Achieving Dalenius' Goal of Data Privacy with Practical Assumptions

Abstract

Current differential privacy frameworks face significant challenges: vulnerability to correlated data attacks and suboptimal utility-privacy tradeoffs. To address these limitations, we establish a novel information-theoretic foundation for Dalenius' privacy vision using Shannon's perfect secrecy framework. By leveraging the fundamental distinction between cryptographic systems (small secret keys) and privacy mechanisms (massive datasets), we replace differential privacy's restrictive independence assumption with practical partial knowledge constraints ($H(X) \geq b$). We propose an information privacy framework achieving Dalenius security with quantifiable utility-privacy tradeoffs. Crucially, we prove that foundational mechanisms -- random response, exponential, and Gaussian channels -- satisfy Dalenius' requirements while preserving group privacy and composition properties. Our channel capacity analysis reduces infinite-dimensional evaluations to finite convex optimizations, enabling direct application of information-theoretic tools. Empirical evaluation demonstrates that individual channel capacity (maximal information leakage of each individual) decreases with increasing entropy constraint $b$, and our framework achieves superior utility-privacy tradeoffs compared to classical differential privacy mechanisms under equivalent privacy guarantees. The framework is extended to computationally bounded adversaries via Yao's theory, unifying cryptographic and statistical privacy paradigms. Collectively, these contributions provide a theoretically grounded path toward practical, composable privacy -- subject to future resolution of the tradeoff characterization -- with enhanced resilience to correlation attacks.