Purely and simply put, you can fill out all the applications you want and if you don't supply your social security number the likelihood of getting work is very slim.
Most companies provide a secure website for you to register. Just look in the URL bar where it says [
www] and if you see the s after the htpp you are on a secure website.
Make sure you are signing up with legitimate companies. Maritz is definitely a legitimate company. Get the website information off of a list such as the one here in the first post of the first thread of the Mystery Shopping Company Discussion section of the forum. There are some lists that float around the web that deserve researching every single company they mention before signing up and in some cases, even attempting to go to the website.
While in theory a company does not need your social security number until your earnings approach $600 and they need to send you a 1099 for taxes, most companies at this time require a good and valid social security number from the start. (We used to be able to skip it or just put in 000-00-0000, but that really doesn't fly any more. In part, companies use the SS# to make sure that shoppers who have been terminated don't try to sign up again and to make certain that shoppers don't sign up multiple times to defeat rotations.)