We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal (ϵ, δ)-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for (ϵ, δ)-DP, improving upon previous results that only apply to at most three colors and for ϵ-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism.

This paper considers an information theoretic model of secure integrated sensing and communication, represented as a wiretap channel with action dependent states. This model allows securing part of a transmitted message against a sensed target that eavesdrops the communication, while enabling transmitter actions to change the channel statistics. An exact secrecy-distortion region is given for a physically-degraded channel. A finite-length achievability region is established for the model using an output statistics of random binning method, giving an achievable bound for low-latency applications.

A novel distributed computing model called Multiaccess Distributed Computing (MADC) was recently introduced in [B. Federico and P. Elia, "Multi-Access Distributed Computing," June 2022, [online] Available: http://www.arXiv:2206.12851]. The MADC models with Combinatorial Topology (CT) were studied, where there are Lambda mapper nodes and K = ((Lambda)(alpha)) reducer nodes with each reducer node connected to distinct ff mapper nodes. In this paper, we represent MADC models via 2-layered bipartite graphs called Map-Reduce Graphs (MRGs), and a set of arrays called Map-Reduce Arrays (MRAs) inspired from the Placement Delivery Arrays (PDAs) used in the coded caching literature. The connection between MRAs and MRGs is established, thereby providing coded shuffling schemes for the MADC models using the structure of MRAs. Moreover, a set of gregular MRAs is provided which corresponds to the existing scheme for MADC models with CT. One of the major limitations of the existing scheme for CT is that it requires an exponentially large number of reducer nodes for large Lambda. This can be overcome by representing CT by MRAs, where coding schemes can be derived even if some of the reducer nodes are not present.

This paper considers an information theoretic model for secure integrated sensing and communication (ISAC) with the goal of establishing fundamental limits in low-latency scenarios. In this secure ISAC model, a message is transmitted through a state-dependent wiretap channel with decoder-side state availability. The model is studied under a strong secrecy constraint when only a part of the transmitted message should be kept secret. First, the secrecy-distortion rate region is established for a degraded channel by treating the model as a special case of a feed-backed secure ISAC model. Finite-length inner bounds are then proved by applying nonasymptotic random binning techniques. Bounds on the rates have a similar form to common finite-length bounds, and the distortion bound follows from a bound for letter-typical sequences.

This paper studies the shuffling phase in a distributed computing model with rate-limited links between nodes. Each node is connected to all other nodes via a noiseless broadcast link with a finite capacity. For this network, the shuffling phase is described as a distributed index-coding problem to extend an outer bound for the latter to the distributed computing problem. An inner bound on the capacity region is also established by using the distributed composite-coding scheme introduced for the distributed index-coding problem. We consider some special cases of the distributed computing problem through two examples for which we prove that the inner and outer bounds agree, thereby establishing the capacity regions. We, then, generalize the special cases to any number of nodes and computation loads under certain constraints.

We consider two critical aspects of security in the distributed computing (DC) model: secure data shuffling and secure coded computing. It is imperative that any external entity overhearing the transmissions does not gain any information about the intermediate values (IVs) exchanged during the shuffling phase of the DC model. Our approach ensures IV confidentiality during data shuffling. Moreover, each node in the system must be able to recover the IVs necessary for computing its output functions but must also remain oblivious to the IVs associated with output functions not assigned to it. We design secure DC methods and establish achievable limits on the tradeoffs between the communication and computation loads to contribute to the advancement of secure data processing in distributed systems.

This work models a secure integrated sensing and communication (ISAC) system as a wiretap channel with action-dependent channel states and channel output feedback, e.g., obtained through reflections. The transmitted message is split into a common and a secure message, both of which must be reliably recovered at the legitimate receiver, while the secure message needs to be kept secret from the eavesdropper. The transmitter actions, such as beamforming vector design, affect the corresponding state at each channel use. The action sequence is modeled to depend on both the transmitted message and channel output feedback. For perfect channel output feedback, the secrecy-distortion regions are provided for physically-degraded and reversely-physically-degraded secure ISAC channels with transmitter actions. The corresponding rate regions when the entire message should be kept secret are also provided. The results are illustrated through characterizing the secrecy-distortion region of a binary example.

This work considers the problem of mitigating information leakage between communication and sensing in systems jointly performing both operations. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to convey information, while simultaneously performing channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a key attribute, e.g., location. For independent and identically distributed states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The characterization is exact when the broadcast channel is either physically-degraded or reversely-physically-degraded. The partial characterization is also extended to the situation in which the entire transmitted message should be kept secret. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with binary joint communication and sensing models.

We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The distributed function computation is subject to constraints, including not only reliability and storage but also secrecy and privacy. Specifically, 1) the function computed should remain secret from an eavesdropper observing the public communication and correlated observations, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used; 2) the remote source should remain private from the eavesdropper and the fusion center, measured in terms of the information leaked about the remote source itself. We derive the exact rate regions for lossless and lossy single-function computation and illustrate the lossy single-function computation rate region for an information bottleneck example, in which the optimal auxiliary random variables are characterized for binary-input symmetric-output channels. We extend the approach to lossless and lossy asynchronous multiple-function computations with joint secrecy and privacy constraints, in which case inner and outer bounds for the rate regions that differ only in the Markov chain conditions imposed are characterized.