ElGamal: Why is reusing the same $k$ not secure?
In ElGamal encryption like you said for unknown $m_1$ and known $m_2$ we have:

$m_1: C_1=g^k\ mod\ p,\  D_1=m_1.g^{a.k}$

$m_2: C_2=g^k\ mod\ p,\  D_2=m_2.g^{a.k}$

$k$ is the same in both encryptions, by dividing $D_1$ and $D_2$ we have:

${D_1\over D_2}={m_1\over m_2} =&gt; D_1.m_2 = D_2.m_1$

$m_2$ , $D_1$ and $D_2$ and are known so now we can calculate $m_1$. This is how can attacker proceed and find unknown $m_1$.