Its known that all wifi encryption methods to secure your network from attackers are broken, WEP, WPA, WPA2... With some amount of time someone can break in in your network.
Why we can't use some kind of public key cryptography, (For example, SSL (used in https) allows to connect using a encrypted and authenticated channel to a server) to connect to our home router?
I mean, instead of using WPA the router could start a SSL like connection (with a self signed certificate) to a client, when the handshake is done the client can provide a password, if the password is correct the router trust the client as a valid client (not an attacker).
This way no one can get inside a network without knowing the password and the clients of a network cannot sniff eachother or perform a MITM attack.
Also, to limit bruteforce the router can ask for a proof of work for each password attempt.
In summary: Computer wants to connect to a Wifi network, it contacts to the router to stablish a secure encrypted channel, then the computer provides a password to the router, if the router validates it adds the computer's public key to a whitelist (that computer is trusted and cann access the internet and the network).
I dont know if this is even possible and I might be wrong in some things, please answer if this can be done (by router manufacturers) or if it is planned to be done (or similar systems to be the future of current methods).