The browser could generate an unique key pair for every website that request a public key. Or there could be a dialog like "news.ycombinator.com want's to know

The browser could generate an unique key pair for every website that request a public key. Or there could be a dialog like "news.ycombinator.com want's to know your identify, which profile to use?" (option to generate a new profile), kinda like password managers work today.' The advantage with reusing "profiles" is that you could use the same profile on many web apps like Facebook and Instagram, then you could allow your Facebook friend to access your Instagram photos. Or your "contact list" could be offline (eg. managed by your browser, and not by web apps) and you manage access rights via your contact list, rather then on each and every app.