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Black-Box Parallel Garbled RAM

  • Steve Lu
  • Rafail Ostrovsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10402)

Abstract

In 1982, Yao introduced a technique of “circuit garbling” that became a central building block in cryptography. The question of garbling general random-access memory (RAM) programs was introduced by Lu and Ostrovsky in 2013. The most recent results of Garg, Lu, and Ostrovsky (FOCS 2015) achieve a garbled RAM with black-box use of any one-way functions and poly-log overhead of data and program garbling in all the relevant parameters, including program run-time. The advantage of Garbled RAM is that large data can be garbled first, and act as persistent garbled storage (e.g. in the cloud) and later programs can be garbled and sent to be executed on this garbled database in a non-interactive manner.

One of the main advantages of cloud computing is not only that it has large storage but also that it has a large number of parallel processors. Despite multiple successful efforts on parallelizing (interactive) Oblivious RAM, the non-interactive garbling of parallel programs remained open until very recently. Specifically, Boyle, Chung and Pass in their TCC 2016-A [4] have shown how to garble PRAM programs with poly-logarithmic (parallel) overhead assuming non-black-box use of identity-based encryption (IBE). The question of whether the IBE assumption, and in particular, the non-black-box use of such a strong assumption is needed. In this paper, we resolve this question and show how to garble parallel programs, with black-box use of only one-way functions and with only poly-log overhead in the (parallel) running time. Our result works for any number of parallel processors.

Keywords

PRAM Garbled RAM Black-box cryptography One-way functions Secure computation 

Notes

Acknowledgments

We thank Alessandra Scafuro for helpful discussions. We thank the anonymous reviewers for their useful comments.

References

  1. 1.
    Ananth, P., Chen, Y.-C., Chung, K.-M., Lin, H., Lin, W.-K.: Delegating RAM computations with adaptive soundness and privacy. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 3–30. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-53644-5_1 CrossRefGoogle Scholar
  2. 2.
    Applebaum, B., Ishai, Y., Kushilevitz, E.: From secrecy to soundness: efficient verification via secure computation. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 152–163. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14165-2_14 CrossRefGoogle Scholar
  3. 3.
    Bitansky, N., Garg, S., Lin, H., Pass, R., Telang, S.: Succinct randomized encodings and their applications. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th Annual ACM Symposium on Theory of Computing, Portland, OR, USA, June 14–17, 2015, pp. 439–448. ACM Press (2015)Google Scholar
  4. 4.
    Boyle, E., Chung, K.-M., Pass, R.: Oblivious parallel RAM and applications. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 175–204. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49099-0_7 CrossRefGoogle Scholar
  5. 5.
    Canetti, R., Chen, Y., Holmgren, J., Raykova, M.: Adaptive succinct garbled RAM or: how to delegate your database. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 61–90. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-53644-5_3 CrossRefGoogle Scholar
  6. 6.
    Canetti, R., Holmgren, J.: Fully succinct garbled RAM. In: Sudan, M. (ed.) ITCS 2016: 7th Innovations in Theoretical Computer Science, Cambridge, MA, USA, January 14–16, 2016, pp. 169–178. Association for Computing Machinery (2016)Google Scholar
  7. 7.
    Canetti, R., Holmgren, J., Jain, A., Vaikuntanathan, V.: Succinct garbling and indistinguishability obfuscation for RAM programs. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th Annual ACM Symposium on Theory of Computing, Portland, OR, USA, June 14–17, 2015, pp. 429–437. ACM Press (2015)Google Scholar
  8. 8.
    Chen, B., Lin, H., Tessaro, S.: Oblivious parallel RAM: improved efficiency and generic constructions. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 205–234. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49099-0_8 CrossRefGoogle Scholar
  9. 9.
    Chen, Y.-C., Chow, S.S.M., Chung, K.-M., Lai, R.W.F., Lin, W.-K., Zhou, H.-S.: Cryptography for parallel RAM from indistinguishability obfuscation. In: Sudan, M. (ed.) ITCS 2016: 7th Innovations in Theoretical Computer Science, Cambridge, MA, USA, January 14–16, 2016, pp. 179–190. Association for Computing Machinery (2016)Google Scholar
  10. 10.
    Garg, S., Gupta, D., Miao, P., Pandey, O.: Secure multiparty RAM computation in constant rounds. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9985, pp. 491–520. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-53641-4_19 CrossRefGoogle Scholar
  11. 11.
    Garg, S., Lu, S., Ostrovsky, R.: Black-box garbled RAM. In: Guruswami, V. (ed.) 56th Annual Symposium on Foundations of Computer Science, Berkeley, CA, USA, October 17–20, 2015, pp. 210–229. IEEE Computer Society Press (2015)Google Scholar
  12. 12.
    Garg, S., Lu, S., Ostrovsky, R.: Black-box garbled RAM. Cryptology ePrint Archive, Report 2015/307 (2015). http://eprint.iacr.org/2015/307
  13. 13.
    Garg, S., Lu, S., Ostrovsky, R., Scafuro, A.: Garbled RAM from one-way functions. In: Servedio, R.A., Rubinfeld, R. (ed.) 47th Annual ACM Symposium on Theory of Computing, Portland, OR, USA, June 14–17, 2015, pp. 449–458. ACM Press (2015)Google Scholar
  14. 14.
    Gentry, C., Halevi, S., Lu, S., Ostrovsky, R., Raykova, M., Wichs, D.: Garbled RAM revisited. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 405–422. Springer, Heidelberg (2014). doi: 10.1007/978-3-642-55220-5_23 CrossRefGoogle Scholar
  15. 15.
    Gentry, C., Halevi, S., Raykova, M., Wichs, D.: Outsourcing private RAM computation. In: 55th Annual Symposium on Foundations of Computer Science, Philadelphia, PA, USA, October 18–21, 2014, pp. 404–413. IEEE Computer Society Press (2014)Google Scholar
  16. 16.
    Goldreich, O.: Towards a theory of software protection and simulation by oblivious RAMs. In: Aho, A. (ed.) 19th Annual ACM Symposium on Theory of Computing, New York City, NY, USA, May 25–27, 1987, pp. 182–194. ACM Press (1987)Google Scholar
  17. 17.
    Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious RAMs. J. ACM 43(3), 431–473 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Hemenway, B., Jafargholi, Z., Ostrovsky, R., Scafuro, A., Wichs, D.: Adaptively secure garbled circuits from one-way functions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 149–178. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-53015-3_6 CrossRefGoogle Scholar
  19. 19.
    Koppula, V., Lewko, A.B., Waters, B.: Indistinguishability obfuscation for turing machines with unbounded memory. In: Servedio, R.A., Rubinfeld, R. (ed.) 47th Annual ACM Symposium on Theory of Computing, Portland, OR, USA, June 14–17, 2015, pp. 419–428. ACM Press (2015)Google Scholar
  20. 20.
    Lu, S., Ostrovsky, R.: How to Garble RAM programs? In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 719–734. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38348-9_42 CrossRefGoogle Scholar
  21. 21.
    Miao, P.: Cut-and-choose for garbled RAM. Cryptology ePrint Archive, Report 2016/907 (2016). http://eprint.iacr.org/2016/907
  22. 22.
    Ostrovsky, R.: Efficient computation on oblivious RAMs. In: 22nd Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, May 14–16, 1990, pp. 514–523. ACM Press (1990)Google Scholar
  23. 23.
    Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: 23rd Annual Symposium on Foundations of Computer Science, Chicago, Illinois, November 3–5, 1982, pp. 160–164. IEEE Computer Society Press (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  1. 1.Stealth Software Technologies, Inc.Los AngelesUSA
  2. 2.University of CaliforniaLos AngelesUSA

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