Being permutations, this representation should be closed under functional inversion, so ideally, both the "forward" and "inverse" representations should be possible. Note: if it is easy/trivial to invert such a permutation function, such a result might call into question the use of functions of this type in crypto applications. At 09:16 AM 3/25/2016, Dan Asimov wrote:
I'd expect that if there is such a representation, the innermost function would be the one choosing one of p elements, the next one would know from f(x) which element *not* to choose, and would pick one of the p-1 remaining elements, etc.
ÂDan
On Mar 25, 2016, at 9:10 AM, Henryy Baker <hbaker1@pipeline.com> wrote:
With function composition, we can do the following:
f(g(h(...(q(x))...))) can be a representation of one of these p! permutations if
f(x) chooses one of p elements; g(x) chooses one of p-1 elements; h(x) chooses one of p-2 elements, and so forth.