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Adaptive Garbled RAM from Laconic Oblivious Transfer

  • Sanjam Garg
  • Rafail Ostrovsky
  • Akshayaram Srinivasan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10993)

Abstract

We give a construction of an adaptive garbled RAM scheme. In the adaptive setting, a client first garbles a “large” persistent database which is stored on a server. Next, the client can provide garbling of multiple adaptively and adversarially chosen RAM programs that execute and modify the stored database arbitrarily. The garbled database and the garbled program should reveal nothing more than the running time and the output of the computation. Furthermore, the sizes of the garbled database and the garbled program grow only linearly in the size of the database and the running time of the executed program respectively (up to poly logarithmic factors). The security of our construction is based on the assumption that laconic oblivious transfer (Cho et al., CRYPTO 2017) exists. Previously, such adaptive garbled RAM constructions were only known using indistinguishability obfuscation or in random oracle model. As an additional application, we note that this work yields the first constant round secure computation protocol for persistent RAM programs in the malicious setting from standard assumptions. Prior works did not support persistence in the malicious setting.

References

  1. [ACC+16]
    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.D. (eds.) TCC 2016-B, Part II. LNCS, vol. 9986, pp. 3–30. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53644-5_1CrossRefGoogle Scholar
  2. [AIK04]
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Cryptography in NC\(^0\). In: 45th FOCS, pp. 166–175. IEEE Computer Society Press, October 2004Google Scholar
  3. [App17]
    Applebaum, B.: Garbled circuits as randomized encodings of functions: a primer. IACR Cryptology ePrint Archive, 2017:385 (2017)Google Scholar
  4. [BGI+01]
    Barak, B., et al.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_1CrossRefGoogle Scholar
  5. [BGL+15]
    Bitansky, N., Garg, S., Lin, H., Pass, R., Telang, S.: Succinct randomized encodings and their applications. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, pp. 439–448. ACM Press, June 2015Google Scholar
  6. [BHR12a]
    Bellare, M., Hoang, V.T., Rogaway, P.: Adaptively secure garbling with applications to one-time programs and secure outsourcing. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 134–153. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-34961-4_10CrossRefGoogle Scholar
  7. [BHR12b]
    Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 2012, pp. 784–796. ACM Press, October 2012Google Scholar
  8. [BL18]
    Benhamouda, F., Lin, H.: k-round multiparty computation from k-round oblivious transfer via garbled interactive circuits. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part II. LNCS, vol. 10821, pp. 500–532. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78375-8_17CrossRefGoogle Scholar
  9. [BLSV18]
    Brakerski, Z., Lombardi, A., Segev, G., Vaikuntanathan, V.: Anonymous IBE, leakage resilience and circular security from new assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 535–564. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78381-9_20. https://eprint.iacr.org/2017/967CrossRefGoogle Scholar
  10. [BMR90]
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: 22nd ACM STOC, pp. 503–513. ACM Press, May 1990Google Scholar
  11. [BR93]
    Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993, pp. 62–73. ACM Press, November 1993Google Scholar
  12. [BW13]
    Boneh, D., Waters, B.: Constrained pseudorandom functions and their applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 280–300. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-42045-0_15CrossRefGoogle Scholar
  13. [CCHR16]
    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-B, Part II. LNCS, vol. 9986, pp. 61–90. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53644-5_3CrossRefGoogle Scholar
  14. [CDG+17]
    Cho, C., Döttling, N., Garg, S., Gupta, D., Miao, P., Polychroniadou, A.: Laconic oblivious transfer and its applications. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 33–65. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63715-0_2CrossRefGoogle Scholar
  15. [CH16]
    Canetti, R., Holmgren, J.: Fully succinct garbled RAM. In: Sudan, M. (ed.) ITCS 2016, pp. 169–178. ACM, January 2016Google Scholar
  16. [CHJV15]
    Canetti, R., Holmgren, J., Jain, A., Vaikuntanathan, V.: Succinct garbling and indistinguishability obfuscation for RAM programs. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, pp. 429–437. ACM Press, June 2015Google Scholar
  17. [CP13]
    Chung, K.-M., Pass, R.: A simple ORAM. Cryptology ePrint Archive, Report 2013/243 (2013). https://eprint.iacr.org/2013/243
  18. [DG17]
    Döttling, N., Garg, S.: Identity-based encryption from the Diffie-Hellman assumption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 537–569. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_18CrossRefGoogle Scholar
  19. [DGHM18]
    Döttling, N., Garg, S., Hajiabadi, M., Masny, D.: New constructions of identity-based and key-dependent message secure encryption schemes. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10769, pp. 3–31. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-76578-5_1. https://eprint.iacr.org/2017/978CrossRefzbMATHGoogle Scholar
  20. [GGH+13]
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th FOCS, pp. 40–49. IEEE Computer Society Press, October 2013Google Scholar
  21. [GGM86]
    Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792–807 (1986)MathSciNetCrossRefGoogle Scholar
  22. [GGMP16]
    Garg, S., Gupta, D., Miao, P., Pandey, O.: Secure multiparty RAM computation in constant rounds. In: Hirt, M., Smith, A. (eds.) TCC 2016-B, Part I. LNCS, vol. 9985, pp. 491–520. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_19CrossRefGoogle Scholar
  23. [GHL+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).  https://doi.org/10.1007/978-3-642-55220-5_23CrossRefGoogle Scholar
  24. [GHRW14]
    Gentry, C., Halevi, S., Raykova, M., Wichs, D.: Outsourcing private RAM computation. In: 55th FOCS, pp. 404–413. IEEE Computer Society Press, October 2014Google Scholar
  25. [GKK+12]
    Gordon, S.D., Katz, J., Kolesnikov, V., Krell, F., Malkin, T., Raykova, M., Vahlis, Y.: Secure two-party computation in sublinear (amortized) time. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 2012, pp. 513–524. ACM Press, October 2012Google Scholar
  26. [GKP+13]
    Goldwasser, S., Kalai, Y.T., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: Reusable garbled circuits and succinct functional encryption. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 555–564. ACM Press, June 2013Google Scholar
  27. [GLO15]
    Garg, S., Lu, S., Ostrovsky, R.: Black-box garbled RAM. In: Guruswami, V. (ed.) 56th FOCS, pp. 210–229. IEEE Computer Society Press, October 2015Google Scholar
  28. [GLOS15]
    Garg, S., Lu, S., Ostrovsky, R., Scafuro, A.: Garbled RAM from one-way functions. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, pp. 449–458. ACM Press, June 2015Google Scholar
  29. [GMW87]
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Aho, A. (ed.) 19th ACM STOC, pp. 218–229. ACM Press, May 1987Google Scholar
  30. [GO96]
    Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious rams. J. ACM 43(3), 431–473 (1996)MathSciNetCrossRefGoogle Scholar
  31. [Gol87]
    Goldreich, O.: Towards a theory of software protection and simulation by oblivious RAMs. In: Aho, A. (ed.) 19th ACM STOC, pp. 182–194. ACM Press, May 1987Google Scholar
  32. [GS18a]
    Garg, S., Srinivasan, A.: Adaptively secure garbling with near optimal online complexity. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 535–565. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78375-8_18CrossRefGoogle Scholar
  33. [GS18b]
    Garg, S., Srinivasan, A.: Two-round multiparty secure computation from minimal assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part II. LNCS, vol. 10821, pp. 468–499. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78375-8_16CrossRefGoogle Scholar
  34. [HJO+16]
    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, Part III. LNCS, vol. 9816, pp. 149–178. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53015-3_6CrossRefGoogle Scholar
  35. [HY16]
    Hazay, C., Yanai, A.: Constant-round maliciously secure two-party computation in the RAM Model. In: Hirt, M., Smith, A. (eds.) TCC 2016-B, Part I. LNCS, vol. 9985, pp. 521–553. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_20CrossRefGoogle Scholar
  36. [IKO+11]
    Ishai, Y., Kushilevitz, E., Ostrovsky, R., Prabhakaran, M., Sahai, A.: Efficient non-interactive secure computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 406–425. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-20465-4_23CrossRefGoogle Scholar
  37. [JKK+17]
    Jafargholi, Z., Kamath, C., Klein, K., Komargodski, I., Pietrzak, K., Wichs, D.: Be adaptive, avoid overcommitting. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 133–163. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_5CrossRefGoogle Scholar
  38. [JW16]
    Jafargholi, Z., Wichs, D.: Adaptive security of yao’s garbled circuits. In: Hirt, M., Smith, A. (eds.) TCC 2016-B, Part I. LNCS, vol. 9985, pp. 433–458. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_17CrossRefzbMATHGoogle Scholar
  39. [KLW15]
    Koppula, V., Lewko, A.B., Waters, B.: Indistinguishability obfuscation for turing machines with unbounded memory. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, pp. 419–428. ACM Press, June 2015Google Scholar
  40. [KY18]
    Keller, M., Yanai, A.: Efficient maliciously secure multiparty computation for RAM. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 91–124. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78372-7_4. https://eprint.iacr.org/2017/981CrossRefGoogle Scholar
  41. [LO13]
    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).  https://doi.org/10.1007/978-3-642-38348-9_42CrossRefGoogle Scholar
  42. [LO17]
    Lu, S., Ostrovsky, R.: Black-box parallel garbled RAM. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 66–92. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63715-0_3CrossRefGoogle Scholar
  43. [LP09]
    Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. J. Cryptol. 22(2), 161–188 (2009)MathSciNetCrossRefGoogle Scholar
  44. [Mia16]
    Miao, P.: Cut-and-choose for garbled RAM. Cryptology ePrint Archive, Report 2016/907 (2016). http://eprint.iacr.org/2016/907
  45. [ORS15]
    Ostrovsky, R., Richelson, S., Scafuro, A.: Round-optimal black-box two-party computation. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part II. LNCS, vol. 9216, pp. 339–358. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_17CrossRefGoogle Scholar
  46. [OS97]
    Ostrovsky, R., Shoup, V.: Private information storage (extended abstract). In: 29th ACM STOC, pp. 294–303. ACM Press, May 1997Google Scholar
  47. [Ost90]
    Ostrovsky, R.: Efficient computation on oblivious RAMs. In: 22nd ACM STOC, pp. 514–523. ACM Press, May 1990Google Scholar
  48. [WHC+14]
    Wang, X.S., Huang, Y., Chan, T.H.H., Shelat, A., Shi, E.: SCORAM: oblivious RAM for secure computation. In: Ahn, G.-J., Yung, M., Li, N. (eds.) ACM CCS 2014, pp. 191–202. ACM Press, November 2014Google Scholar
  49. [Yao82]
    Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: 23rd FOCS, pp. 160–164. IEEE Computer Society Press, November 1982Google Scholar
  50. [Yao86]
    Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: 27th FOCS, pp. 162–167. IEEE Computer Society Press, October 1986Google Scholar

Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Sanjam Garg
    • 1
  • Rafail Ostrovsky
    • 2
  • Akshayaram Srinivasan
    • 1
  1. 1.University of California, BerkeleyBerkeleyUSA
  2. 2.UCLALos AngelesUSA

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