A question about the theoretical complexity of Private Compare

[lwxxxxxxx]

hello snwagh.
I am confused about the theoretical complexity of Private Compare in Figure 9. For a vector of length n, its communication overhead is 2kn bytes, which means that for n=1, its communication overhead is 2k bytes. But in Step.6 of Private Compare, which requires calling a series of multiplications, is the communication overhead of these multiplications not taken into account ? although it seems to be taken into account in the number of rounds .
Could you please help me solve this confusion ? Thank you very much !