I'm having difficulty understanding this.
Consider two messages are encrypted using the same cyclic group of order $q$, generator $g$, private key $x$, and random parameter $y$. The attacker knows a plaintext $m_1$ and its corresponding ciphertext $c_1=(r_1,s_1)$.
I was told that, under these circumstances, if an attacker also knows the ciphertext $c_2=(r_2,s_2)$ of another message $m_2$, they can recover $m_2$.
How is this possible? Wouldn't the attacker need to know $q$ and $g$?