I was extrapolating a feature based on the inherent qualities of wallets, i.e., keys which can give varying degrees of authority or information about funds to other keys.

Your last question, that is the whole point. Math breakthroughs that can be foreseen are not a threat to current keys and would not threaten new uses of those keys within reason. Quantum computers it makes no sense to speculate about. The strength of keys now would take so many trillions of years to break using an array of supercomputers today. No intelligent guess could be made regarding speeds of future computers using newer technology.

As to what is needed 'to make that happen', for you and me only patience.

I point it out so that people who are less inclined to math will stop falling in these traps so easily. A person must be very simple to buy into the Zerocoin that has been peddled on this thread. What will happen when conners or the academic thugs of governments try to pump something more clever? For that reason I warn people, play along quietly but do not trust a coin as anonymous until the anonymity is derived from the same keys used for transactions now. There is no need for more and someone adds more only because either a) they are unable to solve the problem so they cobble something together or b) they have hidden intentions.

If you want to push the issue start a thread on a more technical board asking for analysis and opinions.
http://s13.zetaboards.com/Crypto/forum/3141/
https://www.physicsforums.com/#mathematics.4
http://crypto.stackexchange.com/

A person with just a moderate amount of effort could use a bitcoin wallet with very high anonymity as long as they were okay with all of the coins being anonymous. The most important aspect of anonymity in cryptocurrency today, of course, is simply the computer. If you are at home you are not anonymous. <period.

The most important use for anonymity is evolving. Some people would like you to think anonymity is for buying drugs or guns for alqaeda. Actually anonymity is liberty in almost every country today. If someone controls your money they control your opinion ultimately. Ask any old person.

To save some time and money for people interested in anonymous currency I will reiterate what has already been pointed out.

To create socalled trustless anonymity no external keys are needed. A conventional wallet can generate 4 keys and from that alone anonymity can be derived that will be a function of time. One wallet will need two protocols and any coins can be switched seemlessly between them. Until you see that do not bet too much.

Of course there are malignant players who want to control currencies. It has always been like that. "We are the good guys. You can trust us to responsibly control your currency, surveil responsibly, only kill bad people blah blah blah".

Until populations are educated sufficiently that bad actors in government cannot survive people must be careful.

Everyone has good intentions. They want to stop drugs, stop terrorism, promote freedom, stop orphan bonobos from starving, save the planet from tyranny, whatever the excuse de jour is.

Until you see an open source trustless anonymity generated from within a conventional wallet using its own keys be wary of the shit being pumped whole chunk into the cryptosphere.