Re: some questions about permutation

"laicko" <yichun.zhang@xxxxxxxxx> writes:
question 1: if f and g are both one-way trapdoor permutation with the
same domain and range. Is it definitely to say f*g = g*f ?

Erm, are these homework problems? Try some concrete examples with
small permutations, say on the numbers (1,2,3,4).

question 2: if f is a psedurandom permutation family. Is it possible to
find such k1,k2 and k3, satisfying f_k1(f_k2) = f_k3? or f_k1(f_k2)=
f_k2(f_k1)?

Rather than worrying about pseudorandom permutation families, again
think about permutations in general. For example, think of ALL of the
N! different permutations on (1,2,3,...,N). Now choose some subset of
them; will the subset likely have the property you're asking about?

question 3: We know m^a = m^b mod N will leak some factor information
for phi(N), so for some deliberately chosen m, is it helpful for
factoring problem?

Not clear what you're asking.
.