It depends on which password you're asking about. If you mean the standard security password that's required to open the document, you do need to know it to be able to decrypt the contents of the file. The password is not stored in the document, just data that's used to validate the user-supplied password. It is all presented in section 7.6 of ISO 32000-1:2008, the document that describes PDF. If the file has an owner password and no user (open) password, the contents can be decrypted without knowing the owner password. There's software available that can readily do this.
Yes, I am refering to the standard security password required to open the file. So it sounds that the only way to figure out the password would be to write a program that would try to decypher the file using possible passwords. Given that the characters & digits set I typically use for such passwords and the small number of password lengths I typically use, such program wouldn't need to run for too long.
Also, would you also send pointers to a couple of good programs you mentioned at the end (just in case I would need such tool). I assume that by "owner password" you mean the password that locks the ability to modify and afew other actions taken against the content of the file, assuming it is openable.
Yes, the owner password is the one that controls the restrictions. The password recovery tool that is use for legitimate purposes is from Elcomsoft. I haven't tried any others.