Amortizing randomness in private multiparty computations

SIAM Journal on Discrete Mathematics

Volumn 16, Issue 4, 2003, Pages 533-544

  Kushilevitz, Eyal ^a   Ostrovsky, Rafail ^b   Rosén, Adi ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b TELCORDIA TECHNOLOGIES   (United States)

Author keywords

Amortization; Private distributed computations; Randomness; Round complexity

Indexed keywords

BOOLEAN FUNCTIONS; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; DISTRIBUTED COMPUTER SYSTEMS; NETWORK PROTOCOLS; THEOREM PROVING; VECTORS;

AMORTIZATION; PRIVATE DISTRIBUTED COMPUTATIONS; PRIVATE MULTIPARTY COMPUTATIONS; RANDOMNESS; ROUND COMPLEXITY;

RANDOM PROCESSES;

EID: 0242442471     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S089548010135274X     Document Type: Article

References (47)

1. N. Alon, O. Goldreich, J. Hastad, and R. Peralta, Simple constructions of almost k-wise independent random variables, Random Structures Algorithms, 3 (1992), pp. 289-304. (Addendum, 4 (1993), pp. 119-120.)
2. J. Bar-Ilan and D. Beaver, Non-cryptographic fault-tolerant computing in constant number of rounds of interaction, in Proc. of the 8th Annual ACM Symposium on Principles of Distributed Computing, ACM, New York, 1989, pp. 201-209.
3. D. Beaver, Perfect Privacy for Two-Party Protocols, Technical Report TR-11-89, Harvard University, Cambridge, MA, 1989.
4. M. Bellare, O. Goldreich, and S. Goldwasser, Randomness in interactive proofs, Comput. Complexity, 3 (1993), pp. 319-354.
5. M. Ben-or, S. Goldwasser, and A. Wigderson, Completeness theorems for non-cryptographic fault-tolerant distributed computation, in Proc. of the 20th Annual ACM Symposium on the Theory of Computing, 1988, pp. 1-10.
6. M. Blum and S. Micali, How to generate cryptographically strong sequences of pseudo-random bits, SIAM J. Comput., 13 (1984), pp. 850-864.
7. C. Blundo, A. De-Santis, G. Persiano, and U. Vaccaro, On the number of random bits in totally private computations, in Automata, Languages and Programming (Szeged 1995), Lecture Notes in Comput. Sci. 944, Springer, Berlin, pp. 171-182.
8. C. Blundo, A. Giorgio Gaggia, and D. R. Stinson, On the dealer's randomness required in secret sharing schemes, Des. Codes Cryptogr., 11 (1997), pp. 235-259.
9. C. Blundo, A. De-Santis, and U. Vaccaro, Randomness in distribution protocols, Inform. and Comput., 131 (1996), pp. 111-139.
10. N. H. Bshouty, On the extended direct sum conjecture, in Proc. of the 21st Annual ACM Symposium on Theory of Computing, 1989, pp. 177-185.
11. R. Canetti and O. Goldreich, Bounds on tradeoffs between randomness and communication complexity, Comput. Complexity, 3 (1993), pp. 141-167.
12. R. Canetti, E. Kushilevitz, R. Ostrovsky, and A. Rosén, Randomness versus fault-tolerance, J. Cryptography, 13 (2000), pp. 107-142.
13. D. Chaum, C. Crepeau, and I. Damgard, Multiparty unconditionally secure protocols, in Proc. of the 20th Annual ACM Symposium on the Theory of Computing, 1988, pp. 11-19.
14. B. Chor and O. Goldreich, Unbiased bits from sources of weak randomness and probabilistic communication complexity, SIAM J. Comput., 17 (1988), pp. 230-261.
15. B. Chor and E. Kushilevitz, A zero-one law for Boolean privacy, SIAM J. Discrete Math., 4 (1991), pp. 36-47.
16. B. Chor and E. Kushilevitz, A communication-privacy tradeoff for modular addition, Inform. Process. Lett., 45 (1993), pp. 205-210.
17. B. Chor, M. Geréb-Graus, and E. Kushilevitz, Private computations over the integers, SIAM J. Comput., 24 (1995), pp. 376-386.
18. B. Chor, M. Geréb-Graus, and E. Kushilevitz, On the structure of the privacy hierarchy, J. Cryptology, 7 (1994), pp. 53-60.
19. A. Cohen and A. Wigderson, Dispersers, deterministic amplification, and weak random sources, in Proc. of the 30th IEEE Symposium on the Foundations of Computer Science, 1989, pp. 14-19.
20. T. Feder, E. Kushilevitz, M. Naor, and N. Nisan, Amortized communication complexity, SIAM J. Comput., 24 (1995), pp. 736-750.
21. M. Franklin and M. Yung, Communication complexity of secure computation, in Proc. of the 24th Annual ACM Symposium on the Theory of Computing, 1992, pp. 699-710.
22. A. Gál and A. Rosén, A theorem on sensitivity and applications in private computation, SIAM J. Comput., 31 (2002), pp. 1424-1437.
23. G. Galibati and M. J. Fischer, On the complexity of 2-output Boolean networks, Theoret. Comput. Sci., 16 (1981), pp. 177-185.
24. O. Goldreich, S. Micali, and A. Wigderson, How to play any mental game, in Proc. of the 19th Annual ACM Symposium on the Theory of Computing, 1987, pp. 218-229.
25. G. Hardy, J. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, UK, 1988.
26. R. Impagliazzo and D. Zuckerman, How to recycle random bits, in Proc. of the 30th IEEE Symposium on the Foundations of Computer Science, 1989, pp. 248-253.
27. M. Karchmer, E. Kushilevitz, and N. Nisan, Fractional covers and communication complexity, SIAM J. Discrete Math., 8 (1995), pp. 76-92.
28. D. Karger and D. Koller, (De)randomized construction of small sample spaces in NC, J. Comput. System Sci., 55 (1997), pp. 402-413.
29. D. Koller and N. Megiddo, Constructing small sample spaces satisfying given constraints, SIAM J. Discrete Math., 7 (1994), pp. 260-274.
30. H. Karloff and Y. Mansour, On construction of k-wise independent random variables, Combinatorica, 17 (1997), pp. 91-107.
31. E. Kushilevitz and Y. Mansour, Randomness in private computations, SIAM J. Discrete Math., 10 (1997), pp. 647-661.
32. E. Kushilevitz and N. Nisan, Communication Complexity, Cambridge University Press, Cambridge, UK, 1997.
33. J. Kilian, E. Kushilevitz, S. Micali, and R. Ostrovsky, Reducibility and completeness in private computations, SIAM J. Comput., 29 (2000), pp. 1189-1208.
34. E. Kushilevitz, R. Ostrovsky, and A. Rosén, Characterizing linear size circuits in terms of privacy, J. Comput. System Sci., 58 (1999), pp. 129-136.
35. E. Kushilevitz and A. Rosén, A randomness-rounds tradeoff in private computation, SIAM J. Discrete Math., 11 (1998), pp. 61-80.
36. D. Krizanc, D. Peleg, and E. Upfal, A time-randomness tradeoff for oblivious routing, in Proc. of the 20th Annual ACM Symposium on the Theory of Computing, 1988, pp. 93-102.
37. E. Kushilevitz, Privacy and communication complexity, SIAM J. Discrete Math., 5 (1992), pp. 273-284.
38. J. Naor and M. Naor, Small-bias probability spaces: Efficient constructions and applications, SIAM J. Comput., 22 (1993), pp. 838-856.
39. N. Nisan, Pseudorandom generators for space bounded computation, Combinatorica, 12 (1992), pp. 449-461.
40. W. Paul, Realizing Boolean function on disjoint sets of variables, Theoret. Comput. Sci., 2 (1976), pp. 383-396.
41. P. Raghavan and M. Snir, Memory versus randomization in on-line algorithms, J. Assoc. Comput. Mach., 40 (1993), pp. 421-453.
42. L. J. Schulman, Sample spaces uniform on neighborhoods, in Proc. of the 24th Annual ACM Symposium on the Theory of Computing, 1992, pp. 17-25.
43. Q. F. Stout, Meshes with multiple buses, in Proc. of the 27th IEEE Symposium on Foundations of Computer Science, 1986, pp. 264-273.
44. U. Vazirani and V. Vazirani, Random polynomial time is equal to slightly-random polynomial time, in Proc. of the 26th IEEE Symposium on the Foundations of Computer Science, 1985, pp. 417-428.
45. A. C. Yao, Theory and applications of trapdoor functions, in Proc. of the 23rd IEEE Symposium on the Foundations of Computer Science, 1982, pp. 80-91.
46. A. Yao, Protocols for secure computation, in Proc. of the 23rd IEEE Symposium on the Foundations of Computer Science, 1982, pp. 160-164.
47. D. Zuckerman, Simulating BPP using a general weak random source, Algorithmica, 16 (1996), pp. 367-391.