skip to main content
10.1145/1755688.1755716acmconferencesArticle/Chapter ViewAbstractPublication Pagesasia-ccsConference Proceedingsconference-collections
research-article

Bureaucratic protocols for secure two-party sorting, selection, and permuting

Published:13 April 2010Publication History

ABSTRACT

In this paper, we introduce a framework for secure two-party (S2P) computations, which we call bureaucratic computing, and we demonstrate its efficiency by designing practical S2P computations for sorting, selection, and random permutation. In a nutshell, the main idea behind bureaucratic computing is to design data-oblivious algorithms that push all knowledge and influence of input values down to small black-box circuits, which are simulated using Yao's garbled paradigm. The practical benefit of this approach is that it maintains the zero-knowledge features of secure two-party computations while avoiding the significant computational overheads that come from trying to apply Yao's garbled paradigm to anything other than simple two-input functions.

References

  1. G. Aggarwal, N. Mishra, and B. Pinkas. Secure computation of the kth-ranked element. In In Advances in Cryptology-Proc. of Eurocrypt'04, pages 40--55, 2004.Google ScholarGoogle Scholar
  2. M. Ajtai, J. Komlos, and E. Szemeredi. Sorting in c log n parallel steps. Combinatorica, 3:1--19, 1983. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. M. J. Atallah and W. Du. Secure multi-party computational geometry. In WADS2001: 7th International Workshop on Algorithms and Data Structures, pages 165--179, Providence, Rhode Island, USA, August 8--10 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. K. E. Batcher. Sorting networks and their applications. In Proceedings of the AFIPS Spring Joint Computer Conference 32, pages 307--314, 1968. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. M. Blum, R. W. Floyd, V. Pratt, R. Rivest, and R. Tarjan. Time bounds for selection, 1973.Google ScholarGoogle Scholar
  6. R. Canetti, Y. Ishai, R. Kumar, M. K. Reiter, R. Rubinfeld, and R. N. Wright. Selective private function evaluation with applications to private statistics (extended abstract). In Proceedings of Twentieth ACM Symposium on Principles of Distributed Computing (PODC), 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. G. Chen and H. Shen. A bitonic selection algorithm on multiprocessor system. J. of Comput. Sci. Technol., 4:315--322, 1989.Google ScholarGoogle ScholarCross RefCross Ref
  8. B. Chor, O. Goldreich, E. Kushilevitz, and M. Sudan. Private information retrieval. In Proceedings of IEEE Symposium on Foundations of Computer Science, Milwaukee, WI USA, October 23--25 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. M. Ciura. Best increments for the average case of shellsort. In International Symposium on Fundamentals of Computation Theory, Riga, Latvia, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms, Second Edition. The MIT Press, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. J. Feigenbaum, Y. Ishai, T. Malkin, K. Nissim, M. Strauss, and R. Wright. Secure multiparty computation of approximations. In Twenty Eighth International Colloquium on Automata, Language and Programming, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. M. Frigo, C. E. Leiserson, H. Prokop, and S. Ramachandran. Cache-oblivious algorithms (extended abstract). In In Proc. 40th Annual Symposium on Foundations of Computer Science, pages 285--397. IEEE Computer Society Press, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. O. Goldreich. The Foundations of Cryptography, volume 2. 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. O. Goldreich, S. Micali, and A. Wigderson. How to play any mental game. In Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pages 218--229, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. L. J. Goldstein and S. W. Leibholz. On the synthesis of signal switching networks with transient blocking, 1967.Google ScholarGoogle Scholar
  16. M. T. Goodrich and R. Tamassia. Algorithm Design: Foundations, Analysis, and Internet Examples. Wiley, 2001.Google ScholarGoogle Scholar
  17. Michael T. Goodrich. Randomized Shellsort: A simple oblivious sorting algorithm. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1--16. SIAM, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. J. Incerpi. A study of the worst case of shellsort. Ph.D. thesis, Brown University, Dept. of Computer Science, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. J. Incerpi and R. Sedgewick. Practical variations of shellsort. Information Processing Letters, 79:223--227, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. D. E. Knuth. Seminumerical algorithms. The Art of Computer Programming, 2.Google ScholarGoogle Scholar
  21. D. E. Knuth. Sorting and searching. The Art of Computer Programming, 3.Google ScholarGoogle Scholar
  22. T. Leighton, Y. Ma, and T. Suel. On probabilistic networks for selection, merging, and sorting. In SPAA'95, pages 106--118, Santa Barbara, CA, USA, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. P. Lemke. The performance of randomized shellsort-like network sorting algorithms. In SCAMP working paper, Institute for Defense Analysis, Princeton, NJ, USA, 1994.Google ScholarGoogle Scholar
  24. Y. Lindell and B. Pinkas. Privacy preserving data mining. In Advances in Cryptology - Crypto2000, Lecture Notes in Computer Science, volume 1880, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. D. Malkhi, N. Nisan, B. Pinkas, and Y. Sella. Fairplay -- a secure two-party computation system. In In USENIX Security Symposium, pages 287--302, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. M. S. Paterson. Improved sorting networks with o(log n) depth. Algorithmica, 5:75--92, 2005.Google ScholarGoogle ScholarCross RefCross Ref
  27. H. Prokop. Cache-oblivious algorithms. Technical report, M.I.T, 1999.Google ScholarGoogle Scholar
  28. R. Sedgewick. Analysis of shellsort and related algorithms. In ESA 96: Fourth Annual European Symposium on Algorithms, pages 25--27, 1996. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. D. L. Shell. A high-speed sorting procedure. Commun. ACM, 2(7):30--32, 1959. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. A. C. Yao. How to generate and exchange secrets. In Proceedings 27th IEEE Symposium on Foundations of Computer Science, pages 162--167, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Bureaucratic protocols for secure two-party sorting, selection, and permuting

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in
    • Published in

      cover image ACM Conferences
      ASIACCS '10: Proceedings of the 5th ACM Symposium on Information, Computer and Communications Security
      April 2010
      363 pages
      ISBN:9781605589367
      DOI:10.1145/1755688

      Copyright © 2010 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 13 April 2010

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article

      Acceptance Rates

      ASIACCS '10 Paper Acceptance Rate25of166submissions,15%Overall Acceptance Rate418of2,322submissions,18%

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader