Customize communities/groups a search widget can search

We want to create a group that is walled garden of sorts. We want to direct people to this group, and within this group you can only find and access content within that group. We do not want search to query the site as a whole. To achieve this I would like the search widget that I can add to a page to offer the following customization:

• Restrict search to these communitiies
• Restrict search to these groups