What E means in Diffie Hellman protocol?

I was looking for an example of protocol to verify user's identity using Diffie Hellman which works like this:

• client sends: $g^x$, ID-Number
• server responds with: $g^y$, $E_H_{pwd} challenge$
• client responds with: challenge

I understand that g^x, g^y are Diffie Hellman keys, plus it's given that H is a hash function and pwd is the user's password but what does E mean here?

$E_{H_{\text{pwd}}} (\text{challenge})$

This is a symmetric encryption of the challenge, using a hash of the password as the key.

That said, this protocol isn't that great if the password has weak entropy (which human entered passwords tend to have). If there is an eavesdropper, he will hear both the plainext $\text{challenge}$ and the corresponding ciphertext $E_{H_{\text{pwd}}} (\text{challenge})$; what he can do is go through his dictionary of passwords, and for each one, hash it, attempt to decrypt the ciphertext, and see if he gets the known plaintext.

$E$ is a keyed symmetric encryption function such as AES or CHACHA. The hash of the password is being used as the key of the encryption function and "challenge" is being used as the plaintext. The client can recover the challenge value because they know their password and can hash it to retrieve the symmetric key and decrypt. This would be hard for anybody that does not know (or cannot work out) the hash of the client's password.