Operation which needs much computing power to be created, but just a little to be solved? Does somebody know a cryptographic/mathematic operation, that needs much computing power to be "encrypted"/"created" but doesn't need much power to be "decrypted"/"solved"?
Lots of problems are hard to solve but easy to check. For example:


finding hash pre-images of particular values such as 0
calculating discrete logs of small numbers modulo a prime
finding the factors of a large composite of a special form like $2^p-1$


I don't think there's an essential difference between solving and checking they're just arbitrary descriptions of the operations.

I imagine an unstated requirement of your question is that it should not be possible to pretend to have solved hard problems by generating random solutions and then saying that you arrived at the solution by solving the hard reverse problem. 
This is a bit like shooting arrows randomly into a wood and then painting targets round the arrows wherever they have stuck in the trees.