> They need access to the private key for that, which ACME (and other certificate signing protocols in general) doesn't share with the CA.

Modern TLS doesn't even rely on the privacy of the private key 'as much' as it used: nowadays with (perfect) forward secrecy it's mainly used to establish trust, and after which the two parties generate transient session keys.

* https://en.wikipedia.org/wiki/Forward_secrecy

So even if the private key is compromised sometime in the future, past conversation cannot be decrypted.

In fact knowing the private key for other people's certificate you issue is strictly forbidden for the publicly trusted CAs. That's what happened years back when a "reseller" company named Trustico literally sent the private keys for all their customers to the issuing CA apparently under the impression this would somehow result in refunding or re-issuing or something. The CA checked, went "These are real, WTF?" and revoked all the now useless certificates.

It is called a private key for a reason. Don't tell anybody. It's not a secret that you're supposed to share with somebody, it's private, tell nobody. Which in this case means - don't let your "reseller" choose the key, that's now their key, your key should be private which means you don't tell anybody what it is.

If you're thinking "But wait, if I don't tell anybody, how can that work?" then congratulations - this is tricky mathematics they didn't cover in school, it is called "Public key cryptography" and it was only invented in the 20th century. You don't need to understand how it works, but if you want to know, the easiest kind still used today is called the RSA Digital Signature so you can watch videos or read a tutorial about that.

If you're just wondering about Let's Encrypt, well, Let's Encrypt don't know or want to know anybody else's private keys either, the ACME software you use will, in entirely automated cases, pick random keys, not tell anybody, but store them for use by the server software and obtain suitable certificate for those keys, despite not telling anybody what the key is.

Even access to the private key doesn't permit a passive adversary to snoop on traffic that's using a ciphersuite that provides perfect forward secrecy, because the private key is only used to authenticate the session key negotiation protocol, which generates a session key that cannot be computed from the captured session traffic. Most SSL and TLS ciphersuites provide PFS nowadays.

An active adversary engaging in a man-in-the-middle attack on HTTPS can do it with the private key, as you suggest, but they can also do it with a completely separate private key that is signed by any CA the browser trusts. There are firewall vendors that openly do this to every single HTTPS connection through the firewall.

HPKP was a defense against this (https://en.wikipedia.org/wiki/HTTP_Public_Key_Pinning) but HPKP caused other, worse problems, and was deprecated in 02017 and later removed. CT logging is another, possibly weaker defense. (It only works for CAs that participate in CT, and it only detects attacks after the fact; it doesn't make them impossible.)

If the CA is somehow able to control the communication (I think usually they don't, but if they are being run by intelligence operatives then maybe they have that capability, although they probably do not use it a lot if so (in order to reduce the chance of being detected)), they could substitute a certificate with their own keys (and then communicate with the original server using the original keys in order to obtain the information required). However, this does not apply if both sides verify by an independent method that the key is correct (and if not, would allow to detect it).

Adding multiple signatures to a certificate would be difficult because the extensions must be a part of the certificate which will be signed. (However, there are ways to do such thing as web of trust, and I had thought of ways to do this with X.509, although it does not normally do that. Another way would be an extension which is filled with null bytes when calculating the extra signatures and then being filled in with the extra signatures when calculating the normal signature.)

(Other X.509 extensions would also be helpful for various reasons, although the CAs might not allow that, due to various requirements (some of which are unnecessary).)

Another thing that helps is using X.509 client certificates for authentication in addition to server certificates. If you do this, then any MITM will not be able to authenticate (unless at least one side allows them to do so). X.509 client authentication has many other advantages as well.

In addition, it might be helpful to allow you to use those certificates to issue additional certificates (e.g. to subdomains); but, whoever verifies the certificate (usually the client, but it can also be the server in case of a client certificate) would then need to check the entire certificate chain to check the permissions allowed by the certificate.

There is also the possibility that certificate authorities will refuse to issue certificates to you for whatever reasons.

I know that. But presumably, Let's Encrypt could participate in a MITM attack since they can sign another key, so that even the visitor who knows that you use them as a CA can't tell there is a MITM. Checking multiple signatures on the same key could raise the bar for a MITM attack, requiring multiple CA's to participate. I can't be the first person to think of this. I'm not even a web security guy.

It might be interesting for ACME to be updated to support signing the same key with multiple CA's. Three sounds like a good number. You ought to be able to trust CA's enough to believe that there won't be 3 of them conspiring against you, but you never really know.