An efficient algorithm for finding the generators of the unit group of $\mathbb{Z}[\zeta_p] $ (ring of cyclotomic integers, where p is a prime)

Question

The group of units of $\mathbb{Z}[\zeta_p]$ has a finite number of generators. I am aware there are algorithms that can find these generators but they don't seem to be that efficient. I was wondering if someone could direct me to resources on more efficient algorithms for finding the generators (By efficient i mean ones that can run relatively fast even when $p$ is large. The ones i have seen become really slow even before $p$ reaches 200). Are there any poly-time algorithms? If not, is the problem of finding the generators an NP-Complete problem?

Thanks in advance

Edit: after reading https://piyush-kurur.github.io/research/publication/Conference/2004-06-08-units.pdf i don't believe a poly-time algorithm exists.