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Lower Bounds in the Hardware Token Model

  • Shashank Agrawal
  • Prabhanjan Ananth
  • Vipul Goyal
  • Manoj Prabhakaran
  • Alon Rosen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8349)

Abstract

We study the complexity of secure computation in the tamperproof hardware token model. Our main focus is on non-interactive unconditional two-party computation using bit-OT tokens, but we also study computational security with stateless tokens that have more complex functionality. Our results can be summarized as follows:

  • There exists a class of functions such that the number of bit-OT tokens required to securely implement them is at least the size of the sender’s input. The same applies for receiver’s input size (with a different class of functionalities).

  • Non-adaptive protocols in the hardware token model imply efficient (decomposable) randomized encodings. This can be interpreted as evidence to the impossibility of non-adaptive protocols for a large class of functions.

  • There exists a functionality for which there is no protocol in the stateless hardware token model accessing the tokens at most a constant number of times, even when the adversary is computationally bounded.

En route to proving our results, we make interesting connections between the hardware token model and well studied notions such as OT hybrid model, randomized encodings and obfuscation.

Keywords

Turing Machine Input Size Oblivious Transfer Token Model Secure Function Evaluation 
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.
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6:1–6:48 (2012)Google Scholar
  2. 2.
    Beimel, A., Malkin, T.: A quantitative approach to reductions in secure computation. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 238–257. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Beimel, A., Malkin, T., Micali, S.: The all-or-nothing nature of two-party secure computation. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 80–97. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  4. 4.
    Brassard, G., Crepeau, C., Santha, M.: Oblivious transfers and intersecting codes. IEEE Transactions on Information Theory 42(6), 1769–1780 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Black-box concurrent zero-knowledge requires (almost) logarithmically many rounds. SIAM J. Comput. 32(1), 1–47 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Chandran, N., Goyal, V., Sahai, A.: New constructions for UC secure computation using tamper-proof hardware. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 545–562. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Chor, B., Kushilevitz, E.: A zero-one law for boolean privacy. SIAM J. Discrete Math. 4(1), 36–47 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Cover, T.M., Thomas, J.A.: Elements of information theory, vol. 2. Wiley (2006)Google Scholar
  9. 9.
    Damgård, I., Nielsen, J.B., Wichs, D.: Isolated proofs of knowledge and isolated zero knowledge. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 509–526. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Damgård, I., Nielsen, J.B., Wichs, D.: Universally composable multiparty computation with partially isolated parties. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 315–331. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Dodis, Y., Micali, S.: Lower bounds for oblivious transfer reductions. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 42–55. Springer, Heidelberg (1999)Google Scholar
  12. 12.
    Döttling, N., Kraschewski, D., Müller-Quade, J.: Unconditional and composable security using a single stateful tamper-proof hardware token. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 164–181. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Döttling, N., Mie, T., Müller-Quade, J., Nilges, T.: Basing obfuscation on simple tamper-proof hardware assumptions. Technical Report 675 (2011)Google Scholar
  14. 14.
    Döttling, N., Mie, T., Müller-Quade, J., Nilges, T.: Implementing resettable UC-Functionalities with untrusted tamper-proof hardware-tokens. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 642–661. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. 15.
    Dwork, C., Naor, M., Sahai, A.: Concurrent zero knowledge, pp. 409–418 (1998)Google Scholar
  16. 16.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Communications of the ACM 28(6), 637–647 (1985)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Feige, U., Killian, J., Naor, M.: A minimal model for secure computation. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 554–563. ACM (1994)Google Scholar
  18. 18.
    Goldreich, O., Micali, S., Wigderson, A.: How to play ANY mental game, pp. 218–229 (1987)Google Scholar
  19. 19.
    Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious RAMs. J. ACM 43(3), 431–473 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: One-time programs. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 39–56. Springer, Heidelberg (2008)Google Scholar
  21. 21.
    Goyal, V., Ishai, Y., Mahmoody, M., Sahai, A.: Interactive locking, zero-knowledge PCPs, and unconditional cryptography. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 173–190. Springer, Heidelberg (2010)Google Scholar
  22. 22.
    Goyal, V., Ishai, Y., Sahai, A., Venkatesan, R., Wadia, A.: Founding cryptography on tamper-proof hardware tokens. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 308–326. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    Harnik, D., Naor, M., Reingold, O., Rosen, A.: Completeness in two-party secure computation: A computational view. J. Cryptology 19(4), 521–552 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Ishai, Y., Kushilevitz, E.: Private simultaneous messages protocols with applications. In: Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems, 1997, pp. 174–183. IEEE (1997)Google Scholar
  25. 25.
    Ishai, Y., Kushilevitz, E.: Randomizing polynomials: A new representation with applications to round-efficient secure computation. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, 2000, pp. 294–304. IEEE (2000)Google Scholar
  26. 26.
    Ishai, Y., Kushilevitz, E.: Perfect constant-round secure computation via perfect randomizing polynomials. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 244–256. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  27. 27.
    Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Extracting correlations. In: 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2009, pp. 261–270. IEEE (2009)Google Scholar
  28. 28.
    Katz, J.: Universally composable multi-party computation using tamper-proof hardware. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 115–128. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  29. 29.
    Kilian, J.: Founding cryptography on oblivious transfer. In: STOC, pp. 20–31 (1988)Google Scholar
  30. 30.
    Kilian, J.: Founding crytpography on oblivious transfer. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp. 20–31. ACM (1988)Google Scholar
  31. 31.
    Kolesnikov, V.: Gate evaluation secret sharing and secure one-round two-party computation. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 136–155. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  32. 32.
    Lindell, Y.: General composition and universal composability in secure multi-party computation (2003)Google Scholar
  33. 33.
    Lindell, Y.: Lower bounds for concurrent self composition. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 203–222. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  34. 34.
    Mahmoody, M., Xiao, D.: Languages with efficient zero-knowledge pcps are in szk. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 297–314. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  35. 35.
    Maji, H.K., Prabhakaran, M., Rosulek, M.: Complexity of multi-party computation problems: The case of 2-party symmetric secure function evaluation. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 256–273. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  36. 36.
    Prabhakaran, V., Prabhakaran, M.: Assisted common information. In: 2010 IEEE International Symposium on Information Theory Proceedings (ISIT), pp. 2602–2606 (2010)Google Scholar
  37. 37.
    Prabhakaran, V., Prabhakaran, M.: Assisted common information: Further results. In: 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), pp. 2861–2865 (2011)Google Scholar
  38. 38.
    Rabin, M.O.: How to exchange secrets with oblivious transfer. IACR Cryptology ePrint Archive, 2005:187 (2005)Google Scholar
  39. 39.
    Winkler, S., Wullschleger, J.: On the efficiency of classical and quantum oblivious transfer reductions. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 707–723. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  40. 40.
    Wolf, S., Wullschleger, J.: New monotones and lower bounds in unconditional two-party computation. IEEE Transactions on Information Theory 54(6), 2792–2797 (2008)CrossRefMathSciNetGoogle Scholar
  41. 41.
    Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: FOCS, pp. 160–164 (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Shashank Agrawal
    • 1
  • Prabhanjan Ananth
    • 2
  • Vipul Goyal
    • 3
  • Manoj Prabhakaran
    • 1
  • Alon Rosen
    • 4
  1. 1.University of Illinois Urbana-ChampaignUSA
  2. 2.University of California Los AngelesUSA
  3. 3.Microsoft ResearchIndia
  4. 4.IDCHerzliyaIsrael

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