Skip to main content
SpringerLink
Log in

EPiC: efficient privacy-preserving counting for MapReduce

  • Published:
Computing Aims and scope Submit manuscript

Abstract

In the face of an untrusted cloud infrastructure, outsourced data needs to be protected. We present EPiC, a practical protocol for the privacy-preserving evaluation of a fundamental operation on data sets: frequency counting. In an encrypted outsourced data set, a cloud user can specify a pattern, and the cloud will count the number of occurrences of this pattern in an oblivious manner. A pattern is expressed as a Boolean formula on the fields of data records and can specify values counting, value comparison, range counting, and conjunctions/disjunctions of field values. We show how a general pattern, defined by a Boolean formula, is arithmetized into a multivariate polynomial and used in EPiC. To increase the performance of the system, we introduce a new privacy-preserving encoding with “somewhat homomorphic” properties. The encoding is highly efficient in our particular counting scenario. Besides a formal analysis where we prove EPiC ’s privacy, we also present implementation and evaluation results. We specifically target Google’s prominent MapReduce paradigm as offered by major cloud providers. Our evaluation performed both locally and in Amazon’s public cloud with up to 1 TByte data sets shows only a modest overhead of \(20\%\) compared to non-private counting, attesting to EPiC ’s efficiency.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. Domain size \(|\mathcal {D}_k|\) indicates the number of different values a field can take.

  2. \(\Vert X\Vert =\lceil \log _2|X|\rceil \) denotes size in bits of X.

References

  1. Amazon Elastic MapReduce. http://aws.amazon.com/elasticmapreduce/

  2. Apache Hadoop (2010) http://hadoop.apache.org/

  3. Babai L, Fortnow L (1991) Arithmetization: a new method in structural complexity theory. In: Computational complexity, pp 41–66, ISSN: 1016-3328

  4. Boneh D, DiCrescenzo G, Ostrovsky R, Persiano G (2004) Public key encryption with keyword search. In: Proceedings of Eurocrypt, pp 506–522. Barcelona, Spain

  5. Brakerski Z, Vaikuntanathan V (2011) Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway P (eds) Advances in cryptology—CRYPTO 2011, pp 505–524. Springer, Berlin. ISBN: 978-3-642-22792-9

  6. Dean J, Ghemawat S (2004) MapReduce: simplified data processing on large clusters. In: Proceedings of symposium on operating system design and implementation, pp 137–150. San Francisco, USA

  7. Dwork C (2006) Differential privacy. In: Proceedings of colloquium automata, languages and programming, pp 1–12, Venice, Italy, 2006. ISBN: 3-540-35907-9

  8. Gentry C (2009) Fully homomorphic encryption using ideal lattices. In: Proceedings of the forty-first annual ACM symposium on theory of computing, STOC ’09, pp 169–178. New York, NY, 2009. ACM. ISBN: 978-1-60558-506-2

  9. Gentry C, Halevi S (2011) Implementing Gentry’s fully-homomorphic encryption scheme. In: Advances in cryptology—EUROCRYPT 2011, pp 129–148. Tallinn, Estonia, 2011. Springer, Berlin. ISBN: 78-3-642-20464-7

  10. Google (2010) A new approach to China. http://googleblog.blogspot.com/2010/01/new-approach-to-china.html

  11. Hadoop. Powered by Hadoop, list of applications using Hadoop MapReduce (2011). http://wiki.apache.org/hadoop/PoweredBy

  12. Hoffstein J, Pipher J, Silverman JH (1998) NTRU: a ring-based public key cryptosystem. In: Algorithmic number theory, third international symposium, ANTS-III, Portland, Oregon, USA, June 21–25, 1998, proceedings, pp. 267–288

  13. Kamara S, Raykova M (2013) Parallel homomorphic encryption. In: Adams AA, Brenner M, Smith M (eds) Financial cryptography and data security, pp 213–225. Springer, Berlin. ISBN: 978-3-642-41320-9

  14. Katz J, Lindell Y (2007) Introduction to modern cryptography (Chapman & Hall/CRC Cryptography and network security series). Chapman & Hall/CRC

  15. Lauter K, Naehrig N, Vaikuntanathan V (2011) Can homomorphic encryption be practical? In: Proceedings of ACM workshop on cloud computing security. Chicago

  16. Lepoint T, Tibouchi M (2015) Cryptanalysis of a (somewhat) additively homomorphic encryption scheme used in PIR. In: Financial cryptography and data security—FC 2015 international workshops, BITCOIN, WAHC, and Wearable, San Juan, Puerto Rico, January 30, 2015, Revised Selected Papers, pp 184–193

  17. Rocha F, Correia M (2011) Lucy in the sky without diamonds: stealing confidential data in the cloud. In: Proceedings of international workshop on dependability of clouds, data centers and virtual computing y environments, pp 129–134, Hong Kong, China

  18. Shamir A (1992) IP = PSPACE. J ACM 39(4):869–877. ISSN: 0004-5411

  19. Song D, Wagner D, Perrig A (2000) Practical techniques for searches on encrypted data. In: Proceedings of symposium on security and privacy, pp 44–55, Berkeley, USA

  20. Techcrunch. Google confirms that it fired engineer for breaking internal privacy policies (2010). http://techcrunch.com/2010/09/14/google-engineer-spying-fired/

  21. The Telegraph (2011) Patient records go online in data cloud. http://bit.ly/1yb28bw

  22. Trostle J, Parrish A (2010) Efficient computationally private information retrieval from anonymity or trapdoor groups. In: Proceedings of conference on information security, pp 114–128, Boca Raton, USA, 2010. ISBN: 978-3-642-18177-1

  23. Vaikuntanathan V (2011) Computing blindfolded: new developments in fully homomorphic encryption. In: Proceedings of the 2011 IEEE 52nd annual symposium on foundations of computer science, FOCS’11, pp 5–16, Washington, DC, USA 2011. ISBN: 978-0-7695-4571-4

  24. van Dijk M, Gentry C, Halevi S, Vaikuntanathan V (2010) Fully homomorphic encryption over the integers. In: Proceedings of international conference on theory and applications of cryptographic techniques, EUROCRYPT’10, pp 24–43, Monaco, 2010. Springer, Berlin. ISBN: 3-642-13189-1

  25. Vo-Huu TD, Blass E-O, Noubir G EPiC Source Code. http://www.ccs.neu.edu/home/noubir/projects/epic

  26. Whittaker Z (2011) Microsoft admits Patriot Act can access EU-based cloud data. Zdnet http://www.zdnet.com/

Download references

Acknowledgements

This work was partially supported by NSF Grant 1218197.

Author information

Authors and Affiliations

  1. Northeastern University, Boston, MA, 02115, USA

    Triet Dang Vo-Huu & Guevara Noubir

  2. Airbus Group Innovations, 81663, Munich, Germany

    Erik-Oliver Blass

Authors
  1. Triet Dang Vo-Huu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik-Oliver Blass
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guevara Noubir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Triet Dang Vo-Huu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vo-Huu, T.D., Blass, EO. & Noubir, G. EPiC: efficient privacy-preserving counting for MapReduce. Computing 101, 1265–1286 (2019). https://doi.org/10.1007/s00607-018-0634-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00607-018-0634-5

Keywords

Mathematics Subject Classification

Search

Navigation