Privacy via the Johnson-Lindenstrauss Transform

The Journal of Privacy and Confidentiality

Nina Mishra¹  Ilya Mironov¹  Krishnaram Kenthapadi¹  Aleksandra Korolova² 

[1] Microsoft Research, Mountain View, CA;Stanford University, Stanford, CA;

关键词: differential privacy;    Johnson-Lindenstrauss;    sketching;   

DOI  :  10.29012/jpc.v5i1.625

来源: DOAJ

【 摘 要 】

Suppose that party A collects private information about its users, where each user's data is represented as a bit vector. Suppose that party B has a proprietary data mining algorithm that requires estimating the distance between users, such as clustering or nearest neighbors. We ask if it is possible for party A to publish some information about each user so that B can estimate the distance between users without being able to infer any private bit of a user. Our method involves projecting each user's representation into a random, lower-dimensional space via a sparse Johnson-Lindenstrauss transform and then adding Gaussian noise to each entry of the lower-dimensional representation. We show that the method preserves differential privacy---where the more privacy is desired, the larger the variance of the Gaussian noise. Further, we show how to approximate the true distances between users via only the lower-dimensional, perturbed data. Finally, we consider other perturbation methods such as randomized response and draw comparisons to sketch-based methods. While the goal of releasing user-specific data to third parties is more broad than preserving distances, this work shows that distance computations with privacy is an achievable goal.

【 授权许可】

Unknown