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arXiv:1403.5925 · Laser Physics

Position-based quantum cryptography over untrusted networks

Muhammad Nadeem

Published Jul 15, 2014• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1054-660x/24/8/085202

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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.
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.
Abstract Quantum position verification (QPV) enables multiple verifiers to certify a prover’s location using quantum communication and physical assumptions. With experimental demonstrations of QPV becoming increasingly feasible, enhancing the practicality and security of QPV protocols is more important than ever. In this work, we make three key contributions toward this goal. First, we introduce a robust QPV protocol in which the verifier’s state preparation is independent of channel loss, improving reliability in real-world conditions. Second, we refine existing security analysis techniques to bolster protocol resilience against experimental imperfections. Third, we identify and address some implicit assumptions present in existing security analyses, providing a framework to eliminate such assumptions. Additionally, as an example of QPV application beyond location verification, we illustrate how QPV can be leveraged for authenticating classical communication in quantum key distribution.
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.
Signal loss threatens the security of quantum cryptography, especially in quantum position verification (QPV) protocols, where even small losses can compromise security. This Letter modifies traditional QPV to make high transmission loss between verifiers and the prover irrelevant for a class of protocols, including a practically interesting one based on BB84 states (QPV_{BB84}^{f}). Using photon presence detection and a small time delay, as well as a commitment before proceeding, the protocol's relevant loss rate is reduced to only that of the prover's lab, and the modified protocol has essentially the same security guarantees as the original one. The adapted protocol c-QPV_{BB84}^{f} thus offers strong security guarantees and feasibility over longer distances. We also discuss the practical implementation of the protocol and parameter estimates.
Secure position verification certifies that a remote prover occupies a claimed location, a task that is provably impossible with classical resources alone against colluding adversaries. Most existing quantum position verification schemes require transmitting quantum states between verifiers and provers, and the resulting photon loss makes long-distance verification impractical. Classical verifier position verification (CVPV) schemes with classical verifier-prover communication exist, but rely on complex quantum processes that generate certifiable randomness, placing them outside the reach of near-term hardware. Here we introduce a general compiler that maps any complete-support non-local game with the required quantum advantage into a multi-prover CVPV protocol. This addresses both limitations, with entirely classical verifier-prover communication and all quantum resources confined to shared entanglement and local measurements on the prover devices. Instantiating with the CHSH game enables near-term implementation on existing experimental platforms. We prove finite-size security in the quantum random oracle model for both simultaneous verification of multiple provers and verification of a single prover with multiple prover devices. Notably, security in the multi-prover setting is governed not by the certified randomness of the joint provers' outputs, but by certified blind local randomness that depends critically on the spatial arrangement of provers and verifiers.
This thesis deals with position-based quantum cryptography (PBQC), a type of quantum cryptography. More concretely, we focus on the design and study of quantum position verification (QPV) protocols, which act as a building block for PBQC. We prioritise the development of QPV protocols that are loss-tolerant, error-robust, and feasible with current or near-future technology, concentrating on photon-based protocols and linear-optical equipment. We also theoretically study different attack settings on QPV in the context of state discrimination, dealing with the interplay between non-locality and interaction. We introduce a new QPV protocol based on the SWAP test and Hong-Ou-Mandel interference and study it in detail regarding attacks and practical feasibility. We further provide a solution to a major practical issue of QPV -- signal loss. A minor modification of the standard structure of QPV, namely introducing a small time delay and a commitment to play from the honest prover, allows us to provably make the transmission loss between the verifiers and the honest party irrelevant for security for a class of QPV protocols. Moreover, we generalise and study QPV protocols in the continuous-variable setting. Exploring theoretical aspects of QPV attacks, we focus on the difference between quantum and classical communication. We show new bounds on existing protocols, construct protocols that can be attacked with quantum communication but not locally, show a separation between quantum and classical communication attacks on QPV, and derive a necessary condition on the attack error based on the structure of the QPV input ensemble.