I am taking a class on Cryptology, and I'm having a hard time understanding the potential pitfalls of Diffie-Hellman. Specifically, the professor gave the following problem:
Alice and Bob want to use Diffie-Hellman for key agreement and choose p = 982734982635928741927391824619283719654192837198273923771, however, they do not know how to calculate a relative prime, and hire Evan (Eve in disguise) to generate one for them. Evan gives them g = 584451952932889263219289637911613296416146180021897568955.
Explain what Evan did, and how this makes it easy for him to find the secret key that Alice and Bob agreed to, and find that secret key.
I understand that the value of choosing a g that has a large sub group of possible keys (i.e. you wouldn't want to choose g = 1, because then all keys would be = 1, no matter the other numbers) but I'm not understanding how that would impact this case with such a large g. Could anybody explain how I'd go about this question?