Proof isn't always possible

This is an open question. It represents a shortcut to the cryptanalyst between multiple rounds of a cipher algorithm. Represent the cipher as y = f(c) in two dimensions.  For superior ciphers, f(c) is NOT A GROUP. Question: can we devise a y = Ef(c) in three (3) dimensions such that Ef(c) IS A GROUP? Then we apply some creative calculation f(c) and Ef(c) to derive z1 and z2. Then we attempt to use z2 to compute (for example) Ef(z2) == f(f(f(f(f(z1))))), effectively skipping 4 rounds. Is there a way to CALCULATE, or DERIVE these formulae?

The construction of the Schroedinger’s Cat paradox finds application in the discussion of Intellectual Property . If an idea was the Cat, then measurement would be analogous to evaluating the idea for merit, and the quality of life would be analogous to fitness or marketability  of the idea under consideration.