Today's Internet makes hosts and individual networks inherently insecure because permanent addresses turn destinations into permanent attack targets. This paper describes an Evasive Internet Protocol (EIP), a change to the data plane of the Internet that: 1) prevents senders from forging their identities while preserving the current Internet privacy paradigm; 2) gives recipients full control over who can communicate with them and for how long; 3) achieves the above features without requiring global signaling protocols; and 4) allows coexistence with and graceful introduction into the current Internet. We motivate our approach, present the architectural design, and evaluate it through trace-driven and synthetic simulations as well as prototype testing.