Position Based Cryptography

We consider what constitutes identities in cryptography. Typical examples include your name and your social-security number, or your fingerprint/iris-scan, or your address, or your (non-revoked) publickey coming from some trusted public-key infrastructure. In many situations, however, where you are defines your identity. For example, we know the role of a bank-teller behind a bullet-proof bank window not because she shows us her credentials but by merely knowing her location. In this paper, we initiate the study of cryptographic protocols where the identity (or other credentials and inputs) of a party are derived from its geographic location. We start by considering the central task in this setting, i.e., securely verifying the position of a device. Despite much work in this area, we show that in the Vanilla (or standard) model, the above task (i.e., of secure positioning) is impossible to achieve. In light of the above impossibility result, we then turn to the Bounded Retrieval Model (a variant of the Bounded Storage Model) and formalize and construct information theoretically secure protocols for two fundamental tasks: • Secure Positioning; and • Position Based Key Exchange. We then show that these tasks are in fact universal in this setting – we show how we can use them to realize Secure Multi-Party Computation. Our main contribution in this paper is threefold: to place the problem of secure positioning on a sound theoretical footing; to prove a strong impossibility result that simultaneously shows the insecurity of previous attempts at the problem; and to present positive results by showing that the bounded-retrieval framework is, in fact, one of the “right” frameworks (there may be others) to study the foundations of position-based cryptography. ∗Research supported in part by NSF grants 0716835, 0716389, 0830803. †Research supported in part by a Microsoft Research Graduate Fellowship and the above NSF grants. ‡Department of Computer Science and Department of Mathematics. Research supported in part by an IBM Faculty Award, Xerox Innovation Group Award, NSF grants 0430254, 0716835, 0716389, 0830803 and U.C. MICRO grant.