The DOI matches its Crossref record; 49 of the 49 references it cites were found in a registry or an index.
Security of practical private randomness generation
Open accessAbstract
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 to sample the behavior of the quantum devices and to extract uniform randomness from the raw outputs of the devices, 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, however, 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 (London) 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 generation.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“On the basis of the Clauser -Horne -Shimony -Holt (CHSH) inequality, 56 Fehr et al. 57 and Pironio et al. 58 proposed self-testing randomness expansion protocols against classical adversaries.”
From Quantum random number generation (2016) · cites this paper as [58]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2001) · Wiley eBooks · doi:10.1002/0471200611 · Cited by 37,139
Quantum cryptography based on Bell’s theorem
Ekert, A. K. (1991) · Physical Review Letters · doi:10.1103/physrevlett.67.661 · Cited by 10,777
Elements of Information Theory
Jacobs, K. (1992) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-8645-1_7 · Cited by 2,957
Probability and Random Processes.
Grimmett, G. R., & Stirzaker, D. R. (2001) · doi:10.1093/oso/9780198572237.001.0001 · Cited by 1,850
Device-independent security of quantum cryptography against collective attacks
Acín, A., Brunner, N., Gisin, N., Massar, S., Pironio, S., & Scarani, V. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.230501 · Cited by 1,537 · cited 4×
“Consider for instance that the reported attacks [29, 30, 31] on commercial QKD systems did not exploit any intentional, maliciouss flaws in the devices.”
BackgroundInfluentialSelf-citationRandom numbers certified by Bell’s theorem
Pironio, S., Acín, A., Massar, S., de la Giroday, A. B., Matsukevich, D. N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T. A., et al. (2010) · Nature · doi:10.1038/nature09008 · Cited by 1,420 · cited 9×
“For instance, in the experiment reported in [14] no particular measures have been taken to screen-off one device from the other.”
BackgroundMethodInfluentialSelf-citationSpeakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy
Bell, J. S., & Aspect, A. (2004) · doi:10.1017/cbo9780511815676 · Cited by 1,261
Hacking commercial quantum cryptography systems by tailored bright illumination
Lydersen, L., Wiechers, C., Wittmann, C., Elser, D., Skaar, J., & Makarov, V. (2010) · Nature Photonics · doi:10.1038/nphoton.2010.214 · Cited by 1,005
No Signaling and Quantum Key Distribution
Barrett, J., Hardy, L., & Kent, A. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.010503 · Cited by 916 · cited 3×
“o testing for high value uses.” Device-independent randomness generation aims to address these problems by exploiting the intrinsic unpredictability associated with the violation of Bell inequalities [9, 10, 11]. More precisely, consider a quantum system composed of two separated parts A and B which upon receiving res…”
BackgroundMethodInfluentialA convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
Navascués, M., Pironio, S., & Acín, A. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/7/073013 · Cited by 782
Self-citationFrom Bell’s Theorem to Secure Quantum Key Distribution
Acín, A., Gisin, N., & Masanes, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.120405 · Cited by 709 · cited 1×
“…(DI) is not restricted to randomness generation but includes adversarial applications such as quantum key distribution (QKD) [15, 16, 11, 17, 18] and coin tossing [19], and non-adversarial ones such as state estimation [20], entanglement witnesses [21], and self-testing of quantum…”
BackgroundThe Operational Meaning of Min- and Max-Entropy
König, R., Renner, R., & Schaffner, C. (2009) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2025545 · Cited by 645 · cited 2×
“tropy Hmin(R|E)ρ = max σE Hmin(R|E)ρ|σ , (3) where the maximisation is over normalised states σE and Hmin(R|E)ρ|σ = −log2 min{λ ∈ R: ρRE λIR ⊗σE}. (4) For a cq-state of the form (1), it is shown in [13] that Hmin(R|E)ρ = −log2 pguess(R|E), (5) 2 where pguess(R|E) = max ME X r P(r)tr[ρr EM r E] , (6) is the probability…”
BackgroundMethodTight finite-key analysis for quantum cryptography
Tomamichel, M., Lim, C. C. W., Gisin, N., & Renner, R. (2012) · Nature Communications · doi:10.1038/ncomms1631 · Cited by 643 · cited 1×
“Following the definition of security in the context of quantum key distribution outlined in [43, 44], we say that a protocol such as the one just presented is secure if, for any device behaviour and any m , the output R is uniformly random and independent from F .”
BackgroundBounding the Set of Quantum Correlations
Navascués, M., Pironio, S., & Acín, A. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.010401 · Cited by 576
Self-citationZhao, Y., Fung, C.-H. F., Qi, B., Chen, C., & Lo, H.-K. (2008) · Physical Review A · doi:10.1103/physreva.78.042333 · Cited by 511
Quantum And Relativistic Protocols For Secure Multi-Party ComputationPreprint
Colbeck, R. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0911.3814 · Cited by 493 · cited 2×
“evices used nor aboutthe dimensionality of the Hilbert space of the quantumsystems. Applications of the device independent concept include quantum key-distribution [2, 3, 4, 5], random ness expansion [6, 7], state estimation [8] and entanglement witnesses[9], and the self-testing of quantum computers [10]. In device i…”
MethodA fast and compact quantum random number generator
Jennewein, T., Achleitner, U., Weihs, G., Weinfurter, H., & Zeilinger, A. (2000) · Review of Scientific Instruments · doi:10.1063/1.1150518 · Cited by 434 · cited 2×
“andom number generator (RNG) can completely compromise the security. Many solutions have thus been proposed for the generation of random numbers (for recent work on random number generation see, e.g.,[1, 2, 3, 4, 5, 6, 7]), but none is entirely satisfactory. As quoted from Wikipedia [8], every random number generator…”
BackgroundAlgorithms and Complexity: New Directions and Recent Results
Traub, J. F. (1976) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 419
General properties of nonsignaling theories
Masanes, L., Acín, A., & Gisin, N. (2006) · Physical Review A · doi:10.1103/physreva.73.012112 · Cited by 410
Private randomness expansion with untrusted devices
Colbeck, R., & Kent, A. (2011) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/44/9/095305 · Cited by 379
Self testing quantum apparatus
Mayers, D., & Yao, A. C.-C. (2004) · Quantum Information and Computation · doi:10.26421/qic4.4-3 · Cited by 369
Experimental demonstration of phase-remapping attack in a practical quantum key distribution system
Xu, F., Qi, B., & Lo, H. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/11/113026 · Cited by 330
Randomness versus Nonlocality and Entanglement
Acín, A., Massar, S., & Pironio, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.100402 · Cited by 324
Self-citationA Fast and Compact Quantum Random Number GeneratorPreprint
Jennewein, T., Achleitner, U., Weihs, G., Weinfurter, H., & Zeilinger, A. (1999) · Cited by 291
High-speed quantum random number generation by measuring phase noise of a single-mode laser
Qi, B., Chi, Y.-M., Lo, H.-K., & Qian, L. (2010) · Optics Letters · doi:10.1364/ol.35.000312 · Cited by 290
Device-Independent Witnesses of Genuine Multipartite Entanglement
Bancal, J.-D., Gisin, N., Liang, Y.-C., & Pironio, S. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.250404 · Cited by 265
Self-citationThe Universal Composable Security of Quantum Key Distribution
Ben-Or, M., Horodecki, M., Leung, D. W., Mayers, D., & Oppenheim, J. (2005) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-30576-7_21 · Cited by 227 · cited 1×
“[46,47], we say that a protocol such as the one just presented is secure if, for any device behavior and any m, the output R is uniformly random”
BackgroundA high speed, postprocessing free, quantum random number generator
Dynes, J. F., Yuan, Z. L., Sharpe, A. W., & Shields, A. J. (2008) · Applied Physics Letters · doi:10.1063/1.2961000 · Cited by 226 · cited 1×
“andom number generator (RNG) can completely compromise the security. Many solutions have thus been proposed for the generation of random numbers (for recent work on random number generation see, e.g.,[1, 2, 3, 4, 5, 6, 7]), but none is entirely satisfactory. As quoted from Wikipedia [8], every random number generator…”
BackgroundConvergent Relaxations of Polynomial Optimization Problems with Noncommuting Variables
Pironio, S., Navascués, M., & Acín, A. (2010) · SIAM Journal on Optimization · doi:10.1137/090760155 · Cited by 224
Self-citationOptical Quantum Random Number Generator
Stefanov, A., Gisin, N., Guinnard, O., Guinnard, L., & Zbinden, H. (1999) · Archive ouverte UNIGE (University of Geneva) · Cited by 224
Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy
Leggett, T. (1988) · Physics Bulletin · doi:10.1088/0031-9112/39/6/033 · Cited by 214
Bartolini, S., Giorgi, R., & Martinelli, E. (2008) · Springer eBooks · doi:10.1007/978-0-387-71817-0 · Cited by 214 · cited 1×
“It is not easy to construct hardware that generates genuine random numbers and to prove that a chosen design is secure [8].”
BackgroundHigh speed optical quantum random number generation
Fürst, M., Weier, H., Nauerth, S., Marangon, D. G., Kurtsiefer, C., & Weinfurter, H. (2010) · Optics Express · doi:10.1364/oe.18.013029 · Cited by 200
Memory Attacks on Device-Independent Quantum Cryptography
Barrett, J., Colbeck, R., & Kent, A. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.010503 · Cited by 172
Trevisan's Extractor in the Presence of Quantum Side Information
De, A., Portmann, C., Vidick, T., & Renner, R. (2012) · SIAM Journal on Computing · doi:10.1137/100813683 · Cited by 161 · cited 2×
“rity of a DIRE protocol against classical side-information. 3 DIRE against classical side-information We start by recalling some definitions and results that will be used in the following. We refer to [14, 36, 37] for more details. 5 3.1 Preliminaries Random variables. Let R be a random variable over the finite set R an…”
BackgroundMethodInfluentialOptical quantum random number generator
Stefanov, A., Gisin, N., Guinnard, O., Guinnard, L., & Zbinden, H. (2000) · Journal of Modern Optics · doi:10.1080/09500340008233380 · Cited by 124
Device-independent state estimation based on Bell’s inequalities
Bardyn, C.-E., Liew, T. C. H., Massar, S., McKague, M., & Scarani, V. (2009) · Physical Review A · doi:10.1103/physreva.80.062327 · Cited by 123
Self-citationSignal-locality in hidden-variables theories
Valentini, A. (2002) · Physics Letters A · doi:10.1016/s0375-9601(02)00438-3 · Cited by 123
Low-bias high-speed quantum random number generator via shaped optical pulses
Wayne, M. A., & Kwiat, P. G. (2010) · Optics Express · doi:10.1364/oe.18.009351 · Cited by 123
Security and composability of randomness expansion from Bell inequalities
Fehr, S., Gelles, R., & Schaffner, C. (2013) · Physical Review A · doi:10.1103/physreva.87.012335 · Cited by 104 · cited 4×
“y, the problem lies with Eq. (3) and Eq. (A.9) of the Supplementary Information of [14] and with the final steps leading to these equations. 2Note that previous versions of these results (see [25] and [26]) claimed security against quantum side information, but both proofs were incorrect. 3 prevented to communicate wit…”
BackgroundMethodInfluentialThe black paper of quantum cryptography: Real implementation problems
Scarani, V., & Kurtsiefer, C. (2014) · Theoretical Computer Science · doi:10.1016/j.tcs.2014.09.015 · Cited by 95
An Introduction to Randomness Extractors
Shaltiel, R. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-22012-8_2 · Cited by 90 · cited 1×
“rity of a DIRE protocol against classical side-information. 3 DIRE against classical side-information We start by recalling some definitions and results that will be used in the following. We refer to [11, 29, 30] for more details. 3.1 Preliminaries Random variables. Let R be a random variable over the finite set R and…”
MethodInfluentialSecure self-calibrating quantum random-bit generator
Marco Fiorentino, B., Santori, C., Spillane, S. M., Beausoleil, R. G., & Munro, W. J. (2007) · Physical Review A · doi:10.1103/physreva.75.032334 · Cited by 89 · cited 1×
“andom number generator (RNG) can completely compromise the security. Many solutions have thus been proposed for the generation of random numbers (for recent work on random number generation see, e.g.,[1, 2, 3, 4, 5, 6, 7]), but none is entirely satisfactory. As quoted from Wikipedia [8], every random number generator…”
BackgroundProceedings of the 23rd International Colloquium on Automata, Languages and Programming
der Heide, F. M. A., & Monien, B. (1996) · Cited by 69
The Bounded-Storage Model in the Presence of a Quantum Adversary
Konig, R. T., & Terhal, B. M. (2008) · IEEE Transactions on Information Theory · doi:10.1109/tit.2007.913245 · Cited by 65
Fully Distrustful Quantum Bit Commitment and Coin Flipping
Silman, J., Chailloux, A., Aharon, N., Kerenidis, I., Pironio, S., & Massar, S. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.220501 · Cited by 52 · cited 1×
“…(DI) is not restricted to randomness generation but includes adversarial applications such as quantum key distribution (QKD) [15, 16, 11, 17, 18] and coin tossing [19], and non-adversarial ones such as state estimation [20], entanglement witnesses [21], and self-testing of quantum computers [22].”
BackgroundSelf-citationThe black paper of quantum cryptography: real implementation problemsPreprint
Scarani, V., & Kurtsiefer, C. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0906.4547 · Cited by 49
Certifiable Quantum Dice - Or, testable exponential randomness expansionPreprint
Vazirani, U. V., & Vidick, T. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1111.6054 · Cited by 33 · cited 1×
“Finally, we point out that a randomness-expansion scheme with superpolynomial expansion and proven to be secure against quantum side information was recently introduced in [24].”
BackgroundTrevisan's extractor in the presence of quantum side information
De, A., Portmann, C., Vidick, T., et al. (2009) · DSpace@MIT (Massachusetts Institute of Technology) · doi:10.48550/arxiv.0912.5514 · Cited by 3 · cited 2×
“rity of a DIRE protocol against classical side-information. 3 DIRE against classical side-information We start by recalling some definitions and results that will be used in the following. We refer to [14, 36, 37] for more details. 5 3.1 Preliminaries Random variables. Let R be a random variable over the finite set R an…”
BackgroundMethodInfluential
Research works printed but not linked: 2
- D. Mayers, 2004, Quantum Inf. Comput., 4, 273
- U. Vazirani, 2012, STOC'12 Proceedings of the 44th Symposium on Theory of Computing
Cited by
Sorted by citations
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., & Wehner, S. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.419 · Cited by 2,688
Self-citationAdvances in quantum cryptography
Pirandola, S., Andersen, U. L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C., Ottaviani, C., et al. (2020) · Advances in Optics and Photonics · doi:10.1364/aop.361502 · Cited by 2,033
“[709, 710].”
Advances in Quantum Cryptography
Pirandola, S., Andersen, U. L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C., Ottaviani, C., et al. (2019) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 1,566
Quantum random number generators
Herrero-Collantes, M., & García-Escartín, J. C. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.015004 · Cited by 850
“, 2010) had a technical error, but in (Pironio and Massar, 2013) and (Fehr et al.”
BackgroundResultScarani, V. (2019) · doi:10.1093/oso/9780198788416.001.0001 · Cited by 714
Metadata
- Authors
- Pironio, S., & Massar, S.
- Affiliations
- Université Libre de Bruxelles (BE)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2013-01-30
- Volume
- 87
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1988732892
- Cited by
- 169
- References
- 48
- Citations by year
- 2026: 6 · 2025: 9 · 2024: 6 · 2023: 10 · 2022: 4 · 2021: 12 · 2020: 18 · 2019: 38 · 2018: 12 · 2017: 7 · 2016: 9 · 2015: 10 · 2014: 12 · 2013: 13
- FWCI
- 16.19
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Agence Nationale de la Recherche (ANR-11-CHRI-0007)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Computer Networks and Communications › Cryptography and Data Security
- Keywords
- device-independent randomness generation, private randomness, Bell inequality violation, randomness extraction
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
