El Gamal encryption involves picking $(p,g,b)$ which is our public key. We compute $b=a^x$ $mod$ $p$. Here, $x$ is the private key which we don't know.
What are some efficient and strong algorithms today used to finding this $x$?
I am currently dealing with numbers such as $b=42-60$ digits long and $p=30-50$. So $b$ is anywhere between 42 and 60 digits.
Does anyone know of any program and some attacks to finding this $x$ using our given information?