Security of practical private randomness generation
Stefano Pironio, Serge Massar
备注：
18 pages. v3: important changes: the present version focuses on security against classical side-information and a discussion about the significance of these results has been added. v4: minor changes. v5: small typos corrected
Measurements on entangled quantum systems necessarily yield outcomes that are intrinsically unpredictable if they violate a Bell inequality. This property can be used to generate certified randomness in a device-independent way, i.e., without making detailed assumptions about the internal working of the quantum devices used to generate the random numbers. Furthermore these numbers are also private, i.e., they appear random not only to the user, but also to any adversary that might possess a perfect description of the devices. Since this process requires a small initial random seed, one usually speaks of device-independent randomness expansion.
The purpose of this paper is twofold. First, we point out that in most real, practical situations, where the concept of device-independence is used as a protection against unintentional flaws or failures of the quantum apparatuses, it is sufficient to show that the generated string is random with respect to an adversary that holds only classical-side information, i.e., proving randomness against quantum-side information is not necessary. Furthermore, the initial random seed does not need to be private with respect to the adversary, provided that it is generated in a way that is independent from the measured systems. The devices, though, will generate cryptographically-secure randomness that cannot be predicted by the adversary and thus one can, given access to free public randomness, talk about private randomness generation.
The theoretical tools to quantify the generated randomness according to these criteria were already introduced in [S. Pironio et al, Nature 464, 1021 (2010)], but the final results were improperly formulated. The second aim of this paper is to correct this inaccurate formulation and therefore lay out a precise theoretical framework for practical device-independent randomness expansion.
Cryptographic protocols are often based on the two main resources: private randomness and private key. In this paper, we develop a relationship between these two resources. First, we show that any state containing perfect, directly accessible, private key (a private state) is a particular case of the state containing perfect, directly accessible, private randomness (an independent state). We then demonstrate a fundamental limitation on the possibility of transferring the privacy of random bits in quantum networks with an intermediate repeater station. More precisely, we provide an upper bound …
We develop the resource theory of private randomness extraction in the distributed and device-dependent scenario. We begin by introducing the notion of independent random bits, which are bipartite states containing ideal private randomness for each party, and motivate the natural set of free operations. As a conceptual tool, we introduce Virtual Quantum State Merging, which is essentially the flip side of Quantum State Merging, without communication. We focus on the bipartite case and find the rate regions achievable in different settings. Surprisingly, it turns out that local noise can boost …
We investigate whether the heart rate can be treated as a semi-random source with the aim of amplification by quantum devices. We use a semi-random source model called $ε$-Santha-Vazirani source, which can be amplified via quantum protocols to obtain fully private random sequence. We analyze time intervals between consecutive heartbeats obtained from Holter electrocardiogram (ECG) recordings of people of different sex and age. We propose several transformations of the original time series into binary sequences. We have performed different statistical randomness tests and estimated quality para…
Device and semi-device independent quantum randomness generators (DI- and SDI-QRNGs) are crucial for applications requiring private randomness. However, they are vulnerable to detection inefficiency attacks and this limits severely their usage for practical purposes. Here, we present a method for protecting SDI-QRNGs in prepare-and-measure scenarios against detection inefficiency attacks. The key idea is the introduction of a blocking device that adds failures in the communication between the preparation and measurement devices. We prove that, for any detection efficiency, there is a blocking …
We quantify the consequences of a private key leakage and private randomness generated during quantum key distribution. We provide simple lower bounds on the one-way distillable key after the leakage has been detected. We also show that the distributed private randomness does not drop by more than twice the number of qubits of the traced-out system. We further focus on irreducible private states, showing that their two-way distillable key is non-lockable. We then strengthen this result by referring to the idea of recovery maps. We further consider the action of special case of side-channels on…
The ability to produce random numbers that are unknown to any outside party is crucial for many applications. Device-independent randomness generation does not require trusted devices and therefore provides strong guarantees of the security of the output, but it comes at the price of requiring the violation of a Bell inequality for implementation. A further challenge is to make the bounds in the security proofs tight enough to allow randomness expansion with contemporary technology. Although randomness has been generated in recent experiments, the amount of randomness consumed in doing so has …
Measurement Device Independent Quantum Private Query (MDI QPQ) with qutrits is presented. We compare the database security and client's privacy in MDI QPQ for qubits with qutrits. For some instances, we observe that qutrit will provide better security for database than qubit. However, when it comes to the question of client's privacy we have to take additional measures in case of qutrit. Hence we conclude that though in case of Quantum Key Distribution (QKD) higher dimension provides better security but in case of QPQ this is not obvious.
Infinite Randomness Expansion and Amplification with a Constant Number of Devices
我们提出了一个设备无关的随机性扩展协议，只涉及一个常数数量的非信令量子设备，实现\emph{infinite expansion}：从统一的私有随机性的$m$位开始，该协议可以产生无限数量的认证随机性，即$\exp(-Ω(m^{1/3}))$ -接近均匀和安全的量子对手。依赖于输入大小的唯一参数是协议的可靠性和输出的安全性（在$m$中两者都是逆指数）。这解决了随机性扩展和设备独立性领域长期存在的问题。我们的协议的分析涉及克服\emph{adaptive}设备无关协议的研究中的基本挑战。我们的主要技术贡献是设计和分析的设备无关的协议是\emph{Input Secure}，也就是说，他们的输出是保证对量子窃听者，\emph{even if the input randomness was generated by that same eavesdropper}是安全的！输入安全性的概念可能对其他领域（例如与设备无关的量子密钥分发）具有独立的兴趣。
We give an operational meaning to the min-entropy of a quantum state as a resource measure for various interconnected tasks. In particular, we show that the min-entropy without smoothing measures the amount of quantum information that can be hidden or encoded perfectly in the one-shot setting when the quantum state is used as a randomness/correlation source. First, we show that the min-entropy of entanglement of a pure bipartite state is the maximum number of qubits privately transferable when the state is used as quantum one-time pad. Then, through the equivalence of quantum secret sharing(QS…
A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security. A large amount of work to date has focussed on a particular protocol based on spot-checking devices using the CHSH inequality. Here we show how to derive randomness expansion rates for a wide range of protocols, with security against a quantum adversary. Our technique uses semidefinite programming and a recent improvement of the entropy accumulation theorem. To support the work and facilitate its use, we provide cod…
The amplified spontaneous emission (ASE) noise has been extensively studied and employed to build quantum random number generators (QRNGs). While the previous relative works mainly focus on the realization and verification of the QRNG system, the comprehensive physical model and randomness quantification for the general detection of the ASE noise are still incomplete, which is essential for the quantitative security analysis. In this paper, a systematical physical model for the emission, detection and acquisition of the ASE noise with added electronic noise is developed and verified, based on …
The first device-independent quantum private query protocol (MRT17) which is proposed by Maitra \emph{et al.} [Phys. Rev. A 95, 042344 (2017)] to enhance the security through the certification of the states and measurements. However, the MRT17 protocol works under an assumption of perfect detectors, which increases difficulty in the implementations. Therefore, it is crucial to investigate what would affect the security of this protocol if the detectors were imperfect. Meanwhile, Maitra \emph{et al.} also pointed out that this problem remains open. In this paper, we analyze the security of MRT1…
Semi-device independent (Semi-DI) quantum random number generators (QRNG) gained attention for security applications, offering an excellent trade-off between security and generation rate. This paper presents a proof-of-principle time-bin encoding semi-DI QRNG experiments based on a prepare-and-measure scheme. The protocol requires two simple assumptions and a measurable condition: an upper-bound on the prepared pulses' energy. We lower-bound the conditional min-entropy from the energy-bound and the input-output correlation, determining the amount of genuine randomness that can be certified. Mo…
The extraction of randomness from weakly random seeds is a topic of central importance in cryptography. Weak sources of randomness can be considered to be either private or public, where public sources such as the NIST randomness beacon broadcast the random bits once they are generated. The problem of device-independent randomness extraction from weak public sources against no-signalling adversaries has remained open. In this paper, we show protocols for device-independent and one-sided device-independent amplification of randomness from weak public Santha Vazirani (SV) sources that use a fini…
We address the question of existence of private quantum channel for qubits encoded in polarization degrees of freedom of a photon, that remains secure even if multi-photon (instead of single-photon) pulse is emitted. We show that random unitary channel distributed according to SU(2) Haar measure has this property. Further we analyze the qubit unitary k-designs. We show they ensure security if the photons' parity of the source is guaranteed. Otherwise, the qubit unitary k-designs do not guarantee perfect security.
Applications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of $512$ bits with an average experiment time of less than $…
Device-Independent (DI) security is the best form of quantum cryptography, providing information-theoretic security based on the very laws of nature. In its highest form, security is guaranteed against adversaries limited only by the no-superluminal signalling rule of relativity. The task of randomness amplification, to generate secure fully uniform bits starting from weakly random seeds, is of both cryptographic and foundational interest, being important for the generation of cryptographically secure random numbers as well as bringing deep connections to the existence of free-will. DI no-sign…
The field of device-independent quantum cryptography has seen enormous success in the past several years, including security proofs for key distribution and random number generation that account for arbitrary imperfections in the devices used. Full security proofs in the field so far are long and technically deep. In this paper we show that the concept of the mirror adversary can be used to simplify device-independent proofs. We give a short proof that any bipartite Bell violation can be used to generate private random numbers. The proof is based on elementary techniques and is self-contained.
Certified Randomness Generation against Quantum Adversaries via Energy Constraints
Weizmann Institute of Science（魏茨曼科学研究所）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；LMU Munich（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
We present a scheme for quantum randomness certification based on quantum steering. The protocol is one-sided device independent, providing high security, but requires only states and measurements that are simple to realise on quantum optics platforms - entangled squeezed vacuum states and homodyne detection. This ease of implementation is demonstrated by certifying randomness in existing experimental data and implies that giga-hertz random bit rates should be attainable with current technology. Furthermore, the steering-based setting represents the closest to full device independence that can…
Unconditional Certified Randomness without Structure
University of Washington（华盛顿大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；NTT Research（NTT研究所）；Columbia University（哥伦比亚大学）；UC Berkeley（加州大学伯克利分校）
Pervasive Vulnerability Analysis and Defense for QKD-based Quantum Private Query
College of Computer Science, Chongqing University（重庆大学计算机学院）；Science and Technology on Communication Security Laboratory, Institute of Southwestern Communication（西南通信研究所通信安全重点实验室）；State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications（北京邮电大学网络与交换技术国家重点实验室）
Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate $5.47\times10^8$ quantum-proof random bits while consuming $4.39\times10^8$ bits of entropy, expanding our store of randomness by …
