We study differentially private data release, where a database is accessed through successive, possibly adaptive queries and mechanisms. Existing composition theorems and privacy filters almost always combine worst case per-round privacy parameters, leaving room for more refined accounting based on realised leakage, which we term realisation-level accounting. We present a realisation-level filtering approach to determine stopping times for data releases, and design one such filter. Despite technical challenges arising from conditioning on realisations and stopping time, we prove that the filter guarantees $(ε, δ)$-differential privacy, with $ε$ and $δ$ chosen by the data handler. Through numerical evidence, we demonstrate that realisation-level filtering provides a path to better utility beyond mechanism-level methods. Furthermore, our proposed filter applies to arbitrary mechanisms, including those that are badly behaved under Rényi differential privacy.

In this paper, we study the entropy of a hard random geometric graph (RGG), a commonly used model for spatial networks, where the connectivity is governed by the distances between the nodes. Formally, given a connection range $r$, a hard RGG $G_m$ on $m$ vertices is formed by drawing $m$ random points from a spatial domain, and then connecting any two points with an edge when they are within a distance $r$ from each other. The two domains we consider are the $d$-dimensional unit cube $[0,1]^d$ and the $d$-dimensional unit torus $\mathbb{T}^d$. We derive upper bounds on the entropy $H(G_m)$ for both these domains and for all possible values of $r$. In a few cases, we obtain an exact asymptotic characterization of the entropy by proving a tight lower bound. Our main results are that $H(G_m) \sim dm \log_2m$ for $0 < r \leq 1/4$ in the case of $\mathbb{T}^d$ and that the entropy of a one-dimensional RGG on $[0,1]$ behaves like $m\log m$ for all $0

Information leakage metrics quantify the amount of information about a private random variableXthat is leaked through a correlated variableY. They can be used to evaluate the privacy of a system in which an adversary, from whomXshould be kept private, observesY. Global information leakage metrics quantify the overall information leaked upon observing Y , whilst their pointwise counterparts define leakage as a function of the particular realisationY=y, and thus can be viewed as random variables. We consider an adversary who observes many conditionally independent identically distributed realisations ofY. We formalise the essential asymptotic behaviour of an information leakage metric, considering in turn what this means for pointwise and global metrics. With these requirements in mind, we take an axiomatic approach to defining a set of pointwise leakage metrics, and a set of global leakage metrics constructed from them. The global set encompasses many known measures including mutual information, Sibson mutual information, Arimoto mutual information, maximal leakage, min entropy leakage,f-divergence metrics, and g-leakage. We prove that both sets follow the desired asymptotic behaviour. Finally, we derive composition theorems quantifying the rate of privacy degradation as an adversary is given access to many conditionally independent observations ofY. We find that, for pointwise and global metrics, privacy degrades exponentially with increasing observations, at a rate governed by the minimum Chernoff information. This extends the work of Wu et al. (2024), who derived this result for certain known metrics, including some from our global set.

In this paper, we consider the rate-distortion-perception (RDP) trade-off for the lossy compression of a Bernoulli vector source, which is a finite collection of independent binary random variables. The RDP function quantifies in a way the efficient compression of a source when we impose a distortion constraint that limits the dissimilarity between the source and the reconstruction and a perception constraint that restricts the distributional discrepancy of the source and the reconstruction. In this work, we obtain an exact characterization of the RDP function of a Bernoulli vector source with the Hamming distortion function and a single-letter perception function that measures the closeness of the distributions of the components of the source using the total variation distance. The solution can be described by partitioning the set of distortion and perception levels$(D, P)$into three regions, where in each region the optimal distortion and perception levels we allot to the components have a similar nature. Finally, we introduce the RDP function for graph sources and apply our result to the Erdős-Rényi graph model.

In this paper, we address the lossy compression of spatial networks, namely random geometric graphs, where two nodes are connected by an edge with a probability that depends on the distance between the nodes. We carry out this study by considering the$n\mathbf{th}$order information-distortion function, which quantifies the complexity of a random graph under a distortion criterion. Our main result is a partial characterization of the information-distortion function for a random geometric graph with the Hamming distortion measure.

In this paper, we explore the connection between secret key agreement and secure omniscience within the setting of the multiterminal source model with an eavesdropper having side information. While the secret key agreement problem considers the generation of a maximum-rate secret key through public discussion, the secure omniscience problem is concerned with communication protocols for omniscience that minimize the rate of information leakage to the eavesdropper. The starting point of our work is a lower bound on the minimum leakage rate for omniscience,$R_{ \text {L}}$, in terms of the wiretap secret key capacity,$C_{ \text {W}}$. Our interest is in identifying broad classes of sources for which this lower bound is met with equality, in which case we say that there is a duality between secure omniscience and secret key agreement. We show that this duality holds in the case of certain finite linear source (FLS) models, such as two-terminal FLS models and pairwise independent network models on trees with a linear eavesdropper. Duality also holds for any FLS model in which$C_{ \text {W}}$is achieved by a perfect linear secret key agreement scheme. We conjecture that the duality in fact holds unconditionally for any FLS model. On the negative side, we give an example of a (non-FLS) source model for which duality does not hold if we limit ourselves to communication-for-omniscience protocols with at most two (interactive) communications. We also address the secure function computation problem and explore the connection between the minimum leakage rate for computing a function and the wiretap secret key capacity.

In this paper, we propose a strategy for making DNA-based data storage information-theoretically secure through the use of wiretap channel coding. This motivates us to extend the shuffling-sampling channel model of Shomorony and Heckel (2021) to include a wiretapper. Our main result is a characterization of the secure storage capacity of our DNA wiretap channel model, which is the maximum rate at which data can be stored within a pool of DNA molecules so as to be reliably retrieved by an authorized party (Bob), while ensuring that an unauthorized party (Eve) gets almost no information from her observations. Furthermore, our proof of achievability shows that index-based wiretap channel coding schemes are optimal.

In this paper, we propose a strategy for making DNA-based data storage information-theoretically secure through the use of wiretap channel coding. This motivates us to extend the shuffling-sampling channel model of Shomorony and Heckel (2021) to include a wiretapper. Our main result is a characterization of the secure storage capacity of our DNA wiretap channel model, which is the maximum rate at which data can be stored within a pool of DNA molecules so as to be reliably retrieved by an authorized party (Bob), while ensuring that an unauthorized party (Eve) gets almost no information from her observations. Furthermore, our proof of achievability shows that index-based wiretap channel coding schemes are optimal.

The characterization of the secret key capacity with wiretapper side information is a challenging open problem. In this paper, we give a necessary and sufficient condition for the positivity of wiretap secret key capacity for the multiterminal source model. This result extends the existing works for two-terminal sources. However, in the case of hypergraphical source models with a linear wiretapper, we derive a simpler equivalent condition for the positivity. We also show that blocklength need not be larger than the logarithm of the number of edges in order to generate a positive rate key. The proofs of these results involve a subclass called minimally connected hypergraphical sources with a linear wiretapper, for which we obtain a single-letter characterization of wiretap secret key capacity.

In this paper, we obtain a single-letter characterization of the wiretap secret key capacity for a large class of multiterminal source models (namely, tree-PIN models) with a linear wiretapper that can observe arbitrary linear combinations of the source. For this class of sources, we also show a duality between the problems of wiretap secret key agreement and secure omniscience, which suggests that such duality potentially holds for more general sources.

We consider the problem of exchanging sensitive information in public and provide a general formulation that can unify and extend various existing scenarios of information exchange, such as the problems of private information extraction and information bottleneck. The formulation also gives rise to a new scenario called secure omniscience (SO), where users want to exchange all their private information with minimum leakage to a wiretapper with side information. Single-letter lower and upper bounds are obtained for the minimum leakage, and the bounds are shown to be tight under the finite linear source model with two users. The bounds are derived in terms of the solutions of the closely related problems of communication for omniscience (CO) and secret key agreement (SKA). However, we find examples where the bounds are not tight, and so the connections to CO and SKA are not precise. In particular, it is possible that any optimal CO scheme that minimizes communication does not minimize leakage, and any optimal SO scheme that minimizes leakage does not attain the capacity for SKA. Nevertheless, we identify a useful notion of information alignment that can modify an optimal CO scheme to reduce leakage for SO.

We consider a non-asymptotic (one-shot) version of the multiterminal secret key agreement problem on a finite linear source model. In this model, the observation of each terminal is a linear function of an underlying random vector composed of finitely many i.i.d. uniform random variables. By restricting the public discussion to be a linear function of the terminals' observations, we obtain a characterization of the communication complexity (minimum number of symbols of public discussion) of generating a secret key of maximum length. More precisely, we show that the minimum discussion can be achieved by a non-interactive protocol in which each terminal first does a linear processing of its own private observations, following which the terminals all execute a discussion-optimal communication-for-omniscience protocol. The secret key can be chosen to be a linear function of the vector of all observations.

In this paper, we analyze the Gaussian X channel in the mixed interference regime. In this regime, multiple access transmission to one of the receivers is shown to be close to optimal in terms of sum rate. Three upper bounds are derived for the sum capacity in the mixed interference regime, and the subregions where each of these bounds dominate the others are identified. The genie-aided sum capacity upper bounds derived also show that the gap between sum capacity and the sum rate of the multiple access transmission scheme is small for a significant part of the mixed interference region. For any δ > 0, the region where multiple access transmission to one of the receivers is within δ from sum capacity is determined.