Re: crypto challenge

further to comment:
you'll find the order of the group after some time, depending on the
size of \phi(n).

If the order is known, you can calculate the inverse using the oracle.

it is known that knowledge of \phi(n) is equivalent to the knowledge of
the factors of n.
So your method is the naive method of breaking the system by factoring.
I am trying to see if there is a faster method.