Not directly but you can easily do this depends on what circumstances. For example you can filter results of a query to a portal to show records that only that particular person can see and so on. just setup your permissions levels in the security of filemaker for that solution. You can also secure what layouts specific users can go to.
So bottom line is FMP has many security features built-in already, and you can pretty easily control the rest. If you would like to give us an example of how you need to use it I will try to help you a little further, parhaps with an example to get you started if you like. =)
Oh and for a field you can always use a conditional. (food for thought)
Fields can be made visible, invisible, or editable to specific Privilege Sets.
Records can be made visible of not to Privilege Sets. You can specify that certain Privilege Sets can only see records where the Record Creator is the current user, for example.
The relevant help section in FileMaker spells this out fairly well:
See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a detailed description of how to set this up.
Or limiting what user can see what records, like letting users ONLY see their profile, etc.
Or a pre-built solution if you want very controlable security you can implement easily.
I own a copy of this myself... http://www.scriptology.com/permissions