I have no background at all in IT security, but I thought the passwords would be encrypted using a RSA system (the public key would be used to encrypt the passw

I have no background at all in IT security, but I thought the passwords would be encrypted using a RSA system (the public key would be used to encrypt the password, the private key would be used to read them). The private key would be generated randomly when the browser is built, making it unique, and inaccessible (unless maybe with a debugger, but that's not something that could be done in couple of minutes). Maybe what I just said is stupid and not feasible, in which case I'd be curious to know why.