Instantaneous nonlocal quantum computation (INQC) evades apparent quantum and relativistic constraints and allows to attack generic quantum position verification (QPV) protocols (aiming at securely certifying the location of a distant prover) at an exponential entanglement cost. We consider adversaries sharing maximally entangled pairs of qudits and find low-dimensional INQC attacks against the simple practical family of QPV protocols based on single photons polarized at an angle $θ$. We find exact attacks against some rational angles, including some sitting outside of the Clifford hierarchy (e.g. $π/6$), and show no $θ$ allows to tolerate errors higher than $\simeq 5\cdot 10^{-3}$ against adversaries holding two ebits per protocol's qubit.
Instantaneous nonlocal quantum computation (INQC) evades apparent quantum and relativistic constraints and allows to attack generic quantum position verification (QPV) protocols (aiming at securely certifying the location of a distant prover) at an exponential entanglement cost. We consider adversaries sharing maximally entangled pairs of qudits and find low-dimensional INQC attacks against the simple practical family of QPV protocols based on single photons polarized at an angle θ. We find exact attacks against some rational angles, including some sitting outside of the Clifford hierarchy (e.g. π/6), and show no θ allows to tolerate errors higher than ≃5⋅10−3 against adversaries holding two ebits per protocol's qubit.
The goal of position-based cryptography is for an honest party to use her spatio-temporal position as her only credential in a cryptographic protocol. In particular, Position-Verification aims at verifying that a certain party, called the prover, holds a given position in spacetime. Such a protocol typically goes as follows: a set of verifiers will coordinate and send some challenge to the prover, and it is expected that only someone sitting in the supposed position of the prover can successfully pass the challenge. Two papers established that information theoretic security is not possible for Position-Based Quantum Cryptography (PBQC) protocols: neither in the classical [1], nor in the quantum [2] regime. More precisely, it is always possible for a coalition of adversaries to convince the verifiers, even if none of the adversary sits in the spatiotemporal region where the prover is supposed to be. At the same time, the best known attack strategies require the adversaries to share very entangled states: the attacks described in [2] are based on Vaidman’s protocol for nonlocal computation [3] and consist in the cheaters teleporting some quantum state back and forth, with a total cost in terms of required EPR pairs that scales double exponentially in n, the number of qubits involved in the PBQC protocol. Later, new generic attacks based on port-based teleportation[4] were proposed and require only exponential entanglement to succeed [5]. Finally, it is also know that a linear amount of entanglement is not su cient to break the PBQC protocol [5], [6]. A major open question in the field is to bridge the gap between lower and upper bounds: does there exist a protocol that requires exponentially many EPR pairs to break, or are all PBQC protocols insecure against a coalition of adversaries that shares polynomially many EPR pairs? While we do not settle this question in the present paper, we make some progress towards it by exhibiting new attack strategies with polynomial complexity against a large family of practical protocols. These attacks rely on teleportation gates and their precise complexity can be quantified with the notion of Cli↵ord hierarchy [7] of a quantum gate. We then introduce a new family of protocols, that generalizes a construction by Lau and Lo [8], which appears to be immune against these polynomialcomplexity attacks. Another main challenge is to determine whether there exist some PBQC protocol resistant to channel imperfections, either losses or noise, between the verifiers and
Based on the instantaneous nonlocal quantum computation (INQC), Buhrman et al. proposed an excellent attack strategy to quantum position verification (QPV) protocols in 2011, and showed that, if the colluding adversaries are allowed to previously share unlimited entangled states, it is impossible to design an unconditionally secure QPV protocol in the previous model. Here, trying to overcome this no-go theorem, we find some assumptions in the INQC attack, which are implicit but essential for the success of this attack, and present three different QPV protocols where these assumptions are not satisfied. We show that for the general adversaries, who execute the attack operations at every common time slot or the time when they detect the arrival of the challenge signals from the verifiers, secure QPV is achievable. This implies practically secure QPV can be obtained even if the adversaries is allowed to share unlimited entanglement previously. Here by "practically" we mean that in a successful attack the adversaries need launch a new round of attack on the coming qubits with extremely high frequency so that none of the possible qubits, which may be sent at random time, will be missed. On the other side, using such Superdense INQC (SINQC) attack, the adversaries can still attack the proposed protocols successfully in theory. The particular attack strategies to our protocols are presented respectively. On this basis, we demonstrate the impossibility of secure QPV with looser assumptions, i.e. the enhanced no-go theorem for QPV.
Abstract We discuss quantum position verification (QPV) protocols in which the verifiers create and send single-qubit states to the prover. QPV protocols using single-qubit states are known to be insecure against adversaries that share a small number of entangled qubits. We introduce QPV protocols that are practically secure: they only require single-qubit states from each of the verifiers, yet their security is broken if the adversaries sharing an impractically large number of entangled qubits employ teleportation-based attacks. These protocols are a modification of known QPV protocols in which we include a classical random oracle without altering the amount of quantum resources needed by the verifiers. We present a cheating strategy that requires a number of entangled qubits shared among the adversaries that grows exponentially with the size of the classical input of the random oracle.
Quantum position verification (QPV) aims to certify the location of an untrusted prover, but faces two major obstacles: fundamentally, entanglement-based attacks and, experimentally, photon loss. A commitment-based modification introduced in Phys. Rev. Lett. 135, 260801 addresses both in sequentially repeated protocols. Its security analysis, however, relies on the sequential structure and does not extend to parallel repetition. We use a different proof approach to establish security of the commitment modification for a parallel BB84-based QPV protocol. Against bounded-entanglement adversaries, the acceptance probability decays exponentially in the minimum number k of successfully committed qubits. The protocol tolerates arbitrary transmission loss and noise rates up to 3.7%, while allowing arbitrarily slow quantum communication. This yields a fully loss-tolerant, single-execution QPV protocol secure against bounded-entanglement attacks, removing transmission loss as a fundamental limitation on verification distance. We also revisit sequential repetition, correcting the treatment of conditioning on commitment and replacing the earlier conditional guarantee with an unconditional security bound, without the finite-size correction to the correctness gap. The resulting bound provides improved quantitative security parameters for experimental implementations.
Position verification, introduced by Chandran et al. (SIAM J. Computing 2014), allows verifiers to test a prover's claimed position by an interactive protocol. Classical position verification is impossible. Even for Quantum Position Verification (QPV), there always exists an LOCC (Local Operations and Classical Communication) attack if the adversary can hold an exponentially large amount of preshared entanglement.
Somewhat surprisingly, we show that we can circumvent this barrier in the idealized continuous-time model, where time is represented by a real-valued parameter and challenge messages can be sent at a time sampled uniformly from a real interval. In this model, we give a BB84-based protocol that remains secure against any finite coalition of LOCC adversaries with arbitrary finite (possibly exponential) quantum storage and entanglement.
Our construction can also be instantiated in the discrete-time model. Even though the previous impossibility results apply, we are able to obtain an information-theoretic QPV protocol in which the honest parties' total resources (communication and storage) can be significantly smaller than the adversarial resource bound. In fact, we can achieve any desired polynomial gap between honest parties and adversarial resources. To our knowledge, all previous protocols in the literature required resources of the honest parties to be at least as large as the adversarial entanglement.
Interestingly, the resource gap between the honest and adversarial party resources in our protocol depends on how precisely time can be measured. As the precision of the best-known clock improves with further research, the resource gap in our protocol keeps increasing. In particular, the adversarial resource bound keeps increasing while the honest parties' resources remain largely the same. We call this the "I sleep, you work" paradigm.
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.