Just what is the improvement of EDE over one-pass ?
There is strong evidence to support there being a definite improvement; the set
of permutations produced by EDE is almost certainly larger than the set of
permutations produced by a single pass of DES.
Just how much improvement you get is very hard to quantify; the issue basically
boils down to how large is permutation set produced by stacking multiple passes
of DES. (The possibility of special structure which negates some or all of the
overall size also exists, of course.)
The only number I know of in this area is that the group generated by DES
(essentially the set of all possible permutations you can get by stacking up
DES operations in any arbitrary way) is almost certainly larger than 2^68.
That's a lot bigger than 2^56, but not only is EDE selecting from a subset of
this, it isn't 2^112 either. (Always keep in mind that the permutation group of
order 2^64 contains (2^64)! elements, a REALLY large number.)
Ned