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Differential privacy schemes have been widely adopted in recent years toaddress issues of data privacy protection. We propose a new Gaussian schemecombining with another data protection technique, called random orthogonalmatrix masking, to achieve $(\varepsilon, \delta)$-differential privacy (DP)more efficiently. We prove that the additional matrix masking significantlyreduces the rate of noise variance required in the Gaussian scheme to achieve$(\varepsilon, \delta)-$DP in big data setting. Specifically, when $\varepsilon\to 0$, $\delta \to 0$, and the sample size $n$ exceeds the number $p$ ofattributes by $(n-p)=O(ln(1/\delta))$, the required additive noise variance toachieve $(\varepsilon, \delta)$-DP is reduced from$O(ln(1/\delta)/\varepsilon^2)$ to $O(1/\varepsilon)$. With much less noiseadded, the resulting differential privacy protected pseudo data sets allow muchmore accurate inferences, thus can significantly improve the scope ofapplication for differential privacy.

Reducing Noise Level in Differential Privacy through Matrix Masking