Is there any way at all to get Google keywords entered? For example, if I forced Google to index my site with only HTTPS, would I then get the keywords entered by the visitor when they arrive at my site?
Google Webmasters gives you this information. It helps to understand your search traffic and learn how users are finding your site.
After Google Secure Search, referral data has beome more opaque. You cannot get keywords as before, but you can get the following information which might be relevant to you
The 'ved' parameter in the Google referral string held some magic in determining the vertical that result appeared in. Simply, the Google referral string is the “href” value assigned to each URL in a set of search results.
The ‘cd’ parameter tells us the position of the search result in the set.
The ‘ved’ parameter is divided into three parts and tells us which Universal vertical the result is part of, the position within that vertical (relative position), and the position within the search result (absolute position). I will focus on just the Universal aspect for this post and will follow up with relative vs. absolute position in a follow-up.
Example: ved = OCDIQFjAA
OCDI = ?
Other search vertical values: