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Strong Conditional Oblivious Transfer and Computing on Intervals

  • Ian F. Blake
  • Vladimir Kolesnikov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3329)

Abstract

We consider the problem of securely computing the Greater Than (GT) predicate and its generalization – securely determining membership in a union of intervals. We approach these problems from the point of view of Q-Conditional Oblivious Transfer (Q-COT), introduced by Di Crescenzo, Ostrovsky and Rajagopalan [4]. Q-COT is an oblivious transfer that occurs iff predicate Q evaluates to true on the parties’ inputs. We are working in the semi-honest model with computationally unbounded receiver.

In this paper, we propose: (i) a stronger, simple and intuitive definition of COT, which we call strong COT, or Q-SCOT. (ii) A simpler and more efficient one-round protocol for securely computing GT and GT-SCOT. (iii) A simple and efficient modular construction reducing SCOT based on membership in a union of intervals (UI-SCOT) to GT-SCOT, producing an efficient one-round UI-SCOT.

Keywords

Encryption Scheme Secure Protocol Modular Multiplication Homomorphic Encryption Oblivious Transfer 
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.

References

  1. 1.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: Proc. 22nd ACM Symp. on Theory of Computing, pp. 503–513 (1990)Google Scholar
  2. 2.
    Cachin, C., Camenisch, J., Kilian, J., Muller, J.: One-round secure computation and secure autonomous mobile agents. In: Proceedings of the 27th International Colloquium on Automata, Languages and Programming (2000)Google Scholar
  3. 3.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, p. 462. Springer, Heidelberg (1988)Google Scholar
  4. 4.
    Di Crescenzo, G., Ostrovsky, R., Rajagopalan, S.: Conditional oblivious transfer and time-released encryption. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 74–89. Springer, Heidelberg (1999)Google Scholar
  5. 5.
    Desmedt, Y.: Unconditionally secure authentication schemes and practical and theoretical consequences. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 42–55. Springer, Heidelberg (1986)Google Scholar
  6. 6.
    Fischlin, M.: A cost-effective pay-per-multiplication comparison method for millionaires. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 457–471. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Galbraith, S.D.: Elliptic curve paillier schemes. Journal of Cryptology 15(2), 129–138 (2002)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Goldreich, O.: Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004)zbMATHCrossRefGoogle Scholar
  10. 10.
    Goldwasser, S., Micali, S.: Probabilistic encryption and how to play mental poker keeping secret all partial information. In: Proc. 14th ACM Symp. on Theory of Computing, San Francisco, pp. 365–377. ACM, New York (1982)Google Scholar
  11. 11.
    Halevi, S.: Efficient commitment schemes with bounded sender and unbounded receiver. Journal of Cryptology: the journal of the International Association for Cryptologic Research 12(2), 77–89 (1999)zbMATHGoogle Scholar
  12. 12.
    Kantarcioglu, M., Clifton, C.: Privacy-preserving distributed mining of association rules on horizontally partitioned data. In: ACM SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery, DMKD 2002 (2002)Google Scholar
  13. 13.
    Kilian, J.: Founding cryptography on oblivious transfer. In: Proc. 20th ACM Symp. on Theory of Computing, Chicago, pp. 20–31. ACM, New York (1988)Google Scholar
  14. 14.
    Lindell, Y., Pinkas, B.: Privacy preserving data mining. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 20–24. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Lindell, Y., Pinkas, B.: A proof of yao’s protocol for secure two-party computation. Cryptology ePrint Archive, Report 2004/175 (2004), http://eprint.iacr.org/
  16. 16.
    Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: Proceedings of the thirty-third annual ACM symposium on Theory of computing, pp. 590–599. ACM Press, New York (2001)CrossRefGoogle Scholar
  17. 17.
    Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: 1st ACM Conf. on Electronic Commerce, pp. 129–139 (1999)Google Scholar
  18. 18.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)Google Scholar
  19. 19.
    Rabin, M.: How to exchange secrets by oblivious transfer. Technical Report TR-81, Harvard Aiken Computation Laboratory (1981)Google Scholar
  20. 20.
    Rogaway, P.: The round complexity of secure protocols. PhD thesis, MIT (1991)Google Scholar
  21. 21.
    Sander, T., Young, A., Yung, M.: Non-interactive cryptocomputing for NC 1. In: Proceedings 40th IEEE Symposium on Foundations of Computer Science, New York, pp. 554–566. IEEE, Los Alamitos (1999)Google Scholar
  22. 22.
    Yao, A.C.: Protocols for secure computations. In: Proc. 23rd IEEE Symp. on Foundations of Comp. Science, Chicago, pp. 160–164. IEEE, Los Alamitos (1982)Google Scholar
  23. 23.
    Yao, A.C.: How to generate and exchange secrets. In: Proc. 27th IEEE Symp. on Foundations of Comp. Science, Toronto, pp. 162–167. IEEE, Los Alamitos (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ian F. Blake
    • 1
  • Vladimir Kolesnikov
    • 2
  1. 1.Dept. Elec. and Comp. EngUniversity of TorontoTorontoCanada
  2. 2.Dept. Comp. Sci.University of TorontoTorontoCanada

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