You do not run a search engine. You only query it and read the results it outputs. The one who deserves the control of the search engine is who owns it: Surfboard Holdings B.V. (in case of Ixquick and Startpage) and DuckDuckGo, Inc. If they only run free software or software they wrote themselves, then good for them. That does not make much of a difference to you.

And using search engine neither is not SaaS (https://www.gnu.org/philosophy/who-does-that-server-really-serve.html): Services such as search engines collect data from around the web and let you examine it. Looking through their collection of data isn't your own computing in the usual sense—you didn't provide that collection—so using such a service to search the web is not SaaSS.

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