Some questions on how to improve Berlekamp‑Rabin algorithm’s implementation

Bonjour,

the https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Rabin_algorithm is 
an algorithm for computing square roots on prime numbers or prime powers.
It's description makes it mostly trivial to implement using Mod() 
operations but I was wondering if it was possible to use more higher 
level functions like factor() or even nfroots() ?

And at the end use polcoeff() ?

Though in reality I admit I don't understand how to perform some steps 
by hand…

Cordialement,