Abstract
Problems involving the classification of sensitive cloud data, such as medical or financial records, can be solved using a convolutional neural network (CNN) approach. Data privacy and security, however, require extra care. Homomorphic encryption is a potential security solution to allow CNNs to classify cypher data. The convolution layer, for example, is a computation that can be fully homomorphically evaluated; however, non-linear functions, such as the activation layer, cannot be fully homomorphically assessed since they do not follow a linear pattern. This paper uses low-degree polynomials to approximate these non-linear functions. We compare various polynomial approximation approaches to achieve the optimal approximation function for activation functions such as Relu. Finally, we use a proposed CNN and the MNIST dataset to demonstrate the effectiveness of our approximation functions. The resulting proposed CNN achieved a 99.80% accuracy rate.
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References
Chou, E., Beal, J., Levy, D., Yeung, S., Haque, A., Fei-Fei, L.: Faster CryptoNets: leveraging sparsity for real-world encrypted inference. arXiv, November 2018. https://arxiv.org/abs/1811.09953. Accessed 14 Nov 2021
Denning, D.E.R.: Cryptography and data security (1982)
Yassein, H.R., Al-Saidi, N.M.G., Farhan, A.K.: A new NTRU cryptosystem outperforms three highly secured NTRU-analog systems through an innovational algebraic structure. J. Discret. Math. Sci. Cryptogr. (2020). https://doi.org/10.1080/09720529.2020.1741218
Kadhim, A.F., Kamal, Z.A.: Generating dynamic S-box based on particle swarm optimization and chaos theory for AES. Iraqi J. Sci. 59(3), 1733–1745 (2018). https://doi.org/10.24996/IJS.2018.59.3C.18
Alhudhaif, A., Ahmad, M., Alkhayyat, A., Tsafack, N., Farhan, A.K., Ahmed, R.: Block cipher nonlinear confusion components based on new 5-D hyperchaotic system. IEEE Access 9, 87686–87696 (2021). https://doi.org/10.1109/ACCESS.2021.3090163
Zahid, A.H., et al.: Efficient dynamic S-box generation using linear trigonometric transformation for security applications. IEEE Access 9, 98460–98475 (2021). https://doi.org/10.1109/ACCESS.2021.3095618
Podschwadt, R., Takagi, D., Hu, P.: SoK: privacy-preserving deep learning with homomorphic encryption (2021). http://arxiv.org/abs/2112.12855
Yao, A.C.C.: How to generate and exchange secrets. In: Annual Symposium Foundations of Computer Science, no. 1, pp. 162–167 (1986). https://doi.org/10.1109/sfcs.1986.25
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979). https://doi.org/10.1145/359168.359176
Gentry, C.S.: Fully homomorphic encryption from approximate ideal lattices. Ruan Jian Xue Bao J. Softw. 26(10), 2696–2719 (2015). https://doi.org/10.13328/j.cnki.Jos.004808
Cheon, J.H., Han, K., Kim, A., Kim, M., Song, Y.: Bootstrapping for approximate homomorphic encryption. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 360–384. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_14
McKeen, F., et al.: Innovative instructions and software model for isolated execution. In: Proceeding of the 2nd International Workshop HASP (2013). https://doi.org/10.1145/2487726.2488368
Obla, S., Gong, X., Aloufi, A., Hu, P., Takabi, D.: Effective activation functions for homomorphic evaluation of deep neural networks. IEEE Access 8, 153098–153112 (2020). https://doi.org/10.1109/ACCESS.2020.3017436
Dowlin, N., et al.: CryptoNets: applying neural networks to encrypted data with high throughput and accuracy - Microsoft research. Microsoft Res. TechReport 48, 1–12 (2016). http://proceedings.mlr.press/v48/gilad-bachrach16.pdf. http://research.microsoft.com/apps/pubs/?id=260989
Chabanne, H.: Privacy-preserving classification on deep neural network. Med. Today 4(7), 59–64 (2017)
Hesamifard, E., Takagi, H., Ghasemi, M.: CryptoDL: deep neural networks over encrypted data, pp. 1–21 (2017). http://arxiv.org/abs/1711.05189
Bourse, F., Minelli, M., Minihold, M., Paillier, P.: Fast homomorphic evaluation of deep discretized neural networks. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 483–512. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96878-0_17
Deng, L.: The MNIST database of handwritten digit images for machine learning research. IEEE Signal Process. Mag. 29(6), 141–142 (2012). https://doi.org/10.1109/MSP.2012.2211477
Ohn, I., Kim, Y.: Smooth function approximation by deep neural networks with general activation functions. Entropy 21(7), 1–24 (2019). https://doi.org/10.3390/e21070627
Maennel, H., Bousquet, O., Gelly, S.: Gradient descent quantizes ReLU network features, arXiv, vol. abs/1803.0 (2018)
Harrou, F., Zeroual, A., Sun, Y.: Calcuas. In: Proceedings of the American Control Conference, vol. 2018-June, pp. 604–609 (2018). https://doi.org/10.23919/ACC.2018.8431387
Obla, S., Gong, X., Aloufi, A., Hu, P., Takabi, D.: Effective activation functions for homomorphic evaluation of deep neural networks (2020)
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Alsaedi, E.M., Farhan, A.K., Falah, M.W., Oleiwi, B.K. (2022). Classification of Encrypted Data Using Deep Learning and Legendre Polynomials. In: Daimi, K., Al Sadoon, A. (eds) Proceedings of the ICR’22 International Conference on Innovations in Computing Research. ICR 2022. Advances in Intelligent Systems and Computing, vol 1431. Springer, Cham. https://doi.org/10.1007/978-3-031-14054-9_31
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