Eric Michael Cordian, emc@wire.insync.net, writes:
The concerns are generally that we will experience an unexpected "combinatoric explosion" in the higher round problems
Unexpected by you, perhaps, but expected by everyone else. The complexity of the expressions should increase exponentially with the number of rounds. Extrapolating from two and four round results to eight and sixteen is the wrong model. (You can artificially suppress this by introducing new variables for each round, but that doesn't change the underlying complexity of the problem.) Can't you come up with a back-of-the-envelope estimate for the number of terms in your sixteen round expression? Even without fully optimized S-box expressions this information would be useful. If it is greater than the number of atoms on Earth then it would be a strong hint that this approach won't work. If you really want to attract money you need some kind of numbers to show that the approach has a prayer of working. Show the size of the problem you will get, estimate how much improvement you'll get with your improved S-box representations, compare it with the problems tackled by available combinatorial algorithms. You should be able to do this with a few hours of work, at least to show that the basic concept is sound (or unsound).