Index calculus algorithm

The Index Calculus algorithm is a classical algorithm used for solving the discrete logarithm problem in certain algebraic structures, such as finite fields and elliptic curves. The discrete logarithm problem can be described as follows: given a prime \( p \), a generator \( g \) of a group \( G \), and an element \( h \in G \), the goal is to find an integer \( x \) such that \( g^x \equiv h \mod p \).