Make sure all software updates for your Mac are downloaded & installed.However, it can still be compromised if you're careless. More important than your PC though, is your privacy: you don't want anyone, especially dangerous criminals getting a hold of your location. So to maximize anonymity while browsing the deep web using TOR, you should: As you are on a Mac, it is improbable that your computer will catch viruses. The number of security precautions you need to take depends on what you plan on doing in the deep web. Step Three: Browse Websites on the Deep Web.