You only need 30 bits of identifying information to track a billion users.
You need 30 unique bits of information.
Given that there are only a handful of common screen resolutions, for example, they are unlikely to represent more than a few bits in most cases, and if you provided current size of the viewable area in the browser instead (a more useful measurement anyway) then in many cases this would change over time. If you further provide this information only on explicit request, and potentially lock it down to only the host site rather than third party content, then it is of almost no use to anyone with unwelcome intentions.
You need 30 unique bits of information.
Given that there are only a handful of common screen resolutions, for example, they are unlikely to represent more than a few bits in most cases, and if you provided current size of the viewable area in the browser instead (a more useful measurement anyway) then in many cases this would change over time. If you further provide this information only on explicit request, and potentially lock it down to only the host site rather than third party content, then it is of almost no use to anyone with unwelcome intentions.