An approximate quantity of multiplications in $\mathbb{F}_p$ amounting the same bit complexity as one inversion in $\mathbb{F}_p$ Consider a prime finite field $\mathbb{F}_p$ of quite large characteristics $p$, for example $\log_2(p) \approx 256$ bits. I would like to know an approximate quantity of multiplications in $\mathbb{F}_p$ amounting the same bit complexity as one inversion in $\mathbb{F}_p$. Of course, this depends on many factors, hence I propose to listen your ideas rather than exact results. May be, is there an article or book, which discusses this topic?
The standard algorithm for inverting an element is using the extended Euclidean algorithm. You can read all about this connection on Wikipedia.