The algorithm is very simple:
1. Choose a big random value x from some very broad range
(say, {1,2,..,N^2}).
2. Pick a random element g (mod N).
3. Compute y = g^x (mod N).
4. Ask for the discrete log of y to the base g, and get back some
answer x' such that y = g^x' (mod N).
5. Compute x-x'. Note that x-x' is a multiple of phi(N), and
it is highly likely that x-x' is non-zero. It is well-known
that given a non-zero multiple of phi(N), you can factor N in
polynomial time.
Not exactly. Consider N = 3*7 = 21, phi(N) = 12, g = 4, x = 2, x' = 5.
You'll only get a multiple of phi(N) if g was a generator of the
multiplicative group Z_N^*.
Peter
--
[Name] Peter Kosinar [Quote] 2B | ~2B = exp(i*PI) [ICQ] 134813278
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