Differential Privacy via Haar Wavelet Transform and Gaussian Mechanism for Range Query
Authors: 
Dong Chen, Yanjuan Li, Jiaquan Chen, Hongbo Bi, Xiajun Ding Academic Editor: Lorenzo PutzuAuthors Info & Claims
Dong Chen, Yanjuan Li, Jiaquan Chen, Hongbo Bi, Xiajun Ding Academic Editor: Lorenzo PutzuAuthors Info & ClaimsAbstract
Range query is the hot topic of the privacy-preserving data publishing. To preserve privacy, the large range query means more accumulate noise will be injected into the input data. This study presents a research on differential privacy for range query via Haar wavelet transform and Gaussian mechanism. First, the noise injected into the input data via Laplace mechanism is analyzed, and we conclude that it is difficult to judge the level of privacy protection based on the Haar wavelet transform and Laplace mechanism for range query because the sum of independent random Laplace variables is not a variable of a Laplace distribution. Second, the method of injecting noise into Haar wavelet coefficients via Gaussian mechanism is proposed in this study. Finally, the maximum variance for any range query under the framework of Haar wavelet transform and Gaussian mechanism is given. The analysis shows that using Haar wavelet transform and Gaussian mechanism, we can preserve the differential privacy for each input data and any range query, and the variance of noise is far less than that just using the Gaussian mechanism. In an experimental study on the dataset age extracted from IPUM’s census data of the United States, we confirm that the proposed mechanism has much smaller maximum variance of noises than the Gaussian mechanism for range-count queries.
References
[1]
T. Zhu, G. Li, W. Zhou, and S. Y. Philip, Preliminary of Differential Privacy,” Differential Privacy and Applications, pp. 7–16, Springer, Cham, 2017.
[2]
P. Jain, M. Gyanchandani, and N. Khare, “Differential privacy: its technological prescriptive using big data,” Journal of Big Data, vol. 5, no. 1, pp. 15–24, 2018.
[3]
H. B. Kartal, X. Liu, and X. B. Li, “Differential privacy for the vast majority,” ACM Transactions on Management Information Systems (TMIS), vol. 10, no. 2, pp. 1–15, 2019.
[4]
J. Lin, J. Niu, X. Liu, and M. Guizani, “Protecting your shopping preference with differential privacy,” IEEE Transactions on Mobile Computing, vol. 20, no. 5, pp. 1965–1978, 2021.
[5]
H. Wang and H. Wang, “Correlated tuple data release via differential privacy,” Information Sciences, vol. 560, pp. 347–369, 2021.
[6]
J. Soria-Comas, J. Domingo-Ferrer, D. Sánchez, and D. Megias, “Individual differential privacy: a utility-preserving formulation of differential privacy guarantees,” IEEE Transactions on Information Forensics and Security, vol. 12, no. 6, pp. 1418–1429, 2017.
[7]
H. Wang and Z. Xu, “CTS-DP: publishing correlated time-series data via differential privacy,” Knowledge-Based Systems, vol. 122, pp. 167–179, 2017.
[8]
M. U. Hassan, M. H. Rehmani, and J. Chen, “Differential privacy techniques for cyber physical systems: a survey,” IEEE Communications Surveys & Tutorials, vol. 22, no. 1, pp. 746–789, 2020.
[9]
Z. Huang, R. Hu, Y. Guo, E. Chan-Tin, and Y. Gong, “DP-ADMM: ADMM-based distributed learning with differential privacy,” IEEE Transactions on Information Forensics and Security, vol. 15, pp. 1002–1012, 2020.
[10]
X. Li, J. Yang, X. Sun, and Z. Jianpei, “Differential Privacy for Edge Weights in Social Networks,” Security and Communication Networks, vol. 2017, pp. 1–10, 2017.
[11]
P. Liu, Y. X. Xu, Q. Jiang, Y. Tang, Y. Guo, Le Wang, and X. Li, “Local differential privacy for social network publishing,” Neurocomputing, vol. 391, pp. 273–279, 2020.
[12]
H. Huang, D. Zhang, F. Xiao, K. Wang, J. Gu, and R. Wang, “Privacy-preserving approach PBCN in social network with differential privacy,” IEEE Transactions on Network and Service Management, vol. 17, no. 2, pp. 931–945, 2020.
[13]
X. Ren, C. M. Yu, W. Yu, S. Yang, X. Yang, J. A. McCann, and P. S. Yu, “<tex-math notation=LaTeX>$\textsf{LoPub}$ </tex-math>: high-dimensional crowdsourced data publication with local differential privacy,” IEEE Transactions on Information Forensics and Security, vol. 13, no. 9, pp. 2151–2166, 2018.
[14]
J. Wei, Y. Lin, X. Yao, and J. Zhang, “Differential privacy-based location protection in spatial crowdsourcing,” IEEE Transactions on Services Computing, vol. 15, pp. 1–14, 2019.
[15]
N. Almadhoun, E. Ayday, and Ö. Ulusoy, “Differential privacy under dependent tuples—the case of genomic privacy,” Bioinformatics, vol. 36, no. 6, pp. 1696–1703, 2020.
[16]
J. L. Raisaro, G. Choi, S. Pradervand, R. Colsenet, N. Jacquemont, N. Rosat, V. Mooser, and J. P. Hubaux, “Protecting privacy and security of genomic data in i2b2 with homomorphic encryption and differential privacy,” IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 15, no. 5, pp. 1413–1426, 2018.
[17]
M. Z. Hasan, M. S. R. Mahdi, M. N. Sadat, and N. Mohammed, “Secure count query on encrypted genomic data,” Journal of Biomedical Informatics, vol. 81, pp. 41–52, 2018.
[18]
T. Zhu, G. Li, W. Zhou, and P. S. Yu, “Differentially private data publishing and analysis: a survey,” IEEE Transactions on Knowledge and Data Engineering, vol. 29, no. 8, pp. 1619–1638, 2017.
[19]
L. Qian, T. Song, and A. Liang, “The optimization of the range query in differential privacy,” in Proceedings of the International Conference on Computer Science and Network Technology (ICCSNT), vol. 1, pp. 618–623, IEEE, July 2015.
[20]
J. Zhang, X. Xiao, and X. Xie, “Privtree: a differentially private algorithm for hierarchical decompositions,” in Proceedings of the 2016 International Conference on Management of Data, pp. 155–170, San Francisco, CA, USA, January 2016.
[21]
Z. Cai and Z. He, “Trading private range counting over big IoT data,” in Proceedings of the IEEE 39th International Conference on Distributed Computing Systems (ICDCS), IEEE, pp. 144–153, Dallas, TX, USA, July 2019.
[22]
H. Mahdikhani, R. Lu, Y. Zheng, and A. Ghorbani, “Achieving efficient and privacy-preserving range query in fog-enhanced IoT with bloom filter,” in Proceedings of the IEEE International Conference on Communications, pp. 1–6, Dublin, Ireland, July 2020.
[23]
H. Mahdikhani, R. Lu, J. Shao, and A. Ghorbani, “Using reduced paths to achieve efficient privacy-preserving range query in fog-based IoT,” IEEE Internet of Things Journal, vol. 8, no. 6, pp. 4762–4774, 2021.
[24]
J. Xu, Z. Zhang, X. Xiao, Y. Yang, G. Yu, and M. Winslett, “Differentially private histogram publication,” The VLDB Journal, vol. 22, pp. 797–822, 2013.
[25]
X. Meng, H. Li, and J. Cui, “Different strategies for differentially private histogram publication,” Journal of Communications and Information Networks, vol. 2, no. 3, pp. 68–77, 2017.
[26]
Q. Han, B. Shao, L. Li, Z. Ma, H. Zhang, and X. Du, “Publishing histograms with outliers under data differential privacy,” Security and Communication Networks, vol. 9, no. 14, pp. 2313–2322, 2016.
[27]
H. Li, J. Cui, X. Meng, and J. Ma, “IHP: improving the utility in differential private histogram publication,” Distributed and Parallel Databases, vol. 37, no. 4, pp. 721–750, 2019.
[28]
T. Zhu, G. Li, W. Zhou, and S. Y. Philip, Differentially Private Data Publishing: Interactive Setting,” Differential Privacy and Applications, pp. 23–34, Springer, Cham, 2017.
[29]
F. M. Bayer, A. J. Kozakevicius, and R. J. Cintra, “An iterative wavelet threshold for signal denoising,” Signal Processing, vol. 162, pp. 10–20, 2019.
[30]
M. Sharma, S. Patel, and U. R. Acharya, “Automated detection of abnormal EEG signals using localized wavelet filter banks,” Pattern Recognition Letters, vol. 133, pp. 188–194, 2020.
[31]
T. Suzuki, “Wavelet-based spectral–spatial transforms for CFA-sampled raw camera image compression,” IEEE Transactions on Image Processing, vol. 29, pp. 433–444, 2020.
[32]
Y. Zhang, “The fast image encryption algorithm based on lifting scheme and chaos,” Information Sciences, vol. 520, pp. 177–194, 2020.
[33]
S. P. Singh and G. Bhatnagar, “A simplified watermarking algorithm based on lifting wavelet transform,” Multimedia Tools and Applications, vol. 78, no. 15, pp. 20765–20786, 2019.
[34]
M. B. Nagare, B. D. Patil, and R. S. Holambe, “On the design of biorthogonal halfband filterbanks with almost tight rational coefficients,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 4, pp. 790–794, 2020.
[35]
X. Xiao, G. Wang, and J. Gehrke, “Differential privacy via wavelet transforms,” IEEE Transactions on Knowledge and Data Engineering, vol. 23, no. 8, pp. 1200–1214, 2011.
[36]
P. Derbeko, S. Dolev, and E. Gudes, “Wavelet-based dynamic and privacy-preserving similitude data models for edge computing,” Wireless Networks, vol. 27, no. 1, pp. 351–366, 2021.
[37]
C. Lin, P. Wang, H. Song, Y. Zhou, Q. Liu, and G. Wu, “A differential privacy protection scheme for sensitive big data in body sensor networks,” Annals of Telecommunications, vol. 71, no. 9-10, pp. 465–475, 2016.
[38]
C. Dwork, K. Talwar, A. Thakurta, and Li. Zhang, “Analyze gauss: optimal bounds for privacy-preserving principal component analysis,” in Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing, pp. 11–20, May 2014.
[39]
C. Dwork and A. Roth, “The algorithmic foundations of differential privacy,” Foundations and Trends® in Theoretical Computer Science, vol. 9, pp. 211–407, 2013.
[40]
S. Ruggles, K. Genadek, and R. Goeken, Integrated public use microdata series: Version 6.0 [dataset], vol. 10, p. 010, University of Minnesota, Minneapolis, 2017.
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Published: 01 January 2022
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