While quantum position verification aims to certify a prover's location using quantum information, existing security definitions only guarantee that part of the successful adversarial party is in the claimed location. This leaves open the possibility that a distributed team of adversaries can jointly simulate a prover in a way that defeats the intended meaning of `being at a location' in position-based cryptography. We introduce stronger notions of position verification that we call quantum localization, which requires that there is a specified, unclonable state at the verified spacetime point-and that this state can be found nowhere else. We show that quantum localization leads naturally to a meaningful notion of trajectory verification, in which quantum information is verifiably tracked through space and time. We construct quantum localization and trajectory verification protocols using quantum anchor states, which generalize coset states from unclonable cryptography. The security of our schemes is proven in the classical oracle (i.e. ideal obfuscation) model, which can be heuristically instantiated in the plain model using post-quantum indistinguishability obfuscation. We also introduce and instantiate the concept of functionality localization, which guarantees that the adversary has the ability to compute a secret function at the verified spacetime point, and this function cannot be computed anywhere else. This raises the intriguing possibility of localizing computational capabilities in space and time. More broadly, we believe our notions of quantum localization and subsequent feasibility results provide stronger foundations for position-based cryptography. At a conceptual level, our results also explore the tight link between two fundamental notions in physics-location and information-thus serving as a natural foundation for cryptographic capabilities tied to physical spacetime.
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
A and
B of a (possibly) unknown quantum state
∣ψ⟩∈HA⊗HB. Their goal is to calculate and share a new state
∣φ⟩=U∣ψ⟩, where
U 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, we show that the same task can be done using a single round of classical communication in which Alice and Bob exchange two classical messages. Actually, we prove that a relaxed version of the task can be done with no communication at all, where the task is to compute instead a state
∣φ′⟩ that coincides with
∣φ⟩=U∣ψ⟩ up to local operations on
A and on
B, which are determined by classical information held by Alice and Bob. The one-round scheme for the original task then follows as a simple corollary. We also show that these results generalize to more players. As a consequence, we show a generic attack that breaks any position-verification scheme. On the positive side, we show that if adversaries do not share any entangled quantum state but can compute arbitrary quantum operations, secure position-verification is achievable. Jointly, these results suggest the interesting question whether secure position-verification is possible in case of a bounded amount of entanglement. Our positive result can be interpreted as resolving this question in the simplest case, where the bound is set to zero. In models where secure position-verification is achievable, it has a number of interesting applications. For example, it enables secure communication over an insecure channel without having any preshared key, with the guarantee that only a party at a specific location can learn the content of the conversation. More generally, we show that in settings where secure position-verification is achievable, other position-based cryptographic schemes are possible as well, such as secure position-based authentication and position-based key agreement.
Recently, the problem of secure position-verification has been extensively analyzed in a formal notion where distant verifiers send encrypted challenge along with the decryption information to the prover. However, currently it is known that all the existing position-verification scheme are insecure and secure positioning is impossible. We propose here a different notion for position-verification where distant verifiers determine the actions of the prover through non-local correlations generated by local measurements at the provers site. The proposed scheme guarantees secure positioning even if the verifiers do not have any pre-shared data with the prover, position is the only credential of the prover. Our proposed scheme is secure in general and evades known quantum attacks based on instantaneous non-local computations in particular. The scheme enables verifiers to identify dishonest provers with very high probability , where n is the number of entangled pairs used.
In this article, we propose quantum position verification (QPV) schemes where all the channels are untrusted except the position of the prover and distant reference stations of verifiers. We review and analyze the existing QPV schemes containing some pre-shared data between the prover and verifiers. Most of these schemes are based on non-cryptographic assumptions, i.e. quantum/classical channels between the verifiers are secure. It seems impractical in an environment fully controlled by adversaries and would lead to security compromise in practical implementations. However, our proposed formula for QPV is more robust, secure and according to the standard assumptions of cryptography. Furthermore, once the position of the prover is verified, our schemes establish secret keys in parallel and can be used for authentication and secret communication between the prover and verifiers.
A large number of quantum location verification protocols have been proposed. All existing protocols in this field are based on symmetric cryptography where verifiers and the prover use the same secret key. The prover obtains secret key from different verifiers, in pieces through public channels, which may result in security compromise. In this paper, we give a formulism to prove information-theoretic position-based quantum cryptography is possible in asymmetric quantum setting. We propose a quantum location verification protocol based on asymmetric quantum cryptographic where two different keys will be used.
In this thesis we explore position-based quantum cryptography zooming in on the task of position verification. In position verification, the idea is to use an individual's geographical location as a cryptographic credential. In practice, such protocols can authenticate that a message originated from a specific location or ensure that messages can only be read at a certain location. In a position-verification protocol, the limitations imposed by the speed of light, as described by special relativity, are used to verify that a party is at their claimed location. It has been shown that any QPV protocol can be broken by attackers that use an amount of entanglement exponential in the input size. However, from a practical point of view, not all is lost. We can still hope for QPV protocols that are secure in practice. This raises the problem of designing protocols that are secure in a practical setting. An important problem that arises is that of signal loss. Signal loss can be detrimental as it allows attackers to only answer on a subset of rounds. We investigate several questions related to the practical implementation of such protocols. We propose a new experimentally feasible protocol, which is fully loss-tolerant against attackers restricted to classical communication. Furthermore, we consider the role of allowing quantum communication with no pre-shared entanglement for attackers and show that this setting is strictly stronger than the classical one, indicating that allowing for quantum communication may break security. Conversely, we then show that any protocol secure against classical communication can be transformed into a protocol secure against quantum communication. Finally, we invert the picture, and consider the task of non-local quantum computation (NLQC), which corresponds to the operations of the attackers in a QPV protocol. We connect NLQC to the wider context of information-theoretic cryptography by relating it to a number of other cryptographic primitives.