Thinking about this question on testing string rotation, I wondered: Is there was such thing as a circular/cyclic hash function? E.g.

h(abcdef) = h(bcdefa) = h(cdefab) etc

Uses for this include scalable algorithms which can check n strings against each other to see where some are rotations of others.

I suppose the essence of the hash is to extract information which is order-specific but not position-specific. Maybe something that finds a deterministic 'first position', rotates to it and hashes the result?

It all seems plausible, but slightly beyond my grasp at the moment; it must be out there already...