Skip to main content
Springer Nature Link
Log in

Adaptively Secure Computation for RAM Programs

  • Conference paper
  • First Online:
Advances in Cryptology – EUROCRYPT 2022 (EUROCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13276))

  • 1943 Accesses

Abstract

In this work, we study the communication complexity of secure multiparty computation under minimal assumptions in the presence of an adversary that can adaptively corrupt all parties eventually. Specifically, we are interested in understanding the complexity when modeling the underlying function as a RAM program. Under minimal assumptions, the work of Canetti et al. (STOC 2017) and Benhamouda et al. (TCC 2018) give protocols whose communication complexity grows quadratically in the circuit size when the computation is expressed as a Boolean circuit. In this work, we obtain the first two-round two-party computation protocol, which is secure against adaptive adversaries who can adaptively corrupt all parties where the communication complexity is proportional to the square of the RAM complexity of the function up to polylogarithmic factors assuming the existence of non-committing encryption.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Indeed, in this case the static simulator obtains the inputs of all parties in the protocol and thus can simulate the execution by simply running the protocol.

  2. 2.

    We remark that to obtain our result, it sufficient to obtain a circuit-efficient adaptive zero-knowledge proof.

  3. 3.

    In a RAM program, a step circuit performs CPU computations at a particular time step.

  4. 4.

    We adopt the definition of ORAM from [10].

  5. 5.

    Note that for simplicity we only specify the leaf nodes accessed by \(P'^{D'}(x)\) instead of specifying each node accessed along the path from the root to the leaf.

  6. 6.

    We note that the PRF-based scheme \((r, F_k(r) \oplus m)\) satisfies both the properties.

References

  1. 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_10

    Chapter  Google Scholar 

  2. Benhamouda, F., Lin, H., Polychroniadou, A., Venkitasubramaniam, M.: Two-round adaptively secure multiparty computation from standard assumptions. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11239, pp. 175–205. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03807-6_7

    Chapter  Google Scholar 

  3. 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). https://doi.org/10.1007/978-3-642-28914-9_15

    Chapter  Google Scholar 

  4. 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). https://doi.org/10.1007/978-3-662-44381-1_9

    Chapter  Google Scholar 

  5. Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, Pennsylvania, USA, 22–24 May 1996, pp. 639–648 (1996)

    Google Scholar 

  6. Canetti, R., Goldwasser, S., Poburinnaya, O.: Adaptively secure two-party computation from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 557–585. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_22

    Chapter  Google Scholar 

  7. Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: STOC, pp. 494–503 (2002)

    Google Scholar 

  8. Canetti, R., Poburinnaya, O., Venkitasubramaniam, M.: Better two-round adaptive multiparty computation. IACR Cryptology ePrint Archive 2016, 614 (2016). http://eprint.iacr.org/2016/614

  9. Canetti, R., Poburinnaya, O., Venkitasubramaniam, M.: Equivocating Yao: constant-round adaptively secure multiparty computation in the plain model. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, 19–23 June 2017, pp. 497–509 (2017)

    Google Scholar 

  10. Chung, K.M., Pass, R.: A simple oram. Technical report, CORNELL UNIV ITHACA NY (2013)

    Google Scholar 

  11. Cohen, R., Peikert, C.: On adaptively secure multiparty computation with a short CRS. In: Zikas, V., De Prisco, R. (eds.) SCN 2016. LNCS, vol. 9841, pp. 129–146. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44618-9_7

    Chapter  Google Scholar 

  12. Cohen, R., Shelat, A., Wichs, D.: Adaptively secure MPC with sublinear communication complexity. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part II. LNCS, vol. 11693, pp. 30–60. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_2

    Chapter  Google Scholar 

  13. Cook, S.A., Reckhow, R.A.: Time bounded random access machines. J. Comput. Syst. Sci. 7(4), 354–375 (1973)

    Article  MathSciNet  Google Scholar 

  14. Dachman-Soled, D., Katz, J., Rao, V.: Adaptively Secure, Universally Composable, Multiparty Computation in Constant Rounds. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 586–613. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_23

    Chapter  Google Scholar 

  15. Garg, S., Gupta, D., Miao, P., Pandey, O.: Secure multiparty RAM computation in constant rounds. In: Hirt, M., Smith, A. (eds.) TCC 2016, Part I. LNCS, vol. 9985, pp. 491–520. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53641-4_19

    Chapter  Google Scholar 

  16. Garg, S., Lu, S., Ostrovsky, R.: Black-box garbled ram. Cryptology ePrint Archive, Report 2015/307 (2015). https://eprint.iacr.org/2015/307

  17. Garg, S., Lu, S., Ostrovsky, R., Scafuro, A.: Garbled ram from one-way functions. Cryptology ePrint Archive, Report 2014/941 (2014). https://eprint.iacr.org/2014/941

  18. Garg, S., Polychroniadou, A.: Two-round adaptively secure MPC from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 614–637. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_24

    Chapter  Google Scholar 

  19. Garg, S., Sahai, A.: Adaptively secure multi-party computation with dishonest majority. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 105–123. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_8

    Chapter  Google Scholar 

  20. 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_23

    Chapter  Google Scholar 

  21. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229 (1987)

    Google Scholar 

  22. Goyal, V.: Constant round non-malleable protocols using one way functions. In: STOC (2011)

    Google Scholar 

  23. Hazay, C., Venkitasubramaniam, M.: On the power of secure two-party computation. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 397–429. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_14

    Chapter  Google Scholar 

  24. Hazay, C., Yanai, A.: Constant-round maliciously secure two-party computation in the RAM model. In: Hirt, M., Smith, A. (eds.) TCC 2016, Part I. LNCS, vol. 9985, pp. 521–553. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53641-4_20

    Chapter  Google Scholar 

  25. Ishai, Y., Kumarasubramanian, A., Orlandi, C., Sahai, A.: On invertible sampling and adaptive security. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 466–482. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_27

    Chapter  Google Scholar 

  26. Lin, H., Pass, R.: Constant-round non-malleable commitments from any one-way function. In: STOC (2011)

    Google Scholar 

  27. Lindell, Y., Zarosim, H.: Adaptive zero-knowledge proofs and adaptively secure oblivious transfer. J. Cryptol. 24(4), 761–799 (2011)

    Article  MathSciNet  Google Scholar 

  28. 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_42

    Chapter  Google Scholar 

  29. Pippenger, N., Fischer, M.J.: Relations among complexity measures. J. ACM (JACM) 26(2), 361–381 (1979)

    Article  MathSciNet  Google Scholar 

  30. Yao, A.C.: Protocols for secure computations (extended abstract). In: FOCS, pp. 160–164 (1982)

    Google Scholar 

  31. Yao, A.C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167 (1986)

    Google Scholar 

Download references

Acknowledgments

Work of Rafail Ostrovsky was supported by NSF award #2001096, US-Israel BSF grant 2015782, a Google Faculty Award, a JP Morgan Faculty Award, an IBM Faculty Research Award, a Xerox Faculty Research Award, an OKAWA Foundation Research Award, a B. John Garrick Foundation Award, a Teradata Research Award, a Lockheed-Martin Research Award, and the Sunday Group.

Author information

Authors and Affiliations

  1. Georgetown University, Washington, USA

    Laasya Bangalore & Muthuramakrishnan Venkitasubramaniam

  2. UCLA, Los Angeles, USA

    Rafail Ostrovsky

  3. Ligero, Inc., Rochester, USA

    Oxana Poburinnaya

Authors
  1. Laasya Bangalore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rafail Ostrovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Oxana Poburinnaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muthuramakrishnan Venkitasubramaniam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laasya Bangalore .

Editor information

Editors and Affiliations

  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

Rights and permissions

Reprints and permissions

Copyright information

© 2022 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bangalore, L., Ostrovsky, R., Poburinnaya, O., Venkitasubramaniam, M. (2022). Adaptively Secure Computation for RAM Programs. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13276. Springer, Cham. https://doi.org/10.1007/978-3-031-07085-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-07085-3_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07084-6

  • Online ISBN: 978-3-031-07085-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships