Google Drive does not offer the option to search for other users' public documents (see here).
However, it is possible for users to find these documents via Google Search using a filter. In order to search exclusively for public Google documents, a user would have to search using the following:
To create a tool that would allow users to search for these documents, you might consider simply creating an HTML form that submits to google with the site:docs.google.com/document/d prepended.
Here's a quick demo of that using AngularJS:
Navigate to the 'app' folder and then open index.html in your browser. Enter keywords into the text box and click submit: it will return a list of results that are only Google Docs.