$(E,D)$ is a (one-time) semantically secure cipher where the message and ciphertext space is $\{0,1\}^n$. $E'(k,m)$ is defined as
$E′(k,m)=E(0^n,m)$
The question is whether $E'(k,m)$ is (one-time) semantically secure?
I thought that the random chosen key $k$ might be $0^n$, therefore the adversary cannot distinguish the messages $m0$ and $m1$ when encrypted with the key $0^n$. Therefore, the scheme is semantically secure. However, the answer states that
To break semantic security, an attacker would ask for the encryption of $0^n$ and $1^n$ and can easily distinguish $EXP(0)$ from $EXP(1)$ because it knows the secret key, namely $0^n$.
Can you elaborate on the answer more? I don't understand how the key is known ("because it knows the secret key") and how we can find that the messages $0^n$ and $1^n$ should be used to break the semantic security (Can we try the whole message space?)?