Re: some questions about permutation


David Wagner wrote:
laicko wrote:
I know that's true for RSA with any instances.

Two independently chosen RSA trapdoor permutations won't commute.

I have said in former statement that two permutations have the same
range and domain. Or I'm wrong with the concept ---two indepentdently
choosen RSA permutations could have the same range and domain?

If you have some magical way of
finding a,b such that a!=b and m^a = m^b mod N, for a random m, [..]
in this case a-b is likely to be a multiple of phi(N),
I don't think so. if a!=b and m^a= m^b mod N, the a =b mod i, where i
is a factor of lambda(N).

(1) If m is randomly chosen, then with non-negligible probability,
i = \lambda(N).

(2) Even if i is just a factor of \lambda(N), it usually can be used
to learn a non-trivial factor of N.

I don't want choose m randomly, and I want to choose a m right in a
subgroup with the order unknown.

Well, in that case, I think you need to specify the exact algorithm you
will use for choosing N and for choosing m, a, and b before we can give
you any helpful answers. You need to define the problem better before
we can try to solve it for you.

I just find it's a interesting problem when I do a trap-door
permutation chain. No further discussion upon this conjecture. My only
purpose is want to know ---is it valuable to plow?

.

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