Using/modifying WordPress database from my website

I’m currently hosting a website with wordpress installed in one of the subfolders. My website already contains an authentication system and I didn’t want the users to go through the hassle of having a different one for the wordpress part of the site, I decided to join these two together.

The problem begins with the authentication system itself. I decided to get rid of mine and use that of WordPress. I tried including the wordpress files (both separately and in conjuction) by including them in my php code [ include “wp-config.php”, pluggables, etc.] but somehow this messes up my access to the sql database.

Since the encrypting of the password uses salt and some other rather different stuff, I need to call the wp_hash_password ( ) function (i think) to add the given hash as the password in the database, but I don’t know how it keeps giving me a different hash everytime I run it and as i’m saying it does encrypt the password but it doesn’t let me add it to the database by some unknown reason, and if the password keeps changing I have no clue which function then I must use to check whether it is the correct one. I think I need to include only the specific function that will allow me to encrypt the password and compare the encrypted password with that of the DB without having a random key to encrypt it. The other thing i could do is to disable this sort of authentication and use md5 only (which i’m not sure how to do) but this would somehow make me feel as if this thing beat me so i’m not considering this option,

Any thoughts, ideas or anything that can help me?! thanks in advance