New Impossibility Results for Concurrent Composition and a Non-interactive Completeness Theorem for Secure Computation

  • Shweta Agrawal
  • Vipul Goyal
  • Abhishek Jain
  • Manoj Prabhakaran
  • Amit Sahai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7417)

Abstract

We consider the client-server setting for the concurrent composition of secure protocols: in this setting, a single server interacts with multiple clients concurrently, executing with each client a specified protocol where only the client should receive any nontrivial output. Such a setting is easily motivated from an application standpoint. There are important special cases for which positive results are known – such as concurrent zero knowledge protocols – and it has been an open question whether other natural functionalities such as Oblivious Transfer (OT) are possible in this setting.

In this work:
  • We resolve this open question by showing that unfortunately, even in this very limited concurrency setting, broad new impossibility results hold, ruling out not only OT, but in fact all nontrivial finite asymmetric functionalities. Our new negative results hold even if the inputs of all honest parties are fixed in advance, and the adversary receives no auxiliary information.

  • Along the way, we establish a new unconditional completeness result for asymmetric functionalities, where we characterize functionalities that are non-interactively complete secure against active adversaries. When we say that a functionality \(\mathcal {F}\) is non-interactively complete, we mean that every other asymmetric functionality can be realized by parallel invocations of several copies of \(\mathcal {F}\), with no other communication in any direction. Our result subsumes a completeness result of Kilian [STOC’00] that uses protocols which require additional interaction in both directions.

Keywords

Impossibility Result Oblivious Transfer Honest Party Erasure Channel Corrupt Party 
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., Canetti, R., Nielsen, J.B., Pass, R.: Universally composable protocols with relaxed set-up assumptions. In: FOCS (2004)Google Scholar
  2. 2.
    Barak, B., Prabhakaran, M., Sahai, A.: Concurrent non-malleable zero knowledge. In: FOCS (2006)Google Scholar
  3. 3.
    Barak, B., Sahai, A.: How to play almost any mental game over the net - concurrent composition via super-polynomial simulation. In: FOCS (2005)Google Scholar
  4. 4.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS (2001)Google Scholar
  5. 5.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols (2005), http://eprint.iacr.org/2000/067
  6. 6.
    Canetti, R., Fischlin, M.: Universally Composable Commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Canetti, R., Kushilevitz, E., Lindell, Y.: On the Limitations of Universally Composable Two-Party Computation Without Set-Up Assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 68–86. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Canetti, R., Lin, H., Pass, R.: Adaptive hardness and composable security in the plain model from standard assumptions. In: FOCS (2010)Google Scholar
  9. 9.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: STOC (2002)Google Scholar
  10. 10.
    Canetti, R., Pass, R., Shelat, A.: Cryptography from sunspots: How to use an imperfect reference string. In: FOCS (2007)Google Scholar
  11. 11.
    Dwork, C., Naor, M., Sahai, A.: Concurrent zero-knowledge. In: STOC (1998)Google Scholar
  12. 12.
    Garg, S., Goyal, V., Jain, A., Sahai, A.: Concurrently Secure Computation in Constant Rounds. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 99–116. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Garg, S., Kumarasubramanian, A., Ostrovsky, R., Visconti, I.: Impossibility Results for Static Input Secure Computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 419–436. Springer, Heidelberg (2012)Google Scholar
  14. 14.
    Goldreich, O., Micali, S., Wigderson, A.: How to play ANY mental game. In: STOC (1987)Google Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    Goyal, V.: Positive results for concurrently secure computation in the plain model. IACR Cryptology ePrint Archive 2011, 602 (2011)Google Scholar
  17. 17.
    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
  18. 18.
    Goyal, V., Jain, A., Ostrovsky, R.: Password-Authenticated Session-Key Generation on the Internet in the Plain Model. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 277–294. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Ishai, Y., Prabhakaran, M., Sahai, A.: Founding Cryptography on Oblivious Transfer – Efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008), full version on http://www.cs.uiuc.edu/~mmp/
  20. 20.
    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
  21. 21.
    Kidron, D., Lindell, Y.: Impossibility results for universal composability in public-key models and with fixed inputs. J. Cryptology 24(3) (2011)Google Scholar
  22. 22.
    Kilian, J.: More general completeness theorems for secure two-party computation. In: STOC (2000)Google Scholar
  23. 23.
    Kilian, J., Petrank, E.: Concurrent and resettable zero-knowledge in poly-logarithm rounds. In: STOC (2001)Google Scholar
  24. 24.
    Kraschewski, D., Müller-Quade, J.: Completeness Theorems with Constructive Proofs for Finite Deterministic 2-Party Functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 364–381. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  25. 25.
    Lin, H., Pass, R., Venkitasubramaniam, M.: A unified framework for concurrent security: universal composability from stand-alone non-malleability. In: STOC (2009)Google Scholar
  26. 26.
    Lindell, Y.: General composition and universal composability in secure multi-party computation. In: FOCS (2003)Google Scholar
  27. 27.
    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
  28. 28.
    Lindell, Y.: Lower bounds and impossibility results for concurrent self composition. J. Cryptology 21(2) (2008)Google Scholar
  29. 29.
    Micali, S., Pass, R., Rosen, A.: Input-indistinguishable computation. In: FOCS (2006)Google Scholar
  30. 30.
    Pass, R.: Simulation in Quasi-Polynomial Time, and Its Application to Protocol Composition. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 160–176. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  31. 31.
    Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: FOCS (2002)Google Scholar
  32. 32.
    Prabhakaran, M., Rosulek, M.: Cryptographic Complexity of Multi-Party Computation Problems: Classifications and Separations. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 262–279. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  33. 33.
    Prabhakaran, M., Sahai, A.: New notions of security: achieving universal composability without trusted setup. In: STOC (2004)Google Scholar
  34. 34.
    Richardson, R., Kilian, J.: On the Concurrent Composition of Zero-Knowledge Proofs. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 415–431. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  35. 35.
    Yao, A.C.: How to generate and exchange secrets. In: FOCS (1986)Google Scholar

Copyright information

© International Association for Cryptologic Research 2012 2012

Authors and Affiliations

  • Shweta Agrawal
    • 1
  • Vipul Goyal
    • 2
  • Abhishek Jain
    • 1
  • Manoj Prabhakaran
    • 3
  • Amit Sahai
    • 1
  1. 1.UCLALos AngelesUSA
  2. 2.Microsoft ResearchBangaloreIndia
  3. 3.UIUCChampaignUSA

Personalised recommendations