I understand how the Index Calculus algorithm works - I know & understand the steps. I understand how the steps are derived. However, I am not able to figure out why it works.
I can understand why Pohlig-Hellman works - PH reduces the computation of the discrete log in $G$ to the computation of the discrete log in prime order subgroups of $⟨G⟩$. The PH algorithm allows your solve the DLP in the smaller subgroups and then combine the solutions using the Chinese Remainder Theorem to get the solution for the original DLP. I am looking for a similar theoretical explanation for Index Calculus
Why does Index Calculus work for solving a DLP?