Exponential separations for one-way quantum communication complexity, with applications to cryptography

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2007, Pages 516-525

  Gavinsky, Dmitry ^a   Kempe, Julia ^b   Kerenidis, Iordanis ^c   Raz, Ran ^d   De Wolf, Ronald ^e  

^a UNIVERSITY OF WATERLOO   (Canada)

^b TEL AVIV UNIVERSITY   (Israel)

^c UFR 919 Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur   (France)

^d Faculty of Maths   (Israel)

^e CWI   (Netherlands)

Author keywords

Communication complexity; Cryptography; Quantum

Indexed keywords

ADVERSARIES; FOURIER COEFFICIENTS; HIDDEN MATCHING PROBLEMS; QUANTUM STORAGE;

BOOLEAN FUNCTIONS; COMMUNICATION SYSTEMS; COMPUTATIONAL COMPLEXITY; CRYPTOGRAPHY; FOURIER ANALYSIS; NETWORK PROTOCOLS;

QUANTUM THEORY;

EID: 35448991662     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1250790.1250866     Document Type: Conference Paper

References (37)

1. S. Aaronson. The learnability of quantum states. quant-ph/0608142, 18 Aug 2006.
2. Y. Aumann, Y. Z. Ding, and M. Rabin. Everlasting security in the bounded storage model. IEEE Trans. of Information Theory, 48:1668-1680, 2002.
3. N. Alon, Y. Matias, and M. Szegedy. The space complexity of approximating the frequency moments. Journal of Computer and Systems Sciences, 58(1):137-147, 1999.
4. C. H. Bennett, G. Brassard, and J.-M. Robert. Privacy amplification by public discussion. SIAM Journal on Computing, 17(2):210-229, 1988.
5. H. Buhrman, R. Cleve, and A. Wigderson. Quantum vs. classical communication and computation. In 30th ACM STOC, pages 63-68, 1998.
6. H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf. Quantum fingerprinting. Physical Review Letters, 87(16), September 26, 2001.
7. W. Beckner. Inequalities in Fourier analysis. Annals of Mathematics, 102:159-182, 1975.
8. Z. Bar-Yossef, T. S. Jayram, and I. Kerenidis. Exponential separation of quantum and classical one-way communication complexity. In 36th ACM STOC, pages 128-137, 2004.
9. A. Bonami. Etude des coefficients de Fourier des fonctions de Lp(G). Annales de l'Institute Fourier, 20(2):335-402, 1970.
10. B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM Journal on Computing, 17(2):230-261, 1988.
11. S. Dziembowski and U. Maurer. Optimal randomizer efficiency in the bounded-storage model. Journal of Cryptology, 17(1):5-26, 2004.
12. F. Le Gall. Exponential separation of quantum and classical online space complexity. In 18th ACM SPAA, pages 67-73, 2006.
13. D. Gavinsky, J. Kempe, O. Regev, and R. de Wolf. Bounded-error quantum state identification and exponential separations in communication complexity. In 38th ACM STOC, pages 594-603, 2006.
14. A. S. Holevo. Bounds for the quantity of information transmitted by a quantum communication channel. Problemy Peredachi Informatsii, 9(3):3-11, 1973.
15. English translation in Problems of Information Transmission, 9:177-183, 1973.
16. R. Impagliazzo, L. A. Levin, and M. Luby. Pseudo-random generation from one-way functions. In 21st ACM STOC, pages 12-24, 1989.
17. J. Kahn, G. Kalai, and N. Linial. The influence of variables on Boolean functions. In 29th IEEE FOCS, pages 68-80, 1988.
18. H. Klauck. Lower bounds for quantum communication complexity. In 42nd IEEE FOCS, pages 288-297, 2001.
19. E. Kushilevitz, N. Nisan. Communication Complexity. Cambridge Univ. Press, 1997.
20. R. König and B. M. Terhal. The bounded storage model in the presence of a quantum adversary, 11 Aug 2006. quant-ph/0608101.
21. M. Ledoux and M. Talagrand. Probability in Banach Spaces. Springer, 1991.
22. C.-J. Lu. Encryption against storage-bounded adversaries from on-line strong extractors. Journal of Cryptology, 17(1):27-42, 2004.
23. U. Maurer. Conditionally-perfect secrecy and a provably-secure randomized cipher. Journal of Cryptology, 5(1):53-66, 1992.
24. C. McDiarmid. Concentration. In Probabilistic Methods for Algorithmic Discrete Mathematics, pages 195-248. Springer, Berlin, 1998.
25. M. Muthukrishnan. Data Streams:Algorithms and Applications. Now Publishers, 2005.
26. M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
27. I. Newman. Private vs. common random bits in communication complexity. Information Processing Letters, 39(2):67-71, 1991.
28. R. Raz. Fourier analysis for probabilistic communication complexity. Computational Complexity, 5(3/4):205-221, 1995.
29. R. Raz. Exponential separation of quantum and classical communication complexity. In 31st ACM STOC, pages 358-367, 1999.
30. R. Renner. Security of Quantum Key Distribution. PhD thesis, ETH Zürich, 2005.
31. R. Renner and R. König. Universally composable privacy amplification against quantum adversaries. In 2nd TCC, vol. 3378 of LNCS, pages 407-425, 2005.
32. P. W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5):1484-1509, 1997.
33. M. Talagrand. How much are increasing sets correlated? Combinatorica, 16(2):243-258, 1996.
34. S. P. Vadhan. Constructing locally computable extractors and cryptosystems in the bounded-storage model. Journal of Cryptology, 17(1):43-77, 2004.
35. R. de Wolf. Quantum communication and complexity. Theoretical Computer Science, 287(1):337-353, 2002.
36. A. C-C. Yao. Probabilistic computations: Toward a unified measure of complexity. In 18th IEEE FOCS, pages 222-227, 1977.
37. A. C-C. Yao. Some complexity questions related to distributive computing. In 11th ACM STOC, pages 209-213, 1979.