In a normal CAPTCHA scenario, a computer creates a challenge and a correct response to it.  (The challenge is an image of distorted text, for instance, and the response is the characters depicted.)  These are constructed so that hopefully a human can easily determine the response from the challenge, but a computer cannot.  Ordinarily only the originating computer, which already knows the correct response, can determine whether a given response was correct.My question: is it possible to create a CAPTCHA that computers can verify, but not solve?  In other words, is it possible to create a scenario that looks like this:Computer A generates a challenge, sends it to Human B and Computer CComputer C cannot feasibly determine the correct response, other than by brute-force search (which can hopefully be made impractical by the size of the response.)Human B can feasibly determine the correct response.  (Feasibly is not easy to define.  We need the response to be much bigger than normal CAPTCHAs in order to deter simple brute-force searching by computers, so as easy as a normal CAPTCHA is going to be impossible.  But it's not out of the realm of possibility to make a human type in a large response.  It'd just be really annoying. A few hundred printable characters can get to 2048 bits, for instance.  So as a rough definition: it's allowed it to be annoying as hell, but it has to at least be feasible for a person.  Assume the person's physical and mental abilities are roughly average for a literate computer user.)If Human B sends Computer C the correct response, Computer C can feasibly verify that the response is correct, without contacting computer A or having any prior knowledge other than the challenge.Would it be possible, under today's technology and knowledge, to create such a protocol?Furthermore, would it be possible to design the protocol such that even Computer A can't determine the correct response to the challenge it just generated without human input--and Computer C can verify that Computer A could not have known the response without a human providing the solution?  If this all this can be achieved, then the result is analogous to the proof of work seen in bitcoin and other protocols.  Instead of a proof of computational work, we'd have a proof of human work--the combination of the challenge and correct response would constitute proof that a human spent some marginal amount of effort.  This proof would then be verifiable by any computer.  Is such a thing even remotely plausible?Of course, at some point in the future computers will probably overtake humans altogether.  Once that happens, there will not be any problems that are feasible for a human but not a computer, and therefore no CAPTCHAs or CAPTCHA-like protocols will be possible.But what about under currently known human and computer abilities?
Is there a way to create a captcha-like problem that computers can verify, but only humans can solve?
computer vs human;human computing