On Security Properties of Random Matrix Masking

• Activity Number: 689
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Samuel Wu* and Kshitij Khare and Long Zhang and Shigang Chen
• Companies: University of Florida and University of Florida and University of Florida and University of Florida
• Keywords: Random matrix masking ; security analysis ; posterior distribution

Abstract

Many data masking techniques have been developed in the literature. In this paper, a detailed statistical analysis is carried out about the security properties of a class of them called random matrix masking (Ting et al., 2008 and Wu et al., 2014). Specifically, we quantify how much information is known by public users about the original data X using its posterior distribution given the masked data AX, XB, or both. The security analysis relies on a new definition of uniform distribution on the set of orthogonal matrices. We show that: (1) When A is a random orthogonal matrix, then X|AX is uniform over possible domain; (2) When A is a random orthogonal matrix and B is an invertible matrix with entries from U[0, 1], then X|(AX, XB) is uniform over possible domain.