Client-Server secure connection handshake

Question

I would like to know if there are any security concerns regarding the way I want to create a secure client-server connection.

NOTE: I know the most obvious answer to these type of questions is to just use SSL/TLS, but I would appreciate an answer to my specific case.

My connection protocol is as follows (following communication is un-encrypted plain text):

client connects to server socket
server sends a 2048-bit public RSA key to client
client generates a 256-bit AES key, encrypts it with the received public RSA key, and sends it to server (server decrypts it and obtains the secret AES key)
client generates a 256-bit HMAC key, encrypts it a client-embedded public RSA key, and sends it to server (server decrypts it and obtains the secret HMAC key)
server sends to client the HMAC of the AES key, proving it possesses the private RSA key corresponding to the client-embedded public RSA key, and proving the authenticity of the server

All further communication is encrypted with AES and verified with HMAC.

I'm voting to close this question as off-topic because this is not directly related to software development. — Artjom B.
This is vulnerable to a Man-in-the-Middle attack, because the origin of the public key is never verified. — Artjom B.
I would like to say that this is directly related to software development, because it is part of the software I am making. — Htmiel
As I see it, even if the initial public key received form the server is of unknown origin, the entire connection would fail at the moment when the server has to decrypt the message encrypted with the client-embedded public key (step 4 and 5) — Htmiel
The answer is still TLS. Don't think you can improve on it. You can't. The fact that you have to ask here is sufficient evidence. — user207421

Luke Joshua Park Luke Joshua Park · Accepted Answer · 2017-07-09T12:18:59

A man in the middle could easily send their own public key to the client and receive the original public key from the server.

It could then eavesdrop the conversation in both directions.