Abstract
One of the major issues in security is how to protect the privacy of multimedia big data on cloud systems. Homomorphic Encryption (HE) is increasingly regarded as a way to maintain user privacy on the untrusted cloud. However, HE is not widely used in machine learning and signal processing communities because the HE libraries are currently supporting only simple operations like integer addition and multiplication. It is known that division and other advanced operations cannot feasibly be designed and implemented in HE libraries. Therefore, we propose a novel approach to building a practical matrix inversion operation using approximation theory on HE. The approximated inversion operation is applied to reduce unwanted noise on encrypted images. Our research also suggests the efficient computation techniques for encrypted matrices. We conduct the experiment with real binary images using open source library of HE.
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References
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, vol. 9, pp. 169–178 (2009)
Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. ACM Trans. Comput. Theory (TOCT) 6(3), 13 (2014)
Halevi, S., Shoup, V.: Algorithms in HElib. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 554–571. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_31
Lu, W., Kawasaki, S., Sakuma, J.: Using fully homomorphic encryption for statistical analysis of categorical, ordinal and numerical data. In: IACR Cryptology ePrint Archive, 2016, 1163 (2016)
Halevi, S., Shoup, V.: HElib. https://github.com/shaih/HElib
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178 (2009)
Dahl, M., Ning, C., Toft, T.: On secure two-party integer division. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 164–178. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32946-3_13
Veugen, T.: Encrypted integer division. In: 2010 IEEE International Workshop on Information Forensics and Security (WIFS). IEEE (2010)
Veugen, T.: Encrypted integer division and secure comparison. Int. J. Appl. Cryptogr. 3(2), 166–180 (2014)
Hall, R., Fienberg, S.E., Nardi, Y.: Secure multiple linear regression based on homomorphic encryption. J. Off. Stat. 27(4), 669 (2011)
Nikolaenko, V., Weinsberg, U., Ioannidis, S., Joye, M., Boneh, D., Taft, N.: Privacy-preserving ridge regression on hundreds of millions of records. In: 2013 IEEE Symposium on Security and Privacy (SP), pp. 334–348. IEEE, May 2013
Yao, A.C.: Protocols for secure computations. In: 23rd Annual Symposium on Foundations of Computer Science, SFCS 2008, pp. 160–164. IEEE, November 1982
Yao, A.C.C.: How to generate and exchange secrets. In: 27th Annual Symposium on Foundations of Computer Science, pp. 162–167. IEEE, October 1986
Graepel, T., Lauter, K., Naehrig, M.: ML confidential: machine learning on encrypted data. In: Kwon, T., Lee, M.-K., Kwon, D. (eds.) ICISC 2012. LNCS, vol. 7839, pp. 1–21. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37682-5_1
Bost, R., Popa, R.A., Tu, S., Goldwasser, S.: Machine learning classification over encrypted data. In: NDSS, February 2015
Lu, W., Kawasaki, S., Sakuma, J.: Using fully homomorphic encryption for statistical analysis of categorical, ordinal and numerical data. IACR Cryptology ePrint Archive 2016, 1163 (2016)
Acknowledgments
This research was supported by the MSIP (Ministry of Science, ICT & Future Planning), Korea, under the IITP (Institute for Information & communications Technology Promotion) support program (2017-0-00545).
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Lee, S., Yoon, J. (2018). Model Parameter Estimation and Inference on Encrypted Domain: Application to Noise Reduction in Encrypted Images. In: Kang, B., Kim, T. (eds) Information Security Applications. WISA 2017. Lecture Notes in Computer Science(), vol 10763. Springer, Cham. https://doi.org/10.1007/978-3-319-93563-8_10
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DOI: https://doi.org/10.1007/978-3-319-93563-8_10
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