Abstract
Order-preserving encryption (OPE) is an encryption scheme with the property that the ordering of the plaintexts carry over to the ciphertexts. This primitive is particularly useful in the setting of encrypted databases because it enables efficient range queries over encrypted data. Given its practicality and usefulness in the design of databases on encrypted data, OPE’s popularity is growing. Unfortunately, nearly all computationally efficient OPE constructions are vulnerable against ciphertext frequency-leakage, which allows for inferring the underlying plaintext frequency. To overcome this weakness, Kerschbaum recently proposed a security model, designed a frequency-hiding OPE scheme, and analyzed its security in the programmable random oracle model (CCS 2015).
In this work, we demonstrate that Kerschbaum’s definition is imprecise and using its natural interpretation, we describe an attack against his scheme. We generalize our attack and show that his definition is, in fact, not satisfiable. The basic idea of our impossibility result is to show that any scheme satisfying his security notion is also IND-CPA-secure, which contradicts the very nature of OPE. As a consequence, no such scheme can exist. To complete the picture, we rule out the imprecision in the security definition and show that a slight adaption of Kerschbaum’s tree-based scheme fulfills it.
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References
Arasu, A., Blanas, S., Eguro, K., Kaushik, R., Kossmann, D., Ramamurthy, R., Venkatesan, R.: Orthogonal security with cipherbase. In: Proceedings of the Biennial Conference on Innovative Data Systems Research (CIDR 2013) (2013)
Bellare, M., Keelveedhi, S., Ristenpart, T.: DupLESS: server-aided encryption for deduplicated storage. In: Proceedings of the USENIX Security Symposium (USENIX 2013), pp. 179–194. USENIX Association (2013)
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). https://doi.org/10.1007/978-3-642-01001-9_13
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). https://doi.org/10.1007/978-3-642-22792-9_33
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). https://doi.org/10.1007/978-3-662-46803-6_19
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). https://doi.org/10.1007/978-3-662-52993-5_24
Durak, F.B., DuBuisson, T.M., Cash, D.: What else is revealed by order-revealing encryption? In: Proceedings of the Conference on Computer and Communications Security (CCS 2016), pp. 1155–1166. ACM Press (2016)
Grubbs, P., McPherson, R., Naveed, M., Ristenpart, T., Shmatikov, V.: Breaking web applications built on top of encrypted data. In: Proceedings of the Conference on Computer and Communications Security (CCS 2016), pp. 1353–1364. ACM Press (2016)
Grubbs, P., Sekniqi, K., Bindschaedler, V., Naveed, M., Ristenpart, T.: Leakage-abuse attacks against order-revealing encryption. In: Proceedings of the IEEE Symposium on Security and Privacy (S&P 2017). IEEE Computer Society Press (2017)
He, W., Akhawe, D., Jain, S., Shi, E., Song, D.: ShadowCrypt: encrypted web applications for everyone. In: Proceedings of the Conference on Computer and Communications Security (CCS 2014), pp. 1028–1039. ACM Press (2014)
Kerschbaum, F.: Frequency-hiding order-preserving encryption. In: Proceedings of the Conference on Computer and Communications Security (CCS 2015), pp. 656–667. ACM Press (2015)
Kerschbaum, F., Schroepfer, A.: Optimal average-complexity ideal-security order-preserving encryption. In: Proceedings of the Conference on Computer and Communications Security (CCS 2014), pp. 275–286. ACM Press (2014)
Lau, B., Chung, S., Song, C., Jang, Y., Lee, W., Boldyreva, A.: Mimesis aegis: a mimicry privacy shield–a system’s approach to data privacy on public cloud. In: Proceedings of the USENIX Security Symposium (USENIX 2014), pp. 33–48. USENIX Association (2014)
Lewi, K., Wu, D.J.: Order-revealing encryption: new constructions, applications, and lower bounds. In: Proceedings of the Conference on Computer and Communications Security (CCS 2016), pp. 1167–1178. ACM Press (2016)
Naveed, M., Kamara, S., Wright, C.V.: Inference attacks on property-preserving encrypted databases. In: Proceedings of the Conference on Computer and Communications Security (CCS 2015), pp. 644–655. ACM Press (2015)
Popa, R.A., Li, F.H., Zeldovich, N.: An ideal-security protocol for order-preserving encoding. In: Proceedings of the IEEE Symposium on Security and Privacy (S&P 2013), pp. 463–477. IEEE Computer Society Press (2013)
Popa, R.A., Redfield, C.M.S., Zeldovich, N., Balakrishnan, H.: CryptDB: protecting confidentiality with encrypted query processing. In: Proceedings of the ACM Symposium on Operating Systems Principles (SOSP 2011), pp. 85–100. ACM Press (2011)
Popa, R.A., Stark, E., Valdez, S., Helfer, J., Zeldovich, N., Balakrishnan, H.: Building web applications on top of encrypted data using Mylar. In: Proceedings of the USENIX Symposium on Networked Systems Design and Implementation (NSDI 2014), pp. 157–172. USENIX Association (2014)
Roche, D.S., Apon, D., Choi, S.G., Yerukhimovich, A.: POPE: partial order preserving encoding. In: Proceedings of the Conference on Computer and Communications Security (CCS 2016), pp. 1131–1142. ACM Press (2016)
Song, D.X., Wagner, D., Perrig, A.: Practical techniques for searches on encrypted data. In: Proceedings of the IEEE Symposium on Security and Privacy (S&P 2000), pp. 44–55. IEEE Computer Society Press (2000)
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). https://doi.org/10.1007/978-3-662-45608-8_3
Acknowledgements
This research is based upon work supported by the German research foundation (DFG) through the collaborative research center 1223, by the German Federal Ministry of Education and Research (BMBF) through the Center for IT-Security, Privacy and Accountability (CISPA), and by the state of Bavaria at the Nuremberg Campus of Technology (NCT). NCT is a research cooperation between the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) and the Technische Hochschule Nürnberg Georg Simon Ohm (THN). Dominique Schröder is supported by the German Federal Ministry of Education and Research (BMBF) through funding for the project PROMISE. Finally, we thank the reviewers for their helpful comments and our shepherd for the excellent and valuable feedback, which improved the paper.
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Maffei, M., Reinert, M., Schröder, D. (2018). On the Security of Frequency-Hiding Order-Preserving Encryption. In: Capkun, S., Chow, S. (eds) Cryptology and Network Security. CANS 2017. Lecture Notes in Computer Science(), vol 11261. Springer, Cham. https://doi.org/10.1007/978-3-030-02641-7_3
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