Algorithm to generate permutations

In reading the literature on computational group theory there are many
algorithms that assume you have one or more permutations that you can
use as a generator for some computation. The problem with these
algorithms is that they do not scale very well if you have to enumerate
all the mappings of a single permutation. It would be nice to
have an algorithm to generate all the mapping of a particular
permutation.
Well ..., there are a class of algorithms that can generate a
permutation,
these are the algorithms for block ciphers. The question is can you
design a
permutation generator algorithm, aka a block cipher, that can generate
permutations with certain group properties. You might or might not
retain your key and s-boxes, but in this case they are parameters that
can be modified to get the desired computation properties.

Given the symmetric group of 2^k and a chain of subgroups of that are
sylow subgroups of the powers of 2 times all the remaining odd powers,
design an algorithm that can produce one or more generators for each
subgroup.

I would appreciate any comments.

George

.

Relevant Pages

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