A randomness-rounds tradeoff in private computation

SIAM Journal on Discrete Mathematics

Volumn 11, Issue 1, 1998, Pages 61-80

  Kushilevitz, Eyal ^a,b   Rosén, Adi ^c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b HARVARD UNIVERSITY   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

Lower bounds; Private distributed computations; Randomness; Sensitivity

Indexed keywords

EID: 0011217520     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S089548019427634X     Document Type: Article

References (45)

1. N. ALON, O. GOLDREICH, J. HÅSTAD, AND R. PERALTA, Simple constructions of almost k-wise independent random variables, in Proc. 31st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 544-553; also in Random Structures Algorithms, 3 (1992), pp. 289-304; also see addendum in 4 (1993), pp. 119-120.
2. N. ALON, O. GOLDREICH, J. HÅSTAD, AND R. PERALTA, Simple constructions of almost k-wise independent random variables, in Proc. 31st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 544-553; also in Random Structures Algorithms, 3 (1992), pp. 289-304; also see addendum in 4 (1993), pp. 119-120.
3. J. BAR-ILAN AND D. BEAVER, Non-cryptographic fault-tolerant computing in a constant number of rounds, in Proc. 8th Annual ACM Symposium on Principles of Distributed Computing, ACM, New York, 1989, pp. 201-209.
4. D. BEAVER, Perfect Privacy for Two-Party Protocols, Technical Report TR-11-89, Harvard University, 1989.
5. D. BEAVER, J. FEIGENBAUM, J. KILIAN, AND P. ROGAWAY, Security with low communication overhead, in Advances in Cryptology, Proc. Crypto '90, Lecture Notes in Computer Science 537, Springer-Verlag, New York, 1991, pp. 62-76.
6. M. BELLARE, O. GOLDREICH, AND S. GOLDWASSER, Randomness in interactive proofs, in Proc. 31st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 563-571.
7. M. BEN-OR, S. GOLDWASSER, AND A. WIGDERSON, Completeness theorems for non-cryptographic fault-tolerant distributed computation, in Proc. 20th Annual ACM Symposium on the Theory of Computing, ACM, New York, 1988, pp. 1-10.
8. M. BLUM AND S. MICALI, How to generate cryptographically strong sequences of pseudo-random bits, in Proc. 22nd Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1982, pp. 112-117; also in SIAM J. Comput., 13 (1984), pp. 850-864.
9. M. BLUM AND S. MICALI, How to generate cryptographically strong sequences of pseudo-random bits, in Proc. 22nd Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1982, pp. 112-117; also in SIAM J. Comput., 13 (1984), pp. 850-864.
10. C. BLUNDO, A. GIORGIO GAGGIA, AND D. R. STINSON, On the dealer's randomness required in secret sharing schemes, in Proc. EuroCrypt94, Lecture Notes in Computer Science 950, Springer-Verlag, New York, 1995, pp. 35-46.
11. C. BLUNDO, A. DE-SANTIS, AND U. VACCARO, Randomness in distribution protocols, in Proc. 21st Annual Intl. Collegium on Automata, Languages, and Programming, Lecture Notes in Computer Science 820, Springer-Verlag, New York, 1994, pp. 568-579.
12. C. BLUNDO, A. DE-SANTIS, G. PERSIANO, AND U. VACCARO, On the number of random bits in totally private computations, in Proc. 22nd Annual Intl. Collegium on Automata, Languages, and Programming, Lecture Notes in Computer Science 944, Springer-Verlag, New York, 1995, pp. 171-182.
13. R. CANETTI AND O. GOLDREICH, Bounds on tradeoffs between randomness and communication complexity, in Proc. 31st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 35-44; also in Comput. Complexity, 3 (1993), pp. 141-167.
14. R. CANETTI AND O. GOLDREICH, Bounds on tradeoffs between randomness and communication complexity, in Proc. 31st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 35-44; also in Comput. Complexity, 3 (1993), pp. 141-167.
15. R. CANETTI, E. KUSHILEVITZ, R. OSTROVSKY, AND A. ROSEN, Randomness vs. faulttolerance, in Proc. 16th Annual ACM Symposium on Principles of Distributed Computing, ACM, New York, 1997, pp.
16. D. CHAUM, C. CREPEAU, AND I. DAMGARD, Multiparty unconditionally secure protocols, in Proc. 20th Annual ACM Symposium on Theory of Computing, ACM, New York, 1988, pp. 11-19.
17. B. CHOR AND E. KUSHILEVITZ, A zero-one law for boolean privacy, in Proc. 21st Annual ACM Symposium on Theory of Computing, ACM, New York, 1989, pp. 62-72; also in SIAM J. Discrete Math., 4 (1991), pp. 36-47.
18. B. CHOR AND E. KUSHILEVITZ, A zero-one law for boolean privacy, in Proc. 21st Annual ACM Symposium on Theory of Computing, ACM, New York, 1989, pp. 62-72; also in SIAM J. Discrete Math., 4 (1991), pp. 36-47.
19. B. CHOR AND E. KUSHILEVITZ, A communication-privacy tradeoff for modular addition, Inform. Process. Lett., 45 (1993), pp. 205-210.
20. B. CHOR, M. GERÉB-GRAUS, AND E. KUSHILEVITZ, Private computations over the integers, in Proc. 31st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 335-344; also in SIAM J. Comput., 24 (1995), pp. 376-386.
21. B. CHOR, M. GERÉB-GRAUS, AND E. KUSHILEVITZ, Private computations over the integers, in Proc. 31st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 335-344; also in SIAM J. Comput., 24 (1995), pp. 376-386.
22. B. CHOR, M. GERÉB-GRAUS, AND E. KUSHILEVITZ, On the structure of the privacy hierarchy, J. Cryptology, 7 (1994), pp. 53-60.
23. B. CHOR AND O. GOLDREICH, Unbiased bits from sources of weak randomness and probabilistic communication complexity, in Proc. 26th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1985, pp. 429-442; also in SIAM J. Comput., 17 (1988), 230-261.
24. B. CHOR AND O. GOLDREICH, Unbiased bits from sources of weak randomness and probabilistic communication complexity, in Proc. 26th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1985, pp. 429-442; also in SIAM J. Comput., 17 (1988), 230-261.
25. A. COHEN AND A. WIGDERSON, Dispersere, deterministic amplification, and weak random sources, in Proc. 30th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 14-19.
26. M. FRANKLIN AND M. YUNG, Communication complexity of secure computation, in Proc. 24th Annual ACM Symposium on Theory of Computing, ACM, New York, 1992, pp. 699-710.
27. R. IMPAGLIAZZO AND D. ZUCKERMAN, How to recycle random bits, in Proc. 30th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 248-253.
28. D. KARGER AND D. KOLLER, (De)randomized construction of small sample spaces in NC, in Proc. 35th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 252-263.
29. D. KOLLER AND N. MEGIDDO, Constructing small sample spaces satisfying given constraints, in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM, New York, 1993, pp. 268-277.
30. H. KARLOFF AND Y. MANSOUR, On construction of k-wise independent random variables, in Proc. 26th Annual ACM Symposium on Theory of Computing, ACM, New York, 1993, pp. 564-573.
31. D. KRIZANC, D. PELEG, AND E. UPFAL, A time-randomness tradeoff for oblivious routing, in Proc. 20th Annual ACM Symposium on Theory of Computing, ACM, New York, 1988, pp. 93-102.
32. E. KUSHILEVITZ, Privacy and communication complexity, in Proc. 30th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 416-421; also in SIAM J. Discrete Math., 5 (1992), pp. 273-284.
33. E. KUSHILEVITZ, Privacy and communication complexity, in Proc. 30th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 416-421; also in SIAM J. Discrete Math., 5 (1992), pp. 273-284.
34. E. KUSHILEVITZ AND Y. MANSOUR, Randomness in private computations, in Proc. 15th Annual ACM Symposium on Principles of Distributed Computing, ACM, New York, 1996, pp. 181-190; also in SIAM J. Discrete Math., 10 (1997), pp. 647-661.
35. E. KUSHILEVITZ AND Y. MANSOUR, Randomness in private computations, in Proc. 15th Annual ACM Symposium on Principles of Distributed Computing, ACM, New York, 1996, pp. 181-190; also in SIAM J. Discrete Math., 10 (1997), pp. 647-661.
36. E. KUSHILEVITZ, S. MICALI, AND R. OSTROVSKY, Reducibility and completeness in multi-party private computations, in Proc. 35th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 478-489.
37. E. KUSHILEVITZ, R. OSTROVSKY, AND A. ROSEN, Characterizing linear size circuits in terms of privacy, in Proc. 28th Annual ACM Symposium on Theory of Computing, ACM, New York, 1996, pp. 541-550.
38. J. NAOR AND M. NAOR, Small-bias probability spaces: Efficient constructions and applications, in Proc. 22nd Annual ACM Symposium on Theory of Computing, ACM, New York; also in SIAM J. Comput., 22 (1993), pp. 838-856.
39. J. NAOR AND M. NAOR, Small-bias probability spaces: Efficient constructions and applications, in Proc. 22nd Annual ACM Symposium on Theory of Computing, ACM, New York; also in SIAM J. Comput., 22 (1993), pp. 838-856.
40. N. NISAN, Pseudorandom generator for space bounded computation, in Proc. 22nd Annual ACM Symposium on Theory of Computing, ACM, New York, 1990, pp. 204-212.
41. P. RAGHAVAN AND M. SNIR, Memory vs. randomization in on-line algorithms, in Proc. 16th Annual Intl. Collegium on Automata, Languages, and Programming, Lecture Notes in Computer Science 372, Springer-Verlag, Berlin, 1989, pp. 687-703.
42. L. J. SCHULMAN, Sample spaces uniform on neighborhoods, in Proc. 24th Annual ACM Syposium on Theory of Computing, ACM, New York, 1992, pp. 17-25.
43. U. VAZIRANI AND V. VAZIRANI, Random polynomial time is equal to slightly-random polynomial time, in Proc. 26th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1985, pp. 417-428.
44. A. C. YAO, Theory and applications of trapdoor functions, in Proc. 23rd Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1982, pp. 80-91.
45. D. ZUCKERMAN, Simulating BPP using a general weak random source, in Proc. 32nd Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1991, pp. 79-89.