Nobody wants anyone looking at their search history. I get it. I mean, look at mine —oh wait, don't—that's quite embarrassing. Those were for a friend, honestly.
Fortunately for us, it's pretty difficult to dig into someone's search history. Google even forces you to log in again before you can view it in its entirety. Most search engines now encrypt our traffic by default, too —some even using HSTS to make sure our browsers always go secure. This is great news for consumers, and means our privacy is protected (with the noticeable exception of the search provider, who knows everything and owns your life, but that's another story).
This all comes a little unstuck though - sometimes we want to be able to see inside searches. In a web filtered environment it is really useful to be able to do this. Not just in schools where it's important to prevent searches for online games during lessons, but also in the corporate world where, at the very least, it would be prudent to cut out searches for pornographic terms. It's not that difficult to come up with a handful of search terms that give potentially embarrassing image results.
So, how can we prevent users running wild with search engines? The first option is to secure all HTTPS traffic with "decrypt and inspect" type technology —your Smoothwall can do this, but you will need to distribute a certificate to all who want to use your network to browse the web. This certificate tells the browser: "trust this organisation to look at my secure traffic and do the right thing". This will get all the bells and whistles we were used to in the halcyon days of HTTP: SafeSearch, thumbnail blocking, and search term filtering and reporting.
Full decryption isn't as easy when the device in question is user-owned. The alternative option here is to force SafeSearch (Google let us do this without decrypting HTTPS) but it does leave you at their mercy in terms of SafeSearch. This will block anything that's considered porn, but will leave a fair chunk of "adult" content and doesn't intend to cover subjects such as gambling —or indeed online games. You won't be able to report on any of this either, of course.
Some people ask "can we redirect to the HTTP site" - this is a "downgrade attack", and exactly what modern browsers will spot, and prevent us from doing. We also get asked "can we resolve DNS differently, and send secure traffic to a server we have the cert for?" - well, yes, you can, but the browser will spot this too. You won't get a certificate for "google.com", and that's where the browser thinks it is going, so that's where it expects the certificate to be for.
In conclusion: ideally, you MITM or you force Google's SafeSearch & block access to other search engines. For more information read our whitepaper: 'The Risks of Secure Google Search'. It examines the problems associated with mandatory Google HTTPS searches, and suggests methods which can be used to remedy these issues.