We see from the following snippet of hamiltonian knowhow the concept of Sum over Histories
in the world of DES, can we ask: do the 3 Hamiltonian “composition” cycles that compound to make the group underlying the DES SPN network now “sum up the required histories” of the“dependencies of inputs in _active-sboxes_” on the keybits?
ON the one hand, the answer is just obviously yes … since the Hamiltonian components were constructed by looking at the paths through the SPNs, and the way in which keybits interact as inputs.
On the other, one might ask: is there anything about the form or formula for “cycle constituents” of such Hamiltonians generally that induces “maximization” of active sboxes? (Or perhaps maximizes the potential for parallel disruption in a maximum number of species in the general reasoning?)?
Since the thesis of our DES analysis is that one must be using exponential decay to converge onto the lower energy state, what “property” of the SPN – expressed in terms of the constituent cycles or their interplay – is it that foments this action …vs. alternatives such as null-action or exponential runaway?
well obviously, the first thing to look at are the rules for generating a group with a Hamlitonian (i.e. path-enumerating) property.