Is there a practical method, and if so what is the method, to reveal that I have the following type of answer but conceal the answer itself? The answer is, let's say, the solution to a Project Euler problem.
That is all. However, I'm new here. I'll try to explain why I hope this question will be considered appropriate. The explanation is a bit lengthy, maybe too defensive!
The question concerns implementing a specific information security system. To make that clear, I'll pose a birthday problem and the information to conceal will be the answer to that problem. Project Euler doesn't have any birthday problems, but it's not really so different from typical Project Euler problems. The Project Euler organizers believe that preventing widespread publication of their answers is vital to the goal of their project. Many Project Euler participants, including me, believe that it's valuable to convince people that we have solved the problems that we claim we have. (OK, I suppose we can also refer people to the Project Euler leaderboard, but how does anyone know that that is me?)
The specific problem is, what's the least number of people we must plan to select in order to have at least 95% confidence that five of our selected people will have their birthdate (day of the year) in common? Let the problem presuppose the usual sorts of silly assumptions: that birthdates are uniformly distributed throughout the year, no one is ever born on February 29, the world's population is effectively infinite, and we can do perfect random sampling from the world's population. The answer is just some number, possibly a big one.
Now, once I compute the number, can I publish information that proves that I have it without revealing its identity? I realize that there's no asymmetric computation involved. It's OK that others who know my birthday problem can solve it just as I did. It's not OK if others can get the answer from my information without even knowing my birthday problem. Crucially, I'm not sure what to say about people who do know my birthday problem but want to cheat by deriving the answer from my information instead of solving the birthday problem for themselves.