Biblio

Differential privacy is a precise mathematical constraint meant to ensure privacy of individual pieces of information in a database even while queries are being answered about the aggregate. Intuitively, one must come to terms with what differential privacy does and does not guarantee. For example, the definition prevents a strong adversary who knows all but one entry in the database from further inferring about the last one. This strong adversary assumption can be overlooked, resulting in misinterpretation of the privacy guarantee of differential privacy. Herein we give an equivalent definition of privacy using mutual information that makes plain some of the subtleties of differential privacy. The mutual-information differential privacy is in fact sandwiched between ε-differential privacy and (ε,δ)-differential privacy in terms of its strength. In contrast to previous works using unconditional mutual information, differential privacy is fundamentally related to conditional mutual information, accompanied by a maximization over the database distribution. The conceptual advantage of using mutual information, aside from yielding a simpler and more intuitive definition of differential privacy, is that its properties are well understood. Several properties of differential privacy are easily verified for the mutual information alternative, such as composition theorems.

Physical layer security can ensure secure communication over noisy channels in the presence of an eavesdropper with unlimited computational power. We adopt an information theoretic variant of semantic-security (SS) (a cryptographic gold standard), as our secrecy metric and study the open problem of the type II wiretap channel (WTC II) with a noisy main channel is, whose secrecy-capacity is unknown even under looser metrics than SS. Herein the secrecy-capacity is derived and shown to be equal to its SS capacity. In this setting, the legitimate users communicate via a discrete-memory less (DM) channel in the presence of an eavesdropper that has perfect access to a subset of its choosing of the transmitted symbols, constrained to a fixed fraction of the block length. The secrecy criterion is achieved simultaneously for all possible eavesdropper subset choices. On top of that, SS requires negligible mutual information between the message and the eavesdropper's observations even when maximized over all message distributions. A key tool for the achievability proof is a novel and stronger version of Wyner's soft covering lemma. Specifically, the lemma shows that a random codebook achieves the soft-covering phenomenon with high probability. The probability of failure is doubly-exponentially small in the block length. Since the combined number of messages and subsets grows only exponentially with the block length, SS for the WTC II is established by using the union bound and invoking the stronger soft-covering lemma. The direct proof shows that rates up to the weak-secrecy capacity of the classic WTC with a DM erasure channel (EC) to the eavesdropper are achievable. The converse follows by establishing the capacity of this DM wiretap EC as an upper bound for the WTC II. From a broader perspective, the stronger soft-covering lemma constitutes a tool for showing the existence of codebooks that satisfy exponentially many constraints, a beneficial ability for many other applications in information theoretic security.

Physical layer security can ensure secure communication over noisy channels in the presence of an eavesdropper with unlimited computational power. We adopt an information theoretic variant of semantic-security (SS) (a cryptographic gold standard), as our secrecy metric and study the open problem of the type II wiretap channel (WTC II) with a noisy main channel is, whose secrecy-capacity is unknown even under looser metrics than SS. Herein the secrecy-capacity is derived and shown to be equal to its SS capacity. In this setting, the legitimate users communicate via a discrete-memory less (DM) channel in the presence of an eavesdropper that has perfect access to a subset of its choosing of the transmitted symbols, constrained to a fixed fraction of the block length. The secrecy criterion is achieved simultaneously for all possible eavesdropper subset choices. On top of that, SS requires negligible mutual information between the message and the eavesdropper's observations even when maximized over all message distributions. A key tool for the achievability proof is a novel and stronger version of Wyner's soft covering lemma. Specifically, the lemma shows that a random codebook achieves the soft-covering phenomenon with high probability. The probability of failure is doubly-exponentially small in the block length. Since the combined number of messages and subsets grows only exponentially with the block length, SS for the WTC II is established by using the union bound and invoking the stronger soft-covering lemma. The direct proof shows that rates up to the weak-secrecy capacity of the classic WTC with a DM erasure channel (EC) to the eavesdropper are achievable. The converse follows by establishing the capacity of this DM wiretap EC as an upper bound for the WTC II. From a broader perspective, the stronger soft-covering lemma constitutes a tool for showing the existence of codebooks that satisfy exponentially many constraints, a beneficial ability for many other applications in information theoretic security.