Additive

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 $A = ag \mod p$....