Securely Outsourcing Exponentiations with Single Untrusted Program for Cloud Storage

  • Yujue Wang
  • Qianhong Wu
  • Duncan S. Wong
  • Bo Qin
  • Sherman S. M. Chow
  • Zhen Liu
  • Xiao Tan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8712)


Provable Data Possession (PDP) allows a file owner to outsource her files to a storage server such that a verifier can check the integrity of the outsourced file. Public verifiable PDP schemes allow any one other than the file owner to be a verifier. At the client side (file owner or verifier), a substantial number of modular exponentiations is often required. In this paper we make PDP more practical via proposing a protocol to securely outsource the (most generic) variable-exponent variable-base exponentiations in one untrusted program model. Our protocol demonstrates advantages in efficiency or privacy over existing protocols coping with only special cases in two or single untrusted program model. We then apply our generic protocol to Shacham-Waters PDP and a variant of Yuan-Yu PDP. The analyses show that our protocol makes PDP much more efficient at the client side.


Offloading computation Verifiable computation Modular exponentiation Provable Data Possession Cloud storage 


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  1. 1.
    Deng, H., Wu, Q., Qin, B., Chow, S.S.M., Domingo-Ferrer, J., Shi, W.: Tracing and Revoking Leaked Credentials: Accountability in Leaking Sensitive Outsourced Data. In: 9th ACM Symposium on Information, Computer and Communications Security (ASIACCS), pp. 425–443. ACM, New York (2014)CrossRefGoogle Scholar
  2. 2.
    Deng, H., Wu, Q., Qin, B., Domingo-Ferrer, J., Zhang, L., Liu, J., Shi, W.: Ciphertext-Policy Hierarchical Attribute-Based Encryption with Short Ciphertexts. Information Sciences 275, 370–384 (2014)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Deng, H., Wu, Q., Qin, B., Mao, J., Liu, X., Zhang, L., Shi, W.: Who is touching my cloud. In: Kutylowski, M., Vaidya, J. (eds.) ESORICS 2014. LNCS, vol. 8712, pp. 362–379. Springer, Heidelberg (2014)Google Scholar
  4. 4.
    Chow, S.S.M., Yiu, S.M., Hui, L.C.K., Chow, K.P.: Efficient Forward and Provably Secure ID-Based Signcryption Scheme with Public Verifiability and Public Ciphertext Authenticity. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. LNCS, vol. 2971, pp. 352–369. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Qin, B., Wang, H., Wu, Q., Liu, J., Domingo-Ferrer, J.: Simultaneous Authentication and Secrecy in Identity-Based Data Upload to Cloud. Cluster Computing 16, 845–859 (2013)CrossRefGoogle Scholar
  6. 6.
    Ateniese, G., Burns, R., Curtmola, R., Herring, J., Kissner, L., Peterson, Z., Song, D.: Provable Data Possession at Untrusted Stores. In: 14th ACM Conference on Computer and Communications Security (CCS), pp. 598–609. ACM, New York (2007)Google Scholar
  7. 7.
    Juels, A., Kaliski Jr., B.S.: PoRs: Proofs of Retrievability for Large Files. In: 14th ACM Conference on Computer and Communications Security (CCS), pp. 584–597. ACM, New York (2007)Google Scholar
  8. 8.
    Shacham, H., Waters, B.: Compact Proofs of Retrievability. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 90–107. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Wang, B., Chow, S.S.M., Li, M., Li, H.: Storing Shared Data on the Cloud via Security-Mediator. In: 33rd IEEE International Conference on Distributed Computing Systems (ICDCS), pp. 124–133 (2013)Google Scholar
  10. 10.
    Wang, C., Chow, S.S.M., Wang, Q., Ren, K., Lou, W.: Privacy-Preserving Public Auditing for Secure Cloud Storage. IEEE Transactions on Computers 62(2), 362–375 (2013)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Yuan, J., Yu, S.: Proofs of Retrievability with Public Verifiability and Constant Communication Cost in Cloud. In: International Workshop on Security in Cloud Computing, pp. 19–26. ACM, New York (2013)Google Scholar
  12. 12.
    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
  13. 13.
    Chen, X., Li, J., Ma, J., Tang, Q., Lou, W.: New Algorithms for Secure Outsourcing of Modular Exponentiations. In: Foresti, S., Yung, M., Martinelli, F. (eds.) ESORICS 2012. LNCS, vol. 7459, pp. 541–556. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Dijk, M., Clarke, D., Gassend, B., Suh, G., Devadas, S.: Speeding up Exponentiation using an Untrusted Computational Resource. Designs, Codes and Cryptography 39(2), 253–273 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Wang, H., Wu, Q., Qin, B., Domingo-Ferrer, J.: Identity-Based Remote Data Possession Checking in Public Clouds. Information Security, IET 8(2), 114–121 (2014)CrossRefGoogle Scholar
  16. 16.
    Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-Size Commitments to Polynomials and Their Applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177–194. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Benabbas, S., Gennaro, R., Vahlis, Y.: Verifiable Delegation of Computation over Large Datasets. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 111–131. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Li, J., Tan, X., Chen, X., Wong, D.S.: An Efficient Proof of Retrievability with Public Auditing in Cloud Computing. In: 5th International Conference on Intelligent Networking and Collaborative Systems (INCoS), pp. 93–98 (2013)Google Scholar
  19. 19.
    Ma, X., Li, J., Zhang, F.: Outsourcing Computation of Modular Exponentiations in Cloud Computing. Cluster Computing 16(4), 787–796 (2013)CrossRefGoogle Scholar
  20. 20.
    Tsang, P.P., Chow, S.S.M., Smith, S.W.: Batch Pairing Delegation. In: Miyaji, A., Kikuchi, H., Rannenberg, K. (eds.) IWSEC 2007. LNCS, vol. 4752, pp. 74–90. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  21. 21.
    Canard, S., Devigne, J., Sanders, O.: Delegating a Pairing Can Be Both Secure and Efficient. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 549–565. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  22. 22.
    Xu, G., Amariucai, G., Guan, Y.: Delegation of Computation with Verification Outsourcing: Curious Verifiers. In: ACM Symposium on Principles of Distributed Computing (PODC), pp. 393–402. ACM, New York (2013)Google Scholar
  23. 23.
    Gennaro, R., Gentry, C., Parno, B.: Non-interactive Verifiable Computing: Outsourcing Computation to Untrusted Workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  24. 24.
    Carter, H., Mood, B., Traynor, P., Butler, K.: Secure Outsourced Garbled Circuit Evaluation for Mobile Devices. In: 22nd USENIX Conference on Security, pp. 289–304. USENIX Association, Berkeley (2013)Google Scholar
  25. 25.
    Zhang, L.F., Safavi-Naini, R.: Private Outsourcing of Polynomial Evaluation and Matrix Multiplication Using Multilinear Maps. In: Abdalla, M., Nita-Rotaru, C., Dahab, R. (eds.) CANS 2013. LNCS, vol. 8257, pp. 329–348. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  26. 26.
    Wang, B., Li, M., Chow, S.S.M., Li, H.: Computing Encrypted Cloud Data Efficiently Under Multiple Keys. In: 4th IEEE Security and Privacy in Cloud Computing, co-located with IEEE Conference on Communications and Network Security (CNS), pp. 504–513 (2013)Google Scholar
  27. 27.
    Wang, B., Li, M., Chow, S.S.M., Li, H.: A Tale of Two Servers: Efficient Privacy-Preserving Computation over Cloud Data under Multiple Keys. In: 2nd IEEE Conference on Communications and Network Security, CNS (2014)Google Scholar
  28. 28.
    Chow, S.S.M., Lee, J.H., Subramanian, L.: Two-Party Computation Model for Privacy-Preserving Queries over Distributed Databases. In: Network and Distributed System Security Symposium, NDSS (2009)Google Scholar
  29. 29.
    Nguyen, P., Shparlinski, I.E., Stern, J.: Distribution of Modular Sums and the Security of the Server Aided Exponentiation. In: Cryptography and Computational Number Theory. Progress in Computer Science and Applied Logic, vol. 20, pp. 331–342. Birkhäuser, Basel (2001)CrossRefGoogle Scholar
  30. 30.
    Boyko, V., Peinado, M., Venkatesan, R.: Speeding up Discrete Log and Factoring Based Schemes via Precomputations. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 221–235. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  31. 31.
    Boneh, D., Lynn, B., Shacham, H.: Short Signatures from the Weil Pairing. Journal of Cryptology 17(4), 297–319 (2004)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yujue Wang
    • 1
    • 2
    • 3
  • Qianhong Wu
    • 3
    • 1
  • Duncan S. Wong
    • 2
  • Bo Qin
    • 4
  • Sherman S. M. Chow
    • 5
  • Zhen Liu
    • 2
  • Xiao Tan
    • 2
  1. 1.Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education, School of ComputerWuhan UniversityWuhanChina
  2. 2.Department of Computer ScienceCity University of Hong KongHong Kong
  3. 3.School of Electronic and Information EngineeringBeihang UniversityBeijingChina
  4. 4.School of InformationRenmin University of ChinaBeijingChina
  5. 5.Department of Information EngineeringChinese University of Hong KongHong Kong

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