If you think of privacy in terms of "is this information truly secret?" Then it certainly doesn't exist now and arguably never existed. There is a saying the Icelandic elder edda: "It is safe to tell a secret to one, risky to tell it to two. To tell it to three is foolhardy: everyone will know." And I dare say a biblical proverb about privacy would be easy to look up.

But there's a different way of thinking about privacy, which is that two people are involved. There is you and there is the person you are tryibg to conceal the information from. The difficulty of detecting terrorist activity lies in the sheer quantity of information available. Sorting out the relevant from the irrelivant is an immensely labour intensive task even with lots of automation.

But in most cases, that is not the privacy you need to worry about: it is the more personal ones of identity theft, cyber bullying or an abusing partner tracking you down at a refuge. And for these, document shreading and encryption are certainly important.