There's nothing illegal about a landlord discriminating against a potential tenant with an eviction history. You could legally refuse to rent to her for that reason, and that would be discrimination. Most discrimination is perfectly legal.
What you cannot legally do is require a security deposit that is greater than the laws of your state allow (if such a law exists in your state). For example, my state prohibits a landlord from requiring a security deposit that exceeds two months' rent. You need to make sure you understand whether your state imposes such a limit and, if so, that you're not violating that law.
All that said, if it makes you feel better or safer, you're certainly free to have an addendum to your lease that states that the size of the security deposit and length of the lease are because of the tenant's eviction history.