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Secret Shared Random Access Machine

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Algorithmic Aspects of Cloud Computing (ALGOCLOUD 2015)

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Abstract

The computations over RAM are preferred over computations with circuits or Turing machines. Secure and private RAM executions become more and more important in the scope avoiding information leakage when executing programs over a single computer as well as over the clouds. In this paper, we propose a distributed scheme for evaluating RAM programs without revealing any information on the computation including the program, the data and the result. We use the Shamir secret sharing to share all the program instructions and private string matching technique to ensure the correct instruction execution. We stress that our scheme obtains information theoretic security and does not rely on any computational hardness assumptions, therefore, gaining indefinite private and secure RAM execution of perfectly unrevealed programs.

S. Dolev—Partially supported by Kamin grant of the Israeli economy ministry, and the Rita Altura Trust Chair in Computer Sciences.

Y. Li—The author would like to acknowledge the Lynne and William Frankel Center as it supports students travel for presenting their works.

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Notes

  1. 1.

    One can check that Step 6 in Algorithm 1 is equivalent to the bitwise OR operation.

  2. 2.

    The original algorithm is designed for bivariate polynomial, we modified it accordingly.

References

  1. Amazon Elastic Compute Cloud (EC2). http://aws.amazon.com/ec2

  2. Afshar, A., Hu, Z., Mohassel, P., Rosulek, M.: How to efficiently evaluate RAM programs with malicious security, Cryptology ePrint Archive, Report 2014/759 (2014)

    Google Scholar 

  3. Becker, G.T., Regazzoni, F., Paar, C., Burleson, W.P.: Stealthy dopant-level hardware trojans. In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 197–214. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing (STOC 1988), NY, USA, pp. 1–10. ACM, New York (1988)

    Google Scholar 

  5. Boyle, E., Goldwasser, S., Tessaro, S.: Communication locality in secure multi-party computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 356–376. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Boyle, E., Chung, K.M., Pass, R.: Large-scale secure computation, Cryptology ePrint Archive, Report 2014/404 (2014)

    Google Scholar 

  7. Brenner, M., Wiebelitz, J., von Voigt, G., Smith, M.: Secret program execution in the cloud applying homomorphic encryption. In: Proceedings of the 5th IEEE International Conference on Digital Ecosystems and Technologies Conference (DEST), pp. 114–119 (2011)

    Google Scholar 

  8. Brenner, M., Perl, H., Smith, M.: How practical is homomorphically encrypted program execution? An implementation and performance evaluation. In: IEEE 11th International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom), pp. 375–382 (2012)

    Google Scholar 

  9. Clash of the clouds. The Economist. http://www.economist.com/displaystory.cfm?story_id=14637206;2009

  10. Damgård, I., Meldgaard, S., Nielsen, J.B.: Perfectly secure oblivious RAM without random oracles. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 144–163. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Dolev, S., Garay, J., Gilboa, N., Kolesnikov, V.: Swarming secrets. In: 47th Annual Allerton Conference, pp. 1438–1445 (2009)

    Google Scholar 

  12. Dolev, S., Gilboa, N., Li, X.: Accumulating automata and cascaded equations automata for communicationless information theoretically secure multi-party computation. In: Proceedings of the 3rd International Workshop on Security in Cloud Computing (SCC 2015), pp. 21–29. ACM, New York (2015)

    Google Scholar 

  13. Google Cloud Platform. https://cloud.google.com/storage/

  14. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, pp. 169–178. ACM (2009)

    Google Scholar 

  15. Gentry, C.: A fully homomorphic encryption scheme, Ph.D. dissertation, Stanford University (2009)

    Google Scholar 

  16. Gentry, C., Halevi, S.: Implementing Gentry’s fully-homomorphic encryption scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129–148. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Gentry, C., Goldman, K.A., Halevi, S., Julta, C., Raykova, M., Wichs, D.: Optimizing ORAM and using it efficiently for secure computation. In: De Cristofaro, E., Wright, M. (eds.) PETS 2013. LNCS, vol. 7981, pp. 1–18. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  18. Goldreich, O.: Towards a theory of software protection and simulation by oblivious RAMs. In: STOC (1987)

    Google Scholar 

  19. Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious RAMs. J. ACM 43, 431–473 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  20. Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Oblivious RAM simulation with efficient worst-case access overhead. In: ACM Cloud Computing Security Workshop (CCSW) (2011)

    Google Scholar 

  21. HOMOMORPHIC ENCRYPTION. http://sites.nyuad.nyu.edu/moma/projects.html

  22. Liu, C., Huang, Y., Shi, E., Katz, J., Hicks, M.: Automating efficient RAM-model secure computation. In: Proceedings of the 2014 IEEE Symposium on Security and Privacy (SP 2014), pp. 623–638. IEEE Computer Society, Washington, D.C. (2014)

    Google Scholar 

  23. 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)

    Chapter  Google Scholar 

  24. Mazonka, O., Kolodin, A.: A simple multi-processor computer based on subleq, arXiv preprint arxiv:1106.2593 (2011). http://da.vidr.cc/projects/subleq/

  25. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  26. Stefanov, E., Shi, E.: Multi-cloud oblivious storage. In: Proceedings of the 2013 ACM SIGSAC Conference on Computer and Communications Security (CCS 2013), NY, USA, pp. 247–258. ACM, New York (2013)

    Google Scholar 

  27. SUBLEQ. http://mazonka.com/subleq/

  28. Tehranipoor, M., Koushanfar, F.: A survey of hardware trojan taxonomy and detection. IEEE Des. Test Comput. 27(1), 10–25 (2010)

    Article  Google Scholar 

  29. Wang, X., Huang, Y., Chan, T.-H.H., Shelat, A., Shi, E.: SCORAM: oblivious RAM for secure computation. In: The 21st ACM Conference on Computer and Communications Security (CCS), Scottsdale, Arizona, USA, November 2014

    Google Scholar 

  30. Welch, L., Berlekamp, E.R.: Error correction for algebraic block codes, US Patent, 4 633 470 (1983)

    Google Scholar 

  31. Zhuravlev, D., Samoilovych, I., Orlovskyi, R., Bondarenko, I., Lavrenyuk, Y.: Encrypted program execution. In: IEEE 13th International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom), pp. 817—822 (2014)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Ben-Gurion University of the Negev, Beersheba, Israel

    Shlomi Dolev & Yin Li

Authors
  1. Shlomi Dolev
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  2. Yin Li
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Corresponding author

Correspondence to Yin Li .

Editor information

Editors and Affiliations

  1. Dept of Informatics, Ionian Univ, Kerkyra, Greece

    Ioannis Karydis

  2. Ionian University, Corfu, Greece

    Spyros Sioutas

  3. University of Glasgow, Glasgow, United Kingdom

    Peter Triantafillou

  4. Ionian University, Kerkyra, Greece

    Dimitrios Tsoumakos

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Dolev, S., Li, Y. (2016). Secret Shared Random Access Machine. In: Karydis, I., Sioutas, S., Triantafillou, P., Tsoumakos, D. (eds) Algorithmic Aspects of Cloud Computing. ALGOCLOUD 2015. Lecture Notes in Computer Science(), vol 9511. Springer, Cham. https://doi.org/10.1007/978-3-319-29919-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-29919-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29918-1

  • Online ISBN: 978-3-319-29919-8

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