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Impossibility of Black-Box Simulation Against Leakage Attacks

  • Rafail Ostrovsky
  • Giuseppe Persiano
  • Ivan ViscontiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9216)

Abstract

In this work, we show how to use the positive results on succinct argument systems to prove impossibility results on leakage-resilient black-box zero knowledge. This recently proposed notion of zero knowledge deals with an adversary that can make leakage queries on the state of the prover. Our result holds for black-box simulation only and we also give some insights on the non-black-box case. Additionally, we show that, for several functionalities, leakage-resilient multi-party computation is impossible (regardless of the number of players and even if just one player is corrupted).

More in details, we achieve the above results by extending a technique of [Nielsen, Venturi, Zottarel – PKC13] to prove lower bounds for leakage-resilient security. Indeed, we use leakage queries to run an execution of a communication-efficient protocol in the head of the adversary. Moreover, to defeat the black-box simulator we connect the above technique for leakage resilience to security against reset attacks.

Our results show that the open problem of [Ananth, Goyal, Pandey – Crypto 14] (i.e., continual leakage-resilient proofs without a common reference string) has a negative answer when security through black-box simulation is desired. Moreover our results close the open problem of [Boyle et al. – STOC 12] for the case of black-box simulation (i.e., the possibility of continual leakage-resilient secure computation without a leak-free interactive preprocessing).

Keywords

Zero knowledge MPC Resettability Succinct arguments Impossibility results Black-box vs non-black-box simulation 

Notes

Acknowledgments

We thank the anonymous reviewers for their useful comments. The full version of this work appears in [38].

Part of this work was done while the second and third authors were visiting the Computer Science Department of UCLA.

This work has been supported by NSF grants 09165174, 1065276, 1118126 and 1136174, US-Israel BSF grant 2008411, OKAWA Foundation Research Award, IBM Faculty Research Award, Xerox Faculty Research Award, B. John Garrick Foundation Award, Teradata Research Award, and Lockheed-Martin Corporation Research Award. This material is based upon work supported by the Defense Advanced Research Projects Agency through the U.S. Office of Naval Research under Contract N00014 -11 -1-0392. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government.

References

  1. 1.
    Ananth, P., Goyal, V., Pandey, O.: Interactive proofs under continual memory leakage. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 164–182. Springer, Heidelberg (2014) Google Scholar
  2. 2.
    Barak, B.: How to go beyond the black-box simulation barrier. In: 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, pp. 106–115. IEEE Computer Society (2001)Google Scholar
  3. 3.
    Barak, B.: Non-black-box techniques in cryptography. Ph.D. Thesis (2004). http://www.boazbarak.org/Papers/thesis.pdf
  4. 4.
    Barak, B., Goldreich, O., Goldwasser, S., Lindell, Y.: Resettably-sound zero-knowledge and its applications. In: 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, pp. 116–125. IEEE Computer Society (2001)Google Scholar
  5. 5.
    Bellare, M., Goldreich, O.: On defining proofs of knowledge. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 390–420. Springer, Heidelberg (1993) CrossRefGoogle Scholar
  6. 6.
    Bitansky, N., Canetti, R., Halevi, S.: Leakage-tolerant interactive protocols. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 266–284. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  7. 7.
    Bitansky, N., Dachman-Soled, D., Lin, H.: Leakage-tolerant computation with input-independent preprocessing. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 146–163. Springer, Heidelberg (2014) Google Scholar
  8. 8.
    Blum, M., De Santis, A., Micali, S., Persiano, G.: Non-interactive zero knowledge. SIAM J. Comput. 20(6), 1084–1118 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Boyle, E., Garg, S., Jain, A., Kalai, Y.T., Sahai, A.: Secure computation against adaptive auxiliary information. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 316–334. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  10. 10.
    Boyle, E., Goldwasser, S., Jain, A., Kalai, Y.T.: Multiparty computation secure against continual memory leakage. In: Proceedings of the 44th Symposium on Theory of Computing Conference, STOC 2012, pp. 1235–1254. ACM (2012)Google Scholar
  11. 11.
    Boyle, E., Goldwasser, S., Kalai, Y.T.: Leakage-resilient coin tossing. In: Peleg, D. (ed.) Distributed Computing. LNCS, vol. 6950, pp. 181–196. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  12. 12.
    Boyle, E., Goldwasser, S., Kalai, Y.T.: Leakage-resilient coin tossing. Distrib. Comput. 27(3), 147–164 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Boyle, E., Segev, G., Wichs, D.: Fully leakage-resilient signatures. J. Cryptol. 26(3), 513–558 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Brakerski, Z., Kalai, Y.T., Katz, J., Vaikuntanathan, V.: Overcoming the hole in the bucket: Public-key cryptography resilient to continual memory leakage. In: 51th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2010, pp. 501–510. IEEE Computer Society (2010)Google Scholar
  15. 15.
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, pp. 136–145. IEEE Computer Society (2001)Google Scholar
  16. 16.
    Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable zero-knowledge (extended abstract). In: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, STOC 2000, pp. 235–244. ACM (2000)Google Scholar
  17. 17.
    Dagdelen, Ö., Mohassel, P., Venturi, D.: Rate-limited secure function evaluation: definitions and constructions. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 461–478. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  18. 18.
    Damgård, I., Dupuis, F., Nielsen, J.B.: On the orthogonal vector problem and the feasibility of unconditionally secure leakage resilient computation. IACR Cryptology ePrint Archive 2014 (2014). http://eprint.iacr.org/2014/282
  19. 19.
    Dodis, Y., Haralambiev, K., López-Alt, A., Wichs, D.: Cryptography against continuous memory attacks. In: 51th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2010, pp. 511–520. IEEE Computer Society (2010)Google Scholar
  20. 20.
    Dodis, Y., Lewko, A.B., Waters, B., Wichs, D.: Storing secrets on continually leaky devices. In: IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, pp. 688–697. IEEE (2011)Google Scholar
  21. 21.
    Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991, pp. 542–552. ACM (1991)Google Scholar
  22. 22.
    Duc, A., Dziembowski, S., Faust, S.: Unifying leakage models: from probing attacks to noisy leakage. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 423–440. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  23. 23.
    Dwork, C., Naor, M., Sahai, A.: Concurrent zero-knowledge. In: Proceedings of the Thirtieth Annual ACM Symposium on the Theory of Computing, STOC 1998, pp. 409–418. ACM (1998)Google Scholar
  24. 24.
    Dziembowski, S., Faust, S.: Leakage-resilient circuits without computational assumptions. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 230–247. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  25. 25.
    Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, pp. 293–302. IEEE Computer Society (2008)Google Scholar
  26. 26.
    Faust, S., Rabin, T., Reyzin, L., Tromer, E., Vaikuntanathan, V.: Protecting circuits from leakage: the computationally-bounded and noisy cases. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 135–156. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  27. 27.
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, pp. 40–49. IEEE Computer Society (2013)Google Scholar
  28. 28.
    Garg, S., Jain, A., Sahai, A.: Leakage-resilient zero knowledge. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 297–315. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  29. 29.
    Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM J. Comput. 25(1), 169–192 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or A completeness theorem for protocols with honest majority. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing, STOC 1987, pp. 218–229. ACM (1987)Google Scholar
  31. 31.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems (extended abstract). In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, STOC 1985, pp. 291–304. ACM (1985)Google Scholar
  32. 32.
    Goldwasser, S., Rothblum, G.N.: Securing computation against continuous leakage. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 59–79. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  33. 33.
    Goldwasser, S., Rothblum, G.N.: How to compute in the presence of leakage. In: 53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012, pp. 31–40. IEEE Computer Society (2012)Google Scholar
  34. 34.
    Ishai, Y., Sahai, A., Wagner, D.: Private circuits: securing hardware against probing attacks. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 463–481. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  35. 35.
    Micali, S., Reyzin, L.: Physically observable cryptography. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 278–296. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  36. 36.
    Nielsen, J.B., Venturi, D., Zottarel, A.: On the connection between leakage tolerance and adaptive security. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 497–515. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  37. 37.
    Ostrovsky, R., Persiano, G., Visconti, I.: Constant-round concurrent non-malleable zero knowledge in the bare public-key model. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 548–559. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  38. 38.
    Ostrovsky, R., Persiano, G., Visconti, I.: Impossibility of black-box simulation against leakage attacks. IACR Cryptology ePrint Archive 2014 (2014). http://eprint.iacr.org/2014/865
  39. 39.
    Pandey, O.: Achieving constant round leakage-resilient zero-knowledge. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 146–166. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  40. 40.
    Standaert, F.-X., Malkin, T., Yung, M.: Does physical security of cryptographic devices need a formal study? (Invited Talk). In: Safavi-Naini, R. (ed.) ICITS 2008. LNCS, vol. 5155, pp. 70–70. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  41. 41.
    Standaert, F.-X., Malkin, T.G., Yung, M.: A unified framework for the analysis of side-channel key recovery attacks. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 443–461. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  42. 42.
    Standaert, F., Pereira, O., Yu, Y., Quisquater, J., Yung, M., Oswald, E.: Leakage resilient cryptography in practice. In: Sadeghi, A., Naccache, D. (eds.) Towards Hardware-Intrinsic Security - Foundations and Practice. Information Security and Cryptography, pp. 99–134. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  43. 43.
    Yu, Y., Standaert, F., Pereira, O., Yung, M.: Practical leakage-resilient pseudorandom generators. In: Al-Shaer, E., Keromytis, A.D., Shmatikov, V. (eds.) Proceedings of the 17th ACM Conference on Computer and Communications Security, CCS 2010, pp. 141–151. ACM (2010)Google Scholar

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  • Rafail Ostrovsky
    • 1
  • Giuseppe Persiano
    • 2
  • Ivan Visconti
    • 2
    Email author
  1. 1.University of CaliforniaLos AngelesUSA
  2. 2.Università di SalernoFiscianoItaly

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