 1 \mod {p-1}$. Bob also holds a different private key $(e_2,d_2)$ with the same property.
Let's say Alice wants to send a message $\large m \in Z_p^*$ to Bob:
$1.$ Alice computes and sends $\large m^{e_1} \mod p$ to Bob.
$2.$ Bob computes and sends $\large m^{e_1e_2} \mod p$ to Alice.
$3.$ Alice computes and sends $\large m^{e_1e_2d_1} = m^{e_2} \mod p $ to Bob.
$4.$ Bob decrypts by computing $\large m^{e_2d_2} = m \mod p$
Assuming Eve can read (but not modify) the messages exchanged between Alice and Bob, can she obtain any meaningful information about $\large m$ ? What happens if Alice and Bob use the same protocol to exchange multiple messages $\large m_1,m_2,...,m_t$ using the same private keys ?