In this work, we study position-based cryptography in the quantum setting. The aim is to use the geographical position of a party as its only credential. On the negative side, we show that if adversaries are allowed to share an arbitrarily large entangled quantum state, the task of secure position-verification is impossible. To this end, we prove the following very general result. Assume that Alice and Bob hold respectively subsystems @math and @math of a (possibly) unknown quantum state @math . Their goal is to calculate and share a new state @math , where @math is a fixed unitary operation. The question that we ask is how many rounds of mutual communication are needed. It is easy to achieve such a task using two rounds of classical communication, whereas, in general, it is impossible with no communication at all. Surprisingly, in case Alice and Bob share enough entanglement to start with and we allow an arbitrarily small failure probability,...
Concurrent and independent of our work and the work on quantum tagging described above, the approach of using quantum techniques for secure position-verification was proposed by Malaney @cite_1 @cite_17 . However, the proposed scheme is merely claimed secure, and no rigorous security analysis is provided. As pointed out in @cite_19 , Malaney's schemes can also be broken by a teleportation-based attack. @ have proposed and proved secure a quantum scheme for position-verification @cite_33 . However, their proof implicitly assumed that the adversaries have no pre-shared entanglement; as shown in @cite_19 , their scheme also becomes insecure without this assumption.
@cite_19 @cite_1 @cite_33 @cite_17
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We define the task of quantum tagging, that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is unbounded. We define simple security models for this task and briefly discuss alternatives. We illustrate the pitfalls of naive quantum cryptographic reasoning in this context by describing several protocols which at first sight appear unconditionally secure but which, as we show, can in fact be broken by teleportation-based attacks. We also describe some protocols which cannot be broken by these specific attacks, but do not prove they are unconditionally secure. We review the history of quantum tagging protocols, and show that protocols previously proposed by Malaney and are provably insecure. The ability to unconditionally verify the location of a communication receiver would lead to a wide range of new security paradigms. However, it is known that unconditional location verification in classical communication systems is impossible. In this work we show how unconditional location verification can be achieved with the use of quantum communication channels. Our verification remains unconditional irrespective of the number of receivers, computational capacity, or any other physical resource held by an adversary. Quantum location verification represents an application of quantum entanglement that delivers a feat not possible in the classical-only channel. It gives us the ability to deliver real-time communications viable only at specified geographical coordinates. 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) public-key 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 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-storage framework is, in fact, one of the "right" frameworks (there may be others) to study the foundations of position-based cryptography.