Diffie-Hellman - Group Theory

This video from NUS Greyhats should help you with this challenge. Basically, in the additive group of $\mathcal F_p$, the discrete logarithms are simply the inverses. Denote $a, b$ as the secret keys of Alice and Bob. The public key of Alice and Bob are given by $A = ag \mod p$ and $B = bg \mod p$ (it’s normally $g^a$, but we are working with addition here, hence). Hence, the secret key $a$ can be recovered by multiplying the multiplicative inverse of $g$ on both sides of $A = ag \mod p$....

The idea may stem from this question on Crypto StackExchange. We use the same idea as the “nuke” solution in Static Client earlier. We will use some groups where the order is smooth, and thus we can efficiently use Pohlig-Hellman. We thus need to pick some weak primes that passes some checks on the server side. Some of the checks are the following: Using number in the form of $p^k$: this may not work (the solution in Static Client won’t work here) as there is some primality check on the server side....