/sci/ - Science & Math

Is it possible to create a circuit which does calculations that cannot be done in software if the dedicated hardware doesn't exist? Or perhaps is many (emphasis on many) orders of magnitude slower if the dedicated hardware doesn't exist?
I assume the answers are no (Turing completeness) and yes (coin mining algorithms for instance), but I'm not entirely sure.

I ask because I want to know whether I can make an algorithm that can 'only' run on a computer equipped with the dedicated hardware, even if people reverse engineer the source code (that is, the output of the hardware exclusive/accelerated operation must be included in the calculation of the result of the algorithm).