There is an attack on PDF encryption described at https://www.researchgate.net/profile/Juergen_Fuss/publication/258119337_Cuteforce_Analyzer_A_Distributed_Bruteforce_Attack_on_PDF_Encryption_with_GPUs_and_FPGAs/links/004635270d13918b57000000.pdf
Conference Paper Cuteforce analyzer: A distributed bruteforce attack on PDF e...
when entering a password to open a secured, encrypted, PDF file, let us say using Acrobat, it needs to compare and validate the "hash" of that password with something, "key", stored in the file, isn't that the way it works?