# Re: some questions about permutation

*From*: Paul Rubin <http://phr.cx@xxxxxxxxxxxxxx>*Date*: 15 May 2006 21:01:00 -0700

"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.

.

**References**:**some questions about permutation***From:*laicko

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