PHP session fixation
Preferably, you would generate a random salt. Add a function to generate random salt, then be sure to call it in your constructor. If a user discovers you salt, that is a major security hole right now. 

In my opinion, it would be best to separate this class into a separate file for easier use in multiple situations. Also, a separate file with useful functions like generating salt could be useful.

Your code is relatively secure, but you need a random salt generator. Otherwise, your code looks good.