If your adversary is a powerful nation-state threat actor, web PKI will not protect you.
Nothing is preventing them from issuing their own certificate. In fact, many governments run their own certificate authorities, such as the US FPKI and affiliates. See a list of CAs currently trusted by Firefox:
- Government of France
- Government of Hong Kong (SAR), Hongkong Post
- Government of Japan, Ministry of Internal Affairs and Communications
- Government of Spain, Autoritat de Certificació de la Comunitat Valenciana (ACCV)
- Government of Spain (CAV), Izenpe S.A.
- Government of The Netherlands, PKIoverheid
- Government of Taiwan, Government Root Certification Authority (GRCA)
- Government of Turkey, Kamu Sertifikasyon Merkezi (Kamu SM)
While Firefox currently refuses to trust the US FPKI, it still trusts many other government-run CAs, and a sophisticated nation-state actor absolutely has access to some existing, commercial CAs. Chrome, Internet Explorer, and Edge use the system trust store which, for Windows, does include many government certificate authorities, including the US FPKI. Any of these could be used to sign a valid certificate for any website and your browser would happily trust them without batting an eye.
While the new and experimental standard for Certificate Transparency (CT) helps reduce the impact of mistakenly-issued certificates, it does not protect against a dedicated attacker who controls a malicious CA. Once it has seen greater adoption it may, however, make it easier to spot malicious or misbehaving CAs after a short period of time, but it will not prevent the attack immediately as it is performed.
Some browsers use certificate pinning where important and high-profile domains are validated against a hardcoded list of permitted certificate authorities. Signing a fraudulent certificate for those domains would require compromising the CA that they currently use. Unfortunately, this only applies to a small handful of domains and does not protect the web at large.
A partial solution would be to refuse to trust a domain without the .gov TLD whose certificate was issued by a government CA, which could be implemented client-side, but it would likely have little real-world impact. An adversarial government is not going to sign a malicious website with a state-run CA, since that would immediately attribute the attack to them. Rather, they would exploit covert relationships with existing CAs to trick them or force them into signing the certificate. CT, as mentioned in the previous paragraph, would detect this and the attack would be quickly noticed, but it does not prevent it.