What efficient algorithms are there for solving the discrete log problem where $p$ has $> 100$ digits? I.e. large primes.
$$a^x=b \mod p$$
Where $a$ is a positive integer, and $x$ and $b$ are integers.
Update: I am looking for examples to this as answers - the Wikipedia page of the discrete log problem I am familiar with.
Eg examples of solutions to this using:
1) Extended Euclidean algorithm
2) Index calculus algorithm
3) Function field sieve
4) Pollards Rho
with code that shows efficient and secure implementations of them.