Answer:

Eve could establish a secret with both Alice and Bob. Since Eve knows N and P, she could pick her own secret exponent E and could act as Bob to Alice and as Alice to Bob. Here how Eve would do this:

1. Eve computes L = N^E (mod P).
2. When Alice sends out J = N^A (mod P), Eve intercepts it (J never reaches Bob, and neither Bob nor Alice know this fact). In addition, when Bob sends out K = N^B (mod P), Eve intercepts K.
3. Eve then sends L to Alice AND Bob. Eve at this point has duped Alice into believing that L is from Bob, and she has duped Bob into believing that L is from Alice.
4. Alice proceeds as usual (mistakenly thinking that L is from Bob) and calculates L^A (mod P). Bob also proceeds as usual (mistakenly thinking that L is from Alice) and calculates L^B (mod P).
5. Alice then thinks that her result is her shared secret with Bob, even though it's really a "shared secret" with Eve! [Keeping track of things, Alice and Eve's shared secret number is N^AE (mod P).] Bob thinks the same thing [Bob and Eve have the different shared number of N^BE (mod P)].
6. Now, when Alice sends Bob a message using what she thinks is their secret, Eve is able to decipher the message from Alice, read it, and encipher it again to send to Bob. Bob and Alice are none the wiser, and Eve reads all of their correspondence! Yikes!