Security of practical private randomness generation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 87, Issue 1, 2013, Pages

  Pironio, Stefano ^a   Massar, Serge ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

BELL INEQUALITIES; DEVICE INDEPENDENCE; ENTANGLED QUANTUM SYSTEMS; LAY-OUT; MEASURED SYSTEM; QUANTUM DEVICE; RANDOM NUMBERS; RANDOM SEEDS; SIDE INFORMATION; THEORETICAL FRAMEWORK;

QUANTUM ELECTRONICS; QUANTUM OPTICS; RANDOM NUMBER GENERATION;

RANDOM PROCESSES;

EID: 84873172592     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.87.012336     Document Type: Article

References (51)

1. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. RSINAK 0034-6748 10.1063/1.1150518 71, 1675 (2000).
2. A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, J. Mod. Opt. 10.1080/09500340008233380 47, 595 (2000).
3. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2961000 93, 031109 (2008).
4. M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032334 75, 032334 (2007). (Pubitemid 46494669)
5. B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.35.000312 35, 312 (2010).
6. M. Fürst, H. Weier, S. Nauerth, D. G. Marangon, C. Kurtsiefer, and H. Weinfurter, Opt. Express OPEXFF 1094-4087 10.1364/OE.18.013029 12, 13029 (2010).
7. M. A. Wayne and P. G. Kwiat, Opt. Express OPEXFF 1094-4087 10.1364/OE.18.009351 18, 9351 (2010).
8. W. Schindler, in Cryptographic Engineering, edited by, Ç Koç, (Springer, New York, 2009), p. 25.
9. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge University Press, Cambridge, 2004).
10. A. Valentini, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00438- 3 297, 273 (2002).
11. J. Barrett, L. Hardy, and A. Kent, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010503 95, 010503 (2005). (Pubitemid 41506418)
12. Ll. Masanes, A. Acin, and N. Gisin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012112 73, 012112 (2006). (Pubitemid 43270068)
13. R. Colbeck, Ph.D. dissertation, University of Cambridge, 2007.
14. R. Colbeck and A. Kent, J. Phys. A 1751-8113 10.1088/1751-8113/44/9/ 095305 44, 095305 (2011).
15. S. Pironio, Nature (London) NATUAS 0028-0836 10.1038/nature09008 464, 1021 (2010).
16. A. K. Ekert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.661 67, 661 (1991).
17. D. Mayers and A. Yao, Quantum Inf. Comput. 4, 273 (2004).
18. A. Acín, N. Gisin, and L. Masanes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.120405 97, 120405 (2006). (Pubitemid 44434927)
19. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.230501 98, 230501 (2007).
20. J. Silman, A. Chailloux, N. Aharon, I. Kerenidis, S. Pironio, and S. Massar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.220501 106, 220501 (2011).
21. C. E. Bardyn, T. C. H. Liew, S. Massar, M. McKague, and V. Scarani, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.062327 80, 062327 (2009).
22. J.-D. Bancal, N. Gisin, Y.-C. Liang, and S. Pironio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.250404 106, 250404 (2011).
23. F. Magniez, in Proceedings of the 33rd International Colloquium on Automata, Languages and Programming, (Springer, Berlin, 2006), p. 72.
24. Specifically, the problem lies with Eqs. (3) and (A9) of the Supplementary Information of Ref. and with the final steps leading to these equations.
25. S. Fehr, R. Gelles, and C. Schaffner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.87.012335 87, 012335 (2013).
26. U. Vazirani and T. Vidick, STOC'12 Proceedings of the 44th Symposium on Theory of Computing (ACM, NY, 2012), p. 61.
27. Note that previous versions of these results claimed security against quantum side information, but both proofs were incorrect.
28. V. Scarani and C. Kurtsiefer, arXiv: 0906.4547.
29. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, Nat. Photonics 1749-4885 10.1038/nphoton.2010.214 4, 686 (2010).
30. Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.042333 78, 042333 (2008).
31. F. Xu, B. Qi, and H.-K. Lo, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/11/113026 12, 113026 (2010).
32. Note in particular that it is highly unlikely that the attack reported in Ref. would spontaneously occur in nonmalicious devices.
33. HotBits: Genuine random numbers, generated by radioactive decay, http://www.fourmilab.ch/hotbits.
34. Random.org, http://www.random.org.
35. entropypool and entropy filter, http://random.hd.org/index.html.
36. R. Shaltiel, An Introduction to Randomness Extractors, Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 6756 (Springer, Berlin, 2011), p. 21.
37. A. De, C. Portmann, T. Vidick, and R. Renner, SIAM J. Comput. 0097-5397 10.1137/100813683 41, 915 (2012).
38. Note that the definition of (classical) extractors does not usually involve side information, but the definition given here and the conventional one can be shown to be essentially equivalent.
39. A. Acin, S. Massar, and S. Pironio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.100402 108, 100402 (2012).
40. M. Navascués, S. Pironio, and A. Acín, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.010401 98, 010401 (2007); (Pubitemid 46135119)
41. M. Navascués, S. Pironio, and A. Acín, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/7/073013 10, 073013 (2008).
42. S. Pironio, M. Navascues, and A. Acín, SIAM J. Optim. 1052-6234 10.1137/090760155 20, 2157 (2010).
43. This is the novel ingredient that fixes the issue in Ref..
44. G. Grimmett and D. Stirzaker, Probability and Random Processes (Oxford University Press, Oxford, 2001).
45. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991), Chap. 5.12.
46. D. Knuth and A. Yao, in Algorithms and Complexity: New Directions and Recent Results (Academic Press, New York, 1976), p. 357.
47. M. Ben-Or, M. Horodecki, D. W. Leung, D. Mayers, and J. Oppenheim, The Universal Composable Security of Quantum Key Distribution, Lecture Notes in Computer Science, Vol. 3378 (Springer, Berlin, 2005), pp. 386-406.
48. M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, Nat. Commun. 2041-1723 10.1038/ncomms1631 3, 634 (2012).
49. Note, however, that even in a trusted provider situation, condition may fail if the adversary can modify the behavior of the devices by controlling external parameters such as the power supply of the devices.
50. J. Barrett, R. Colbeck, and A. Kent, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.110.010503 110, 010503 (2013).
51. R. Koenig and B. Terhal, IEEE Trans. Inf. Theory 0018-9448 10.1109/TIT.2007.913245 54, 749 (2008). (Pubitemid 351314663)