The Keyword Search functionality currently searches all fields in the table for that keyword.
If you want users who are not logged in (or have a certain user role) to not be able to see certain fields, you don't include those fields on the page ... but there doesn't seem to be a corresponding way to limit the users' ability to keyword search those fields.
There are some situations where this is not acceptable (e.g. an HR app where employees can keyword search for "disciplinary" and get a list of all coworkers who have that word in their record).
When setting up the keyword search field on the search page, it would be great to have a configuration option to specify which fields in the table will be searched by the keyword search.
There may be other ways to solve the general issue (how to make certain fields inaccessible to certain users), but this configuration option seems like a relatively simple way to achieve the immediate objective of making those fields not keyword searchable to users of that form.