Because you specifically ask about security:

 - For comparing hashes like SHA, you should use [`hash_equals()`](https://secure.php.net/hash_equals).

 - If you are requiring the use of a password, you shouldn't use SHA-512. While it's certainly better than MD5, instead use [bcrypt](https://en.wikipedia.org/wiki/Bcrypt). Bcrypt is [heavily recommended](https://security.stackexchange.com/q/4781) for password storage, especially long-term.

 With bcrypt, instead of using `hash()` and `hash_equals()`, you would use [`password_hash()`](https://secure.php.net/password_hash) and [`password_verify()`](https://secure.php.net/manual/en/function.password-verify.php).

 - Should new directories really have read and execute permissions for the group and other users? Likewise, I would check the permissions of the file itself.

 I would personally have the files as `0600` and directories as `0700` unless other permissions are needed.

 - Checking the file extension is only helpful for preventing naive false uploads. On Linux and most UNIX-like operating systems, a file extension means very little (if anything). It could be any type of file with a JPEG extension, likewise anything could have a JPEG file extension.

I don't know about the rest of the code.