# Diffie–Hellman key exchange, why it's hard to break it?

I'm a bit confused why it's hard to break Diffie–Hellman

Let's take the example

ALICE has G, a, and n

BOB had G, b and n

Eve (the third party) succeded to intercept G, n, $$G^a, G^b$$

ALICE generate the key G^(ab) mod n

BOB generate same key G^ba mod n

What I don't understand is why Eve cant' get a or b by knowing G^a and G^b.?

For me he can just use dichotomy:

Eve will take a random number r_a.