Outsource-Secured Calculation of Closest Pair of Points

  • Chandrasekhar Kuruba
  • Kethzi Gilbert
  • Prabhav Sidhaye
  • Gaurav PareekEmail author
  • Purushothama Byrapura Rangappa
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 625)


Outsourcing data/computation intensive tasks to servers having great computing power and data analytics skills is gaining popularity. While this outsourcing model, due to its cost efficiency, has been widely used by numerous clients, making sure that loss of privacy and integrity of results are not affected remain as challenges, especially in public cloud infrastructure. For addressing these challenges, clients must outsource their data in a privacy-preserving and verifiable manner. The cost of assuring both privacy of data and correctness of results must impose cost marginally less than the cost of actual computation. In this paper, we address the problem of secure outsourcing of Closest Pair of Points computation. Finding Closest Pair of Points is central to many complex applications like clustering. Our scheme involves the client sending encrypted points to the server and receiving the result which is a pair of points (with smallest distance between them) along with a proof of correctness. Data encryption done to ensure privacy of input points must be such that the encrypted points retain the same order as the original points. For this, we designed and used a novel encryption scheme which is additively homomorphic and order-preserving for encrypting input points in our protocol. The protocol requires the server to compute almost all distances to be able to provide the proof of it having computed the results honestly.


Verifiable computing Secure outsourcing Closest-pair-of points Cloud security 


  1. 1.
    Benjamin, D., Atallah, M.: Private and cheating-free outsourcing of algebraic computations. In: 2008 Sixth Annual Conference on Privacy, Security and Trust (2008)Google Scholar
  2. 2.
    Boldyreva, A., Chenette, N., Lee, Y., O’Neill, A.: Order-preserving symmetric encryption. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 224–241. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Tu, S., Kaashoek, M., Madden, S., Zeldovich, N.: Processing analytical queries over encrypted data. Proc. VLDB Endow. 6, 289–300 (2013)CrossRefGoogle Scholar
  4. 4.
    Ateniese, G., Burns, R., Curtmola, R., Herring, J., Kissner, L., Peterson, Z., Song, D.: Provable data possession at untrusted stores. In: Proceedings of the 14th ACM Conference on Computer and Communications Security (CCS 2007) (2007)Google Scholar
  5. 5.
    Purushothama, B., Amberker, B.: Efficient query processing on outsourced encrypted data in cloud with privacy preservation. In: 2012 International Symposium on Cloud and Services Computing (2012)Google Scholar
  6. 6.
    Vyas, R., Singh, A., Singh, J., Soni, G., Purushothama, B.R.: Design of an efficient verification scheme for correctness of outsourced computations in cloud computing. In: Abawajy, J.H., Mukherjea, S., Thampi, S.M., Ruiz-Martínez, A. (eds.) SSCC 2015. CCIS, vol. 536, pp. 66–77. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-22915-7_7 CrossRefGoogle Scholar
  7. 7.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 223. Springer, Heidelberg (1999)Google Scholar
  8. 8.
    Atallah, M.J., Pantazopoulos, K.N., Rice, J.R., Spafford, E.E.: Secure outsourcing of scientific computations. Adv. Comput. 54, 215–272 (2002)CrossRefGoogle Scholar
  9. 9.
    Seitkulov, Y.N.: New methods of secure outsourcing of scientific computations. J. Supercomputing 65(1), 469–482 (2013)CrossRefGoogle Scholar
  10. 10.
    Hohenberger, S., Lysyanskaya, A.: How to securely outsource cryptographic computations. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 264–282. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Tysowski, P.K.: Highly Scalable and Secure Mobile Applications in Cloud Computing Systems (Doctoral dissertation, University of Waterloo) (2013)Google Scholar
  12. 12.
    Hu, X., Tang, C.: Secure outsourced computation of the characteristic polynomial and eigenvalues of matrix. J. Cloud Comput. 4(1), 1–6 (2015)CrossRefGoogle Scholar
  13. 13.
    Mohassel, P.: Efficient and Secure Delegation of Linear Algebra. IACR Cryptology ePrint Archive, 605 (2011)Google Scholar
  14. 14.
    Wang, C., Ren, K., Wang, J., Urs, K.M.R.: Harnessing the cloud for securely solving large-scale systems of linear equations. In: 31st International Conference on Distributed Computing Systems (ICDCS), pp. 549–558. IEEE (2011)Google Scholar
  15. 15.
    Fiore, D., Gennaro, R.: Publicly verifiable delegation of large polynomials and matrix computations, with applications. In: Proceedings of the 2012 ACM Conference on Computer and Communications Security, pp. 501–512. ACM (2012)Google Scholar
  16. 16.
    Jagannathan, G., Wright, R.N.: Privacy-preserving distributed k-means clustering over arbitrarily partitioned data. In: Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, pp. 593–599. ACM (2005)Google Scholar
  17. 17.
    Bunn, P., Ostrovsky, R.: Secure two-party k-means clustering. In: Proceedings of the 14th ACM Conference on Computer and Communications Security, pp. 486–497. ACM (2007)Google Scholar
  18. 18.
    Liu, D., Bertino, E., Yi, X.: Privacy of outsourced k-means clustering. In: Proceedings of the 9th ACM Symposium on Information, Computer and Communications Security, pp. 123–134. ACM (2014)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  • Chandrasekhar Kuruba
    • 1
  • Kethzi Gilbert
    • 1
  • Prabhav Sidhaye
    • 1
  • Gaurav Pareek
    • 1
    Email author
  • Purushothama Byrapura Rangappa
    • 1
  1. 1.National Institute of TechnologyPondaIndia

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