Is E_k(M)||H(m) form of MAC secure? Would this encryption and signing scenario be considered tamper-proof?
plaintext = &quot;hello world&quot;
password = &quot;secret key&quot;
hash = sha3_512(plaintext)
ciphertext = encrypt(plaintext,password)
output = ciphertext+hash

I'm computing the hash of the plaintext and then adding it to the end of the ciphertext output. I know this isn't exactly MAC or HMAC, but does this scenario work? Is it secure? From my perspective, the only way to forge the plaintext is if you know the key. Otherwise, any change will be reflected in the hash. Is this secure? Assume that the cipher is non-malleable. I believe this is the scheme used by Mcrypt for file encryption. Thanks.
This is not a duplicate because it would be infeasible to brute-force the plaintext from the hash as described in the possible duplicate question, scenario 3.
The point (( also see this answer)) is that the hash calculation is free for everybody and we assume that your methodology is known by Kerckhoffs's principles. Anybody can calculate the hash of any information and this may leak the encrypted message.
In Cryptography, we consider the attackers computationally bounded, but not restricted to adapt any method on their advantage.
If the possible attacker one of the three-word agencies, that we can assume that they collect all public information, where available, including your personal information, your networks, your habits, etc. Then they can keep the hash of each information on their humongous database ( like the Utah Data Center ) and once they see a message is transmitted with $E_k(m)||H(m)$ then they will check the existence of the $H(m)$. A hit today will reveal the message you send. They will not stop here if they fail. They will store this message and regularly will check the hash with the updated database.
Therefore this is not a good way to authenticate the messages. In modern cryptography, we have Authenticated Encryption (AE) modes like AES-GCM and ChaCha20-Poly1305 that provide confidentiality, integrity, and authentication in a bundle. Remember nothing is perfect and keep the obligations like for AES-GCM to be secure.