Communication complexity of key agreement on small ranges

Preliminary version
  • Jin-Yi Cai
  • Richard J. Lipton
  • Luc Longpré
  • Mitsunori Ogihara
  • Kenneth W. Regan
  • D. Sivakumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 900)


We study a variation on classical key-agreement and consensus problems in which the key space S is the range of a random variable that can be sampled. We give tight upper and lower bounds of [log2k] bits on the communication complexity of agreement on some key in S, using a form of Sperner's Lemma, and give bounds on other problems. In the case where keys are generated by a probabilistic polynomial-time Turing machine, we show agreement possible with zero communication if every fully polynomial-time approximation scheme (fpras) has a certain symmetry-breaking property.


Polynomial Time Success Probability Communication Complexity Consensus Problem Common Randomness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    R. Ahlswede and I. Csiszàr. Common randomness in information theory and cryptography-part I: Secret sharing. IEEE Trans. Info. Thy., 39:1121–1132, 1993.Google Scholar
  2. 2.
    N. Alon and J. Spencer. The Probabilistic Method. Wiley, 1992. With an appendix by P. Erdös.Google Scholar
  3. 3.
    E. Borowsky and E. Gafni. Generalized FLP impossibility result for t-resilient asynchronous computations. In Proc. 25th STOC, pages 91–100, 1993.Google Scholar
  4. 4.
    S. Chari, P. Rohatgi, and A. Srinivasan. Randomness-optimal unique element isolation, with applications to perfect matching and related problems. In Proc. 25th STOC, pages 458–467, 1993.Google Scholar
  5. 5.
    S. Chaudhuri, M. Herlihy, N. Lynch, and M. Tuttle. A tight lower bound for k-set agreement. In Proc. 34th FOCS, pages 206–215, 1993.Google Scholar
  6. 6.
    A. Goldberg and M. Sipser. Compression and ranking. SIAM J. Comput., 20, 1991.Google Scholar
  7. 7.
    O. Goldreich, R. Ostrovsky, and E. Petrank. Computational complexity and knowledge complexity. In Proc. 26th STOC, pages 534–543, 1994.Google Scholar
  8. 8.
    S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM J. Comput., 18:186–208, 1989.Google Scholar
  9. 9.
    J. Grollmann and A. Selman. Complexity measures for public-key cryptosystems. SIAM J. Comput., 17:309–335, 1988.Google Scholar
  10. 10.
    M. Herlihy and N. Shavit. The asynchronous computability theorem for t-resilient tasks. In Proc. 25th STOC, pages 111–120, 1993.Google Scholar
  11. 11.
    M. Herlihy and N. Shavit. A simple constructive computability theorem for wait-free computation. In Proc. 26th STOC, pages 243–252, 1994.Google Scholar
  12. 12.
    M. Jerrum and A. Sinclair. Approximating the permanent. SIAM J. Comput., 18:1149–1178, 1989.Google Scholar
  13. 13.
    M. Jerrum, L. Valiant, and V. Vazirani. Random generation of combinatorial structures from a uniform distribution. Theor. Comp. Sci., 43:169–188, 1986.Google Scholar
  14. 14.
    R. Karp and M. Luby. Monte-Carlo algorithms for enumeration and reliability problems. In Proc. 24th FOCS, pages 56–64, 1983.Google Scholar
  15. 15.
    M. Kearns. Efficient noise-tolerant learning from statistical queries. In Proc. 25th STOC, pages 392–401, 1993.Google Scholar
  16. 16.
    M. Kearns, Y. Mansour, D. Ron, R. Rubinfeld, R. Schapire, and L. Sellie. On the learnability of discrete distributions. In Proc. 26th STOC, pages 273–282, 1994.Google Scholar
  17. 17.
    U. Maurer. Perfect cryptographic security from partially independent channels. In Proc. 23rd STOC, pages 561–572, 1991.Google Scholar
  18. 18.
    U. Maurer. Secret key agreement by public discussion from common information. IEEE Trans. Info. Thy., 39:733–742, 1993.Google Scholar
  19. 19.
    K. Mulmuley, U. Vazirani, and V. Vazirani. Matching is as easy as matrix inversion. Combinatorica, 7:105–113, 1987.Google Scholar
  20. 20.
    M. Naor, A. Orlitsky, and P. Shor. Three results on interactive communication. IEEE Trans. Info. Thy., 39:1608–1615, 1993.Google Scholar
  21. 21.
    A. Orlitsky. Worst-case interactive communication I: Two messages are almost optimal. IEEE Trans. Info. Thy., 36:1111–1126, 1990.Google Scholar
  22. 22.
    A. Orlitsky. Worst-case interactive communication II: Two messages are not optimal. IEEE Trans. Info. Thy., 37:995–1005, 1991.Google Scholar
  23. 23.
    A. Orlitsky. Average-case interactive communication. IEEE Trans. Info. Thy., 38:1534–1547, 1992.Google Scholar
  24. 24.
    A. Orlitsky and A. El Gamal. Average and randomized communication complexity. IEEE Trans. Info. Thy., 36:3–16, 1990.Google Scholar
  25. 25.
    M. Saks and F. Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. In Proc. 25th STOC, pages 101–110, 1993.Google Scholar
  26. 26.
    L. Sanchis and M. Fulk. On the efficient generation of language instances. SIAM J. Comput., 19:281–296, 1990.Google Scholar
  27. 27.
    A. Selman. A taxonomy of complexity classes of functions. J. Comp. Sys. Sci., 48:357–381, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Jin-Yi Cai
    • 1
  • Richard J. Lipton
    • 2
  • Luc Longpré
    • 3
  • Mitsunori Ogihara
    • 4
  • Kenneth W. Regan
    • 1
  • D. Sivakumar
    • 1
  1. 1.Department of Computer ScienceState Univ. of NY at BuffaloBuffalo
  2. 2.Department of Computer SciencePrinceton UniversityPrinceton
  3. 3.Computer Science DepartmentUniversity of Texas at El PasoEl Paso
  4. 4.Department of Computer ScienceUniversity of RochesterRochester

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