Security of Stateful Order-Preserving Encryption

  • Kee Sung Kim
  • Minkyu Kim
  • Dongsoo Lee
  • Je Hong Park
  • Woo-Hwan Kim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10779)


Most of the proposed order-preserving encryption (OPE) schemes in the early stage of development including the first provably secure one are stateless and work efficiently, but guarantee only weak security. Additionally, subsequent works have shown that an ideal security notion IND-OCPA can be achieved using statefulness, ciphertexts mutability, and interactivity between client and server. Though such properties hinder availability of IND-OCPA secure OPE schemes, the only definitively known result is the impossibility of constructing a feasible IND-OCPA secure OPE scheme without ciphertext mutability. In this work, we study the security that can be fulfilled by only statefulness, from a viewpoint different from the existing research. We first consider a new security notion, called \(\delta \)-IND-OCPA, which is a natural relaxation of IND-OCPA. In comparison to IND-OCPA in which ciphertexts reveal no additional information beyond the order of the plaintexts, our notion can quantify the rate of plaintext bits that are leaked. To show achievability of our notion, we construct a new \(\delta \)-IND-OCPA secure OPE scheme. The proposed scheme is stateful and non-interactive, but does not require ciphertext mutation. Through several experiments, we show that our construction is also feasible and that has an advantage in the correlation analysis compared with the IND-OCPA secure scheme.


Order-preserving encryption Outsourced database Cloud computing 



This work was supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korean government (MSIT) (No. R0101-16-0301).

Supplementary material


  1. 1.
    Boost C++ Libraries.
  2. 2.
    The GNU Multiple Precision Arithmetic Library.
  3. 3.
    The MariaDB Foundation.
  4. 4.
  5. 5.
    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
  6. 6.
    Boldyreva, A., Chenette, N., O’Neill, A.: Order-preserving encryption revisited: improved security analysis and alternative solutions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 578–595. Springer, Heidelberg (2011). CrossRefGoogle Scholar
  7. 7.
    Boneh, D., Lewi, K., Raykova, M., Sahai, A., Zhandry, M., Zimmerman, J.: Semantically secure order-revealing encryption: multi-input functional encryption without obfuscation. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 563–594. Springer, Heidelberg (2015). Google Scholar
  8. 8.
    Chenette, N., Lewi, K., Weis, S.A., Wu, D.J.: Practical order-revealing encryption with limited leakage. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 474–493. Springer, Heidelberg (2016). CrossRefGoogle Scholar
  9. 9.
    Grubbs, P., Sekniqi, K., Bindschaedler, V., Naveed, M., Ristenpart, T.: Leakage-abuse attacks against order-revealing encryption. In: 2017 IEEE Symposium on Security and Privacy (SP), pp. 655–672. IEEE Press, New York (2017).
  10. 10.
    Katz, J., Yung, M.: Characterization of security notions for probabilistic private-key encryption. J. Cryptol. 19(1), 67–96 (2006). MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kellaris, G., Kollios, G., Nissim, L., O’Neill, A.: Generic attacks on secure outsourced database. In: 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 1329–1340. ACM Press, New York (2016).
  12. 12.
    Kerschbaum, F.: Frequency-hiding order-preserving encryption. In: 22nd ACM SIGSAC Conference on Computer and Communications Security, pp. 656–667. ACM Press, New York (2015).
  13. 13.
    Kerschbaum, F., Schröepfer, A.: Optimal average-complexity ideal-security order-preserving encryption. In: 2014 ACM SIGSAC Conference on Computer and Communications Security, pp. 275–286. ACM Press, New York (2014).
  14. 14.
    Lacharité, M.-S., Minaud, B., Paterson, K.G.: Improved reconstruction attacks on encrypted data using range query leakage. In: 2018 IEEE Symposium on Security and Privacy (SP), pp. 19–36. IEEE Press, New York (2018).
  15. 15.
    Naveed, M., Kamara, S., Wright, C.V.: Inference attacks on property-preserving encrypted databases. In: 22nd ACM SIGSAC Conference on Computer and Communications Security, pp. 644–655. ACM Press, New York (2015).
  16. 16.
    Popa, R.A., Li, F.H., Zeldovich, N.: An ideal-security protocol for order-preserving encoding. In: 2013 IEEE Symposium on Security and Privacy (SP), pp. 463–477. IEEE Press, New York (2013).
  17. 17.
    Popa, R.A., Redfield, C.M.S., Zeldovich, N., Balakrishnan, H.: CryptDB: protecting confidentiality with encrypted query processing. In: Twenty-Third ACM Symposium on Operating Systems Principles, pp. 85–100. ACM Press, New York (2011).
  18. 18.
    Teranishi, I., Yung, M., Malkin, T.: Order-preserving encryption secure beyond one-wayness. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 42–61. Springer, Heidelberg (2014). Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Kee Sung Kim
    • 1
  • Minkyu Kim
    • 1
  • Dongsoo Lee
    • 1
  • Je Hong Park
    • 1
  • Woo-Hwan Kim
    • 1
  1. 1.National Security Research InstituteDaejeonSouth Korea

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