how do passwords work?

newbie here. so consider this paradox: let's say you have a pass protected rar file. now the password should be stored somewhere in the file to compare against the inputted password. so if it's there how come you cant just extract it?

It's difficult to tell whether you're just misinformed or just trying to stir up trouble. In any case, joke's on you: AdvanceCOMP uses the Deflate implementation from 7-Zip.
that doesn't change the fact that deflate usually beats your precious lzma. i don't give a shit about your country and its penile deficiencies.

In any case there's no way any implementation of Deflate is ever going to beat LZMA, not even in specially crafted data. I could see how it could beat the block sorting compressors in some cases though.
out of about 50 files (mostly c code and elf binaries) that i've tried it on, advancecomp's implementation of deflate beats lzma on all of them except one.