If sent the same message m to Alice and Bob, how someone who follow the channel can find m ?

Question

Alice has public key (n,ea) and Bob has public key (n,eb) with gcd(ea,eb)=1. If sent the same message m to Alice and Bob, how someone who follow the channel can find m ?

Answer 1

The eavesdropper gets $r=m^{e_a}\mod n$ and $s=m^{e_b}\pmod n$. Since $\gcd(e_a,e_b)=1$, eavesdropper can find $x,y$ with $e_ax+e_by=1$ (right?). Eavesdropper calculates $r^xs^y$. Can you take it from there?