Abstract
Fully homomorphic cryptosystems allow the evaluation of arbitrary Boolean circuits on encrypted inputs and therefore have very important applications in the area of secure multi-party computation. Since every computable function can be expressed as a Boolean circuit, it is theoretically clear how to achieve function evaluation on encrypted inputs. However, the transformation to Boolean circuits is not trivial in practice. In this work, we design such a transformation for certain functions, i.e., we propose algorithms and protocols which make use of fully homomorphic encryption in order to achieve privacy-preserving multi-party reconciliation on ordered sets. Assuming a sufficiently efficient encryption scheme, our solution performs much better than existing approaches in terms of communication overhead and number of homomorphic operations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd SFCS, pp. 160–164. IEEE Computer Society, Washington, DC (1982)
Meyer, U., Wetzel, S., Ioannidis, S.: Distributed privacy-preserving policy reconciliation. In: ICC, pp. 1342–1349 (2007)
Meyer, U., Wetzel, S., Ioannidis, S.: New Advances on Privacy-Preserving Policy Reconciliation. In: IACR eprint 2010/64, http://eprint.iacr.org/2010/064
Mayer, D.A., Teubert, D., Wetzel, S., Meyer, U.: Implementation and Performance Evaluation of Privacy-Preserving Fair Reconciliation Protocols on Ordered Sets. In: First ACM CODASPY (2011)
Freedman, M.J., Nissim, K., Pinkas, B.: Efficient Private Matching and Set Intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004)
Neugebauer, G., Meyer, U., Wetzel, S.: Fair and Privacy-Preserving Multi-party Protocols for Reconciling Ordered Input Sets. In: Burmester, M., Tsudik, G., Magliveras, S., Ilić, I. (eds.) ISC 2010. LNCS, vol. 6531, pp. 136–151. Springer, Heidelberg (2011)
Neugebauer, G., Meyer, U., Wetzel, S.: Fair and Privacy-Preserving Multi-Party Protocols for Reconciling Ordered Input Sets, Extended Version (2011), http://eprint.iacr.org/2011/200
Kissner, L., Song, D.: Privacy-preserving set operations. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005)
Cheon, J.H., Jarecki, S., Seo, J.H.: Multi-party privacy-preserving set intersection with quasi-linear complexity. Cryptology ePrint Archive, Report 2010/512 (2010)
Li, R., Wu, C.: An unconditionally secure protocol for multi-party set intersection. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 226–236. Springer, Heidelberg (2007)
Sathya Narayanan, G., Aishwarya, T., Agrawal, A., Patra, A., Choudhary, A., Pandu Rangan, C.: Multi party distributed private matching, set disjointness and cardinality of set intersection with information theoretic security. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds.) CANS 2009. LNCS, vol. 5888, pp. 21–40. Springer, Heidelberg (2009)
Patra, A., Choudhary, A., Rangan, C.P.: Selected areas in cryptography, pp. 71–91. Springer, Heidelberg (2009)
Frikken, K.: Privacy-Preserving Set Union. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 237–252. Springer, Heidelberg (2007)
Hong, J., Kim, J.W., Kim, J., Park, K., Cheon, J.H.: Constant-round privacy preserving multiset union. IACR Cryptology ePrint Archive, 138 (2011)
Mayer, D., Neugebauer, G., Meyer, U., Wetzel, S.: Enabling fair and privacy-preserving applications using reconciliation protocols on ordered sets. In: 34th IEEE Sarnoff Symposium. IEEE, Princeton (2011)
Gentry, C.: Fully Homomorphic Encryption using Ideal Lattices. In: Proceedings of the 41st STOC, pp. 169–178. ACM, New York (2009)
van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully Homomorphic Encryption over the Integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)
Goldreich, O., Micali, S.M., Wigderson, A.: How to play ANY mental game. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, STOC 1987, pp. 218–229. ACM, New York (1987)
Goldwasser, S., Micali, S.: Probabilistic encryption & how to play mental poker keeping secret all partial information. In: Proceedings of the 14th STOC, pp. 365–377. ACM Press, New York (1982)
Wegener, I.: The complexity of Boolean functions. John Wiley & Sons, Inc., New York (1987)
Weingarten, F.: Evaluating the Use of Fully Homomorphic Encryption in Secure Multi-Party Computation. Diploma Thesis, Research Group IT-Security, RWTH Aachen University (2011)
Myers, S., Sergi, M., Shelat, A.: Threshold fully homomorphic encryption and secure computation, vol. 2011 (2011)
Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University, Stanford, CA, USA, AAI3382729 (2009)
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Weingarten, F., Neugebauer, G., Meyer, U., Wetzel, S. (2013). Privacy-Preserving Multi-party Reconciliation Using Fully Homomorphic Encryption. In: Lopez, J., Huang, X., Sandhu, R. (eds) Network and System Security. NSS 2013. Lecture Notes in Computer Science, vol 7873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38631-2_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-38631-2_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38630-5
Online ISBN: 978-3-642-38631-2
eBook Packages: Computer ScienceComputer Science (R0)