A MITM doesn't require decrypting. It just requires telling a convincing enough lie to each side of a conversation that they think they're talking to the other party. Then you end up encrypting to their key which they can just read. That's different from breaking the encryption.

Are you sure they can’t decrypt?

No, and none of the state actors who do that kind of stuff will ever tell you. Watch The Imitation Game for a good/bad time and some context.

If you had a break for the modern crypto schemes and published it right now you would shut down all digital commerce, a lot of the spy traffic if not most of it^1^, and nothing could be started back up again until everything was redone from scratch. Best hope would be that the post quantum algorithms^2^ the cryptographers have aren't succeptible to whatever you did to break the existing algorithms. It'd take a bit to get the software implementations and keys in place, etc. The hardware stuff would take longer.

• [1] The stuff using One Time Pads would still be fine, but its limitations wouldn't take the place all of all the rest of it.
• [2] The rollout of post quantum algorithms is going on now on a more accelerated schedule than originally planned.

Yes, the private key never leaves your machine.

You send them a certificate signing request with your public key, they put their verification stamp on it and send it to you.

The only part they have to play is verifying that your certificate is trusted by a root certificate.

The CA cannot decypt: they don't have the secret key which only the server has. When requesting a new certificate from the CA, the server generated a secret key (aka private key) and then generated a derived public key that goes into a Certificate Signing Request (CSR). The CSR is what the CA receives, not the secret key, and then the CA returns the certificate file to the server, which has been endorsed by the CA and thus trusted by the user base.

Phrased another way, a certificate is the instrument that confirms that a purported public key can in-fact be safely used, and that no MITM attack is happening (assuming you trust the CA that signed the cert). But once you've confirmed the public key, the rest of the cryptography is public key cryptography, meaning the secrecy of the secret key is the whole game.

The certificate is only used for authentication. The actual data is encrypted with a temporary symmetric key that is generated via a diffie-hellman exchange

Even if they had your private key they still wouldn't be able to decrypt the data

They don't have your private key