2014/02/25 by Naoise Holohan, Holohan, Naoise, Douglas J. Leith +3
Computer Science · Engineering · Mathematics · #Cryptography and Data Security #Databases (cs.DB) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Privacy-Preserving Technologies in Data #Probability (math.PR) #Random Matrices and Applications #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1402.6124
openalex publication_date 2014/02/25 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We study Differential Privacy in the abstract setting of Probability on\nmetric spaces. Numerical, categorical and functional data can be handled in a\nuniform manner in this setting. We demonstrate how mechanisms based on data\nsanitisation and those that rely on adding noise to query responses fit within\nthis framework. We prove that once the sanitisation is differentially private,\nthen so is the query response for any query. We show how to construct\nsanitisations for high-dimensional databases using simple 1-dimensional\nmechanisms. We also provide lower bounds on the expected error for\ndifferentially private sanitisations in the general metric space setting.\nFinally, we consider the question of sufficient sets for differential privacy\nand show that for relaxed differential privacy, any algebra generating the\nBorel \σ-algebra is a sufficient set for relaxed differential privacy.\n