On the (Im)possibility of cryptography with imperfect randomness

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2004, Pages 196-205

  Dodis, Yevgeniy ^a   Prabhakaran, Manoj ^b   Ong, Shien Jin ^c   Sahai, Amit ^b  

^a NEW YORK UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY SOURCES; NON-TRIVIAL FUNCTION; RANDOMNESS; SECURE SIGNATURES SCHEMES;

ALGORITHMS; COMPUTER SCIENCE; FUNCTIONS; NETWORK PROTOCOLS; POLYNOMIALS; SECURITY OF DATA; THEOREM PROVING;

CRYPTOGRAPHY;

EID: 17744370165     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (49)

1. M. Ajtai and N. Linial. The influence of large coalitions. Combinatorica, 13(2): 129-145, 1993.
2. L. Babai and S. Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. J. Comput. Syst. Sci., 36(2):254-276, 1988.
3. B. Barak, R. Impagliazzo, and A. Wigderson. Extracting randomness from few independent sources. In Proc. 45th FOCS, 2004.
4. A. Beimel, T. Malkin, and S. Micali. The all-or-nothing nature of two-party secure computation. In Proc. CRYPTO '99, pages 80-97, 1999.
5. M. Bellare, O. Goldreich, and S. Goldwasser. Randomness in interactive proofs. Comput. Complex., 3(4):319-354, 1993.
6. M. Bellare and J. Rompel. Randomness-efficient oblivious sampling. In Proc. 35th FOCS, pages 276-287, 1994.
7. M. Ben-Or, O. Goldreich, S. Goldwasser, J. Hȧstad, J. Kilian, S. Micali, and P. Rogaway. Everything provable is provable in zero-knowledge. In Proc. CRYPTO '88, pages 37-56, 1988.
8. C. H. Bennett, G. Brassard, and J.-M. Robert. Privacy amplification by public discussion. SIAM J. Comput., 17(2):210-229, 1988.
9. M. Blum. Independent unbiased coin flips from a correlated biased source - a finite state Markov chain. Combinatoria, 6(2):97-108, 1986.
10. M. Blum, P. Feldman, and S. Micali. Non-interactive zero-knowledge and its applications. In Proc. 20th STOC, pages 103-112, 1988.
11. R. Canetti, Y. Dodis, S. Halevi, E. Kushilevitz, and A. Sahai. Exposure-resilient functions and all-or-nothing transforms. In Proc. EUROCRYPT '00, pages 453-469, 2000.
12. B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput., 17(2):230-261, 1988.
13. B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, and R. Smolensky. The bit extraction problem of t-resilient functions. In Proc. 26th FOCS, pages 396-407. IEEE, 1985.
14. Y. Dodis, A. Elbaz, R. Oliveira, and R. Raz. Improved randomness extraction from two independent sources. In Proc. RANDOM '04, 2004.
15. Y. Dodis and R. Oliveira. On extracting private randomness over a public channel. In Proc. RANDOM '03, pages 252-263, 2003.
16. Y. Dodis, L. Reyzin, and A. Smith. Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. In Proc. EUROCRYPT '04, pages 523-540, 2004.
17. Y. Dodis, A. Sahai, and A. Smith. On perfect and adaptive security in exposure-resilient cryptography. In Proc. EUROCRYPT '01, pages 301-324, 2001.
18. Y. Dodis and J. Spencer. On the (non)universality of the one-time pad. In Proc. 43rd FOCS, pages 376-388, 2002.
19. P. Elias. The efficient construction of an unbiased random sequence. Ann. Math. Stat., 43(2):865-870, 1972.
20. U. Feige, D. Lapidot, and A. Shamir. Multiple non-interactive zero knowledge proofs under general assumptions. SIAM J. Comput., 29(1): 1-28, 1999.
21. O. Goldreich. Foundations of cryptography, volume 2. Cambridge University Press, Cambridge, 2004. Basic applications.
22. O. Goldreich, S. Micali, and A. Wigderson. How to play any mental game or A completeness theorem for protocols with honest majority. In Proc. 19th STOC, pages 218-229, 1987.
23. O. Goldreich, S. Micali, and A. Wigderson. Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM, 38(1):691-729, 1991.
24. O. Goldreich and Y. Oren. Definitions and properties of zero-knowledge proof systems. J. Cryptology, 7(1): 1-32, 1994.
25. S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM J. Comput., 18(1):186-208, 1989.
26. S. Goldwasser and M. Sipser. Private coins versus public coins in interactive proof systems. Advances in Computing Research, 5:73-90, 1989.
27. R. Impagliazzo and M. Yung. Direct minimum-knowledge computations. In Proc. CRYPTO '87, pages 40-51, 1987.
28. J. Kamp and D. Zuckerman. Deterministic extractors for bit-fixing sources and exposure-resilient cryptography. In Proc. 35th FOCS, pages 92-101, 2003.
29. T. Koshiba. A new aspect for security notions: Secure randomness in public-key encryption schemes. In Proc. 4th PKC, pages 87-103, 2001.
30. T. Koshiba. On sufficient randomness for secure public-key cryptosystems. In Proc. 5th PKC, pages 34-47, 2002.
31. D. Lichtenstein, N. Linial, and M. Saks. Some extremal problems arising from discrete control processes. Combinatorica, 9(3):269-287, 1989.
32. C.-J. Lu, O. Reingold, S. Vadhan, and A. Wigderson. Extractors: optimal up to constant factors. In Proc. 35th STOC, pages 602-611, 2003.
33. C. Lund, L. Fortnow, H. Karloff, and N. Nisan. Algebraic methods for interactive proof systems. J. ACM, 39(4):859-868, 1992.
34. U. Maurer and S. Wolf. Privacy amplification secure against active adversaries. In Proc. CRYPTO '97, pages 307-321, 1997.
35. J. L. McInnes and B. Pinkas. On the impossibility of private key cryptography with weakly random keys. In Proc. CRYPTO '90, pages 421-436, 1991.
36. M. Naor and M. Yung. Universal one-way hash functions and their cryptographic applications. In Proc. 21th STOC, pages 33-43, 1988.
37. N. Nisan and D. Zuckerman. Randomness is linear in space. J. Comput. Syst. Sci., 52(1):43-52, 1996.
38. O. Reingold, S. Vadhan, and A. Wigderson. A note on extracting randomness from Santha-Vazirani sources. Unpublished manuscript, 2004.
39. R. Renner and S. Wolf. Unconditional authenticity and privacy from an arbitrarily weak secret. In Proc. CRYPTO '03, pages 78-95, 2003.
40. M. Santha and U. V. Vazirani. Generating quasi-random sequences from semi-random sources. J. Comput. Syst. Sci., 33(1):75-87, 1986.
41. A. Shamir. How to share a secret. Commun. ACM, 22(11):612-613, 1979.
42. A. Shamir. IP = PSPACE. J. ACM, 39(4):869-877, 1992.
43. L. Trevisan and S. Vadhan. Extracting randomness from samplable distributions. In Proc. 41st FOCS, pages 32-42, 2000.
44. U. V. Vazirani. Efficiency considerations in using semi-random sources. In Proc. 19th STOC, pages 160-168, 1987.
45. U. V. Vazirani. Strong communication complexity or generating quasirandom sequences from two communicating semirandom sources. Combinatorial, 7(4):375-392, 1987.
46. U. V. Vazirani and V. V. Vazirani. Random polynomial time is equal to slightly-random polynomial time. In Proc. 26th FOCS, pages 417-428, 1985.
47. J. von Neumann. Various techniques used in connection with random digits. National Bureau of Standards, Applied Mathematics Series, 12:36-38, 1951.
48. D. Zuckerman. Simulating BPP using a general weak random source. Algorithmica, 16(4/5): 367-391, 1996.
49. D. Zuckerman. Randomness-optimal oblivious sampling. Random. Struct. Algor, 11(4):345-367, 1997.