For bitcoin to work politically, authority over the currency needs to be distributed over a large group of peers. If power is concentrated at a single point, the state can dominate that point, whoever controls that point can steal other people’s currency and do a variety of bad things.
Bitcoin was designed so that “voting” depended on computing power and network connection. Initially, almost everyone who had a client was a miner, there were a huge number of miners, everyone who used bitcoin had roughly equal influence because they contributed roughly equal computing power to the block chain.
Today, bitcoin is controlled by by a single miner., which was a predictable consequence of bitcoin’s scaling problems.
What we need is a crypto currency which is controlled by the top one hundred or so owners of the currency that are well connected to the net and have adequate computing power, with influence over the currency proportional to the amount of currency that they own, rather than the number of cycles that they burn.
In principle it should be possible to do this using bilinear maps, but the details are a bit tricky, because we have to make sure that manageable number of votes reflects an infinitely divisible currency whose ownership changes continually. So the shares (private and public keys in groups with a bilinear map) have to be reissued frequently, while ownership of the infinitely divisible currency is given value by the fact that if you own a lot of it, you get shares proportional to the amount you own. Since shareholders are people who own a lot of currency, they have an incentive to not misbehave, to continue to reissue shares according to currency ownership and validate transactions according to the rules, since to do otherwise would destroy the value of the currency that they own.
The number of shares remains manageably small, however many people use the currency and however many transactions take place. The shares underlie the value of the currency – and absolutely nothing underlies the value of the shares. Of course we still have other scaling problems, to which I have not figured out a solution except in alarmingly vague outline.