Secure multiparty computation of approximations

ACM Transactions on Algorithms

Volumn 2, Issue 3, 2006, Pages 435-472

  Feigenbaum, Joan ^a,g   Ishai, Yuval ^b   Malkin, T A L ^c,h   Nissim, Kobbi ^d   Strauss, Martin J ^e   Wright, Rebecca N ^f,i  

^a YALE UNIVERSITY   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c Columbia University ^*  (United States)

^d BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^e UNIVERSITY OF MICHIGAN   (United States)

^f STEVENS INSTITUTE OF TECHNOLOGY   (United States)

^g Yale University   (United States)

^h Department of Earth and Environmental Sciences   (United States)

ⁱ Stevens Institute of Technology   (United States)

Author keywords

Distributed data processing; Privacy; Sublinear communication

Indexed keywords

DISTRIBUTED DATA PROCESSING; HAMMING DISTANCE; MULTIPARTY COMPUTATION; SUBLINEAR COMMUNICATION;

COMPUTATION THEORY; DATA PRIVACY; DATA PROCESSING; DISTRIBUTED COMPUTER SYSTEMS;

APPROXIMATION THEORY;

EID: 33748996753     PISSN: 15496325     EISSN: 15496333     Source Type: Journal    
DOI: 10.1145/1159892.1159900     Document Type: Article

References (55)

1. AGRAWAL, R., AND SRIKANT, R. 2000. Privacy preserving data mining. In Proceedings of the ACM SIGMOD Conference on Management of Data. ACM Press, 439-450.
2. ALON, N., GIBBONS, P. B., MATIAS, Y., AND SZEGEDY, M. 2002. Tracking join and self-join sizes in limited storage. J. Comput. Syst. Science 64, 3, 719-747.
3. ALON, N., MATIAS, Y., AND SZEGEDY, M. 1999. The space complexity of approximating the frequency moments. J. Comput. Syst. Science 58, 1, 137-147.
4. ALON, N. AND SPENCER, J. 1992. The Probabilistic Method. John Wiley. BAR-YOSSEF, Z. 2004. Personal Communication.
5. BEAVER, D. 1991. Foundations of secure interactive computing. In Advances in Cryptology (CRYPTO'91) Lecture Notes in Computer Science, vol. 576. Springer-Verlag, 377-391.
6. BEAVER, D., MICALI, S., AND ROGAWAY, P. 1990. The round complexity of secure protocols. In Proceedings of the 22th Annual ACM Symposium on the Theory of Computing. 503-513.
7. BEIMEL, A., CARMI, P., NISSIM, K., AND WEINREB, E. 2006. Private approximation of search problems. In Proceedings of the 38th Annual ACM Symposium on the Theory of Computing. 119-128.
8. BEN-OR, M., GOLDWASSER, S., AND WIGDERSON, A. 1988. Completeness theorems for non-cryptographic fault-tolerant distributed computation. In Proceedings of the 20th Annual ACM Symposium on the Theory of Computing. ACM Press, 1-10.
9. BRODER, A. 1986. How hard is it to marry at random? In Proceedings of the 18th Annual ACM Symposium on the Theory of Computing. 50-58. (Erratum in 20th STOC, p. 551.)
10. CACHIN, C., MICALI, S., AND STADLER, M. 1999. Computationally private information retrieval with polylogarithmic communication. In Advances in Cryptology (EUROCRYPT'99). Lecture Notes in Computer Science, vol. 1592. Springer-Verlag, 404-414.
11. CANETTI, R. 2000. Security and composition of multiparty cryptographic protocols. J. Cryptology 13, 1, 143-202.
12. CANETTI, R. 2001. Universally composable security: A new paradigm for cryptographic protocols. In Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science. 136-145.
13. CANETTI, R., ISHAI, Y., KUMAR, R., REITER, M., RUBINFELD, R., AND WRIGHT, R. 2001. Selective private function evaluation with applications to private statistics. In Proceedings of the 20th Annual ACM Symposium on Principles of Distributed Computing. ACM Press, 293-304.
14. CHAUM, D., CRÉPEAU, C., AND DAMGÅRD, I. 1988. Multiparty unconditionally secure protocols. In Proceedings of the 20th Annual ACM Symposium on the Theory of Computing. 11-19.
15. CHOR, B., GOLDREICH, O., KUSHILEVTTZ, E., AND SUDAN, M. 1998. Private information retrieval. J. ACM 45, 965-981.
16. CORMODE, G., PATERSON, M., SAHINALP, S., AND VISHKIN, U. 2000. Communication complexity of document exchange. In the 11th Annual ACM/SIGACT-SIAM Symposium on Discrete Algorithms. 197-206.
17. DIMACS. Special year on massive data sets. 1997-1999. http://dimacs.rutgers.edu/SpecialYears/1997_1998/.
18. DODIS, Y., REYZIN, L., AND SMITH, A. 2004. Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. In Advances in Cryptology (EUROCRYPT'04) Lecture Notes in Computer Science, vol. 3027. Springer-Verlag, 523-540.
19. EVEN, S., GOLDREICH, O., AND LEMPEL, A. 1985. A randomized protocol for signing contracts. Comm. ACM 28, 637-647.
20. FEDER, T., KUSHILEVITZ, E., NAOR, M., AND NISAN, N. 1995. Amortized communication complexity. SIAM J. Comput. 24, 4, 736-750.
21. FEIGENBAUM, J., ISHAI, Y., MALKIN, T., NISSIM, K., STRAUSS, M., AND WRIGHT, R. N. 2001. Secure multiparty computation of approximations. In Proceedings of the 28th International Colloquium on Automata, Languages and Programming. Springer-Verlag, 927-938.
22. FEIGENBAUM, J., KANNAN, S., STRAUSS, M., AND VISWANATHAN, M. 2002. An approximate Lidifference algorithm for massive data streams. SIAM J. Comput. 32, 1, 131-151.
23. FREEDMAN, M., NISSIM, K., AND PINKAS, B. 2004. Efficient private matching and set intersection. In Advances in Cryptology (EUROCRYPT'04) Lecture Notes in Computer Science, vol. 3027. Springer-Verlag, 1-19.
24. GAVINSKY, D., KEMPE, J., AND DE WOLF, R. 2004. Quantum communication cannot simulate a public coin, http://xxx.lanl.gov/abs/quant-ph./0411051.
25. GENTRY, C., AND RAMZAN, Z. 2005. Single-database private information retrieval with constant communication rate. In Proceedings of the 32nd International Colloquium on Automata, Languages and Programming. 803-815.
26. GERTNER, Y., ISHAI, Y., KUSHILEVITZ, E., AND MALKIN, T. 2000. Protecting data privacy in private information retrieval schemes. J. Comput. Syst. Sciences 60, 3, 592-692.
27. GOLDREICH, O. 2004. Foundations of Cryptography Volume II: Basic Applications. Cambridge University Press, Cambridge, UK.
28. GOLDREICH, O., MICALI, S., AND WIGDERSON, A. 1987. How to play any mental game. In Proceedings of the 19th Annual ACM Symposium on the Theory of Computing. ACM Press, 218-229.
29. GOLDWASSER, S., AND MICALI, S. 1984. Probabilistic encryption. J. Comput. Syst. Sciences 28,270-299.
30. HALEVI, S., KUSHILEVITZ, E., KRAUTHGAMER, R., AND NISSIM, K. 2001. Private approximations of NP-hard functions. In Proceedings of the 33th Annual ACM Symposium on the Theory of Computing. 550-559.
31. INDYK, P. 2000. Stable distributions, pseudorandom generators, embeddings and data stream computation. In Proceedings of the 41st IEEE Symposium on Foundations of Computer Science. 189-197.
32. INDYK, P., AND WOODRUFF, D. P. 2006. Polylogarithmic private approximations and efficient matching. In Proceedings of the 3rd Theory of Cryptography Conference. 245-264.
33. ISHAI, Y., KUSHILEVITZ, E., OSTROVSKY, R., AND SAHAI, A. 2004. Batch codes and their applications. In Proceedings of the 36th Annual ACM Symposium on the Theory of Computing. 262-272.
34. JERRUM, M. AND SINCLAIR, A. 1989. Approximating the permanent. SIAM J. Comput. 18, 6, 1149-1178.
35. JERRUM, M., SINCLAIR, A., AND VIGODA, E. 2004. A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries. J. ACM 51, 4, 671-697.
36. JERRUM, M., VALIANT, L., AND VAZIRANI, V. 1986. Random generation of combinatorial structures from a uniform distribution. Theoret. Comput. Science 43, 169-188.
37. KALTOFEN, E. AND SHOUP, V. 1995. Subquadratic-time factoring of polynomials over finite fields. In Proceedings of the 27th Annual ACM Symposium on the Theory of Computing. 398-406.
38. KATZ, J., OSTROVSKY, R., AND SMITH, A. 2003. Round efficiency of multi-party computation with a dishonest majority. In Advances in Cryptology (EUROCRYPT'03) Lecture Notes in Computer Science, vol. 2656. Springer-Verlag, 578-595.
39. KUSHILEVITZ, E. AND NISAN, N. 1997. Communication Complexity. Cambridge University Press, Cambridge, UK.
40. KUSHILEVITZ, E. AND OSTROVSKY, R. 1997. Replication is NOT needed: SINGLE database, computationally-private information retrieval. In Proceedings of the 38th IEEE Symposium on Foundations of Computer Science. 364-373.
41. KUSHILEVITZ, E., OSTROVSKY, R., AND RABANI, Y. 2000. Efficient search for approximate nearest neighbor in high dimensional spaces. SIAM J. Comput. 30, 2, 457-474.
42. LINDELL, Y. 2003. Parallel coin-tossing and constant-round secure two-party computation. J. Cryptol. 16, 3, 143-184.
43. LINDELL, Y. AND PINKAS, B. 2002. Privacy preserving data mining. J. Cryptol. 15, 3, 177-206.
44. LIPMAA, H. 2005. An oblivious transfer protocol with log-squared communication. In Proceedings of the 8th Information Security Conference (ISC'05). J. Zhou and J. Lopez, Eds. Lecture Notes in Computer Science, vol. 3650. Springer-Verlag, 314-328.
45. MANN, E. 1998. Private access to distributed information. M.S. thesis, Technion (Israel Institute of Technology), Haifa, Israel.
46. MICALI, S. AND ROGAWAY, P. 1991. Secure computation. In Advances in Cryptology (CRYPTO'91) Lecture Notes in Computer Science, vol. 576. Springer-Verlag, 392-404.
47. MINC, H. 1982. Permanents. In Encyclopedia of Mathematics and its Applications, vol. 6. Addison-Wesley.
48. NAOR, J. AND NAOR, M. 1993. Small-bias probability spaces: efficient constructions and applications. SIAM J. Comput. 22, 4, 838-856.
49. NAOR, M. AND NISSIM, K. 2001. Communication preserving protocols for secure function evaluation. In Proceedings of the 33th Annual ACM Symposium on the Theory of Computing. 590-599.
50. NAOR, M. AND PINKAS, B. 2005. Computationally secure oblivious transfer. J. Cryptol. 18, 1, 1-35.
51. PASS, R. 2004. Bounded-concurrent secure multi-party computation with a dishonest majority. In Proceedings of the 36th Annual ACM Symposium on the Theory of Computing. 232-241.
52. RABIN, M.O. 1981. How to exchange secrets by oblivious transfer. Tech. rep. TR-81, Aiken Computation Laboratory, Harvard University, Cambridge, MA.
53. STERN, J. P. 1998. A new and efficient all-or-nothing disclosure of secrets protocol. In Advances in Cryptology (ASIACRYPT'98) Lecture Notes in Computer Science, vol. 1514. Springer-Verlag, 357-371.
54. YAO, A. 1982. Protocols for secure computation. In Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science. 160-164.
55. YAO, A. 2003. On the power of quantum fingerprinting. In Proceedings of the 35th Annual ACM Symposium on the Theory of Computing. 77-81.