Certifiable quantum dice: Or, true random number generation secure against quantum adversaries

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2012, Pages 61-76

  Vazirani, Umesh ^a   Vidick, Thomas ^b  

^a Computer Science Division   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

certifiable randomness; entanglement; quantum computing; random number generator

Indexed keywords

CERTIFIABLE RANDOMNESS; ENTANGLEMENT; QUANTUM COMPUTING; QUANTUM-MECHANICAL DEVICES; RANDOM BITS; RANDOM NUMBER GENERATORS; STATISTICAL DISTANCE;

COMPUTATION THEORY; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; RANDOM NUMBER GENERATION; STATISTICAL TESTS;

QUANTUM CRYPTOGRAPHY;

EID: 84862620607     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2213977.2213984     Document Type: Conference Paper

References (24)

1. A. Ambainis, A. Nayak, A. Ta-Shma, and U. Vazirani. Dense quantum coding and quantum finite automata. Journal of the ACM, 49(4):496-511, 2002.
2. J. S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1:195-200, 1964.
3. J. S. Bell. On the problem of hidden variables in quantum theory. Rev. Mod. Phys., 38:447-452, 1966.
4. M. Blum and S. Micali. How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput., 13:850-864, November 1984. (Pubitemid 15510668)
5. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23:880-884, 1969.
6. R. Colbeck. Quantum And Relativistic Protocols For Secure Multi-Party Computation. PhD thesis, Trinity College, University of Cambridge, Nov. 2009.
7. R. Colbeck and A. Kent. Private randomness expansion with untrusted devices. Journal of Physics A: Mathematical and Theoretical, 44(9):095305, 2011.
8. R. Colbeck and R. Renner. Free randomness amplification. arXiv:1105.3195, 2011.
9. A. De, C. Portmann, R. Renner, and T. Vidick. Trevisan's extractor in the presence of quantum side information. CoRR, abs/0912.5, 2009.
10. A. De and T. Vidick. Near-optimal extractors against quantum storage. In Proceedings of the 42nd ACM symposium on Theory of computing, STOC '10, pages 161-170, New York, NY, USA, 2010. ACM.
11. A. Einstein, P. Podolsky, and N. Rosen. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 47:777-780, 1935.
12. S. Fehr, R. Gelles, and C. Schaffner. Security and composability of randomness expansion from Bell inequalities. Technical report arXiv:1111.6052, 2011.
13. D. Gavinsky, J. Kempe, I. Kerenidis, R. Raz, and R. de Wolf. Exponential separation for one-way quantum communication complexity, with applications to cryptography. SIAM Journal of Computing, 38(5):1695-1708, 2008. Preliminary version in Proc. of STOC 2007.
14. V. Guruswami, C. Umans, and S. Vadhan. Unbalanced expanders and randomness extractors from parvaresh-vardy codes. In Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity, CCC '07, pages 96-108, Washington, DC, USA, 2007. IEEE Computer Society.
15. T. Hartman and R. Raz. On the distribution of the number of roots of polynomials and explicit weak designs. Random Structures and Algorithms, 23(3):235-263, 2003.
16. R. Impagliazzo, R. Jaiswal, and V. Kabanets. Approximately list-decoding direct product codes and uniform hardness amplification. In Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on, pages 187 -196, oct. 2006.
17. A. Knuth, D. Yao. Algorithms and Complexity: New Directions and Recent Results, Chapter The complexity of nonuniform random number generation. Academic Press, 1976.
18. R. König, R. Renner, and C. Schaffner. The operational meaning of min- and max-entropy. IEEE Transactions on Information Theory, 55(9):4337-4347, 2009.
19. R. König and B. Terhal. The bounded storage model in presence of a quantum adversary. IEEE Transactions on Information Theory, 54(2):749-762, 2008. (Pubitemid 351314663)
20. M. Nielsen and I. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
21. S. Pironio, A. Acin, S. Massar, A. B. De La Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and et al. Random numbers certified by Bell's theorem. Nature, 464(7291):10, 2009.
22. S. Pironio and S. Massar. Security of practical private randomness generation. Technical report arXiv:1111.6056, 2011.
23. R. Renner. Security of Quantum Key Distribution. PhD thesis, Swiss Federal Institute of Technology Zurich, Sept. 2005.
24. M. Santha and U. V. Vazirani. Generating quasi-random sequences from slightly-random sources.