It's implied in the entire paper. It's the entire reason Bitcoin even exists. Otherwise, why not just use a credit card or a bank?
What the whitepaper did
not anticipate is
chain analysis which makes Bitcoin actually very very
unprivate 
. That's why follow-on products like mixers and Monera came about.
Any transactions are in public not private but all identities who use this address or who made any transaction are private.
So do you think if you send BTC to me or other forum members here did they know your identity or mine? Did you find it on the blockchain?
What makes you think about Chain analysis do to you? What they can only do is to track a transaction but they don't know who owns it and I don't think ChainAnalysis will track you unless you did money laundering.