arXiv subjects

Parastoo Sadeghi

Publications and source records attributed to Parastoo Sadeghi.

At least 19 recordsLinked to original sources

arXiv2026

Sparse Discrete Laplace and Gaussian Mechanisms under Local Differential Privacy

We study sparse locally private channels of the form $M(y\mid x)\propto w(x,y) 1\{y\in S(x)\},$ where the admissible output set $S(x)$ is allowed to depend on the private input $x$ and is assumed to be small. Here, we consider the sparse discrete-Laplace family with kernel $w(x,y)=e^{-λd(x,y)}$ and the sparse Gaussian family with kernel $w(x,y)=e^{-d(x,y)^2/(2σ^2)}$. For both families we give exact characterizations of pure and approximate local differential privacy. For pure $\varepsilon$-local differential privacy, we show that input-dependent sparse supports are obtained when all supports coincide. For $(\varepsilon,δ)$-local differential privacy, we derive exact formulas for the privacy defect in terms of support leakage and excess privacy loss on the overlap region. We then specialize the analysis to radius-truncated sparse discrete-Laplace and radius-truncated sparse Gaussian mechanisms and obtain explicit privacy-sparsity tradeoffs in terms of the support size $s$. In particular, we show that nontrivial approximate local privacy requires a minimum support size, whereas larger supports reduce support leakage but increase distortion. For the Gaussian family, the overlap term exhibits an additional quadratic dependence on the support radius, which implies a sharper tradeoff between privacy and sparsity. These results identify the support cardinality as the intrinsic complexity parameter of the mechanism and yield an optimal design principle: choose the smallest support size that satisfies the target privacy constraint.

cs.IT↗

arXiv2026

Information Density Bounds for Privacy

This paper explores the implications of guaranteeing privacy by imposing a lower bound on the information density between the private and the public data. We introduce a novel and operationally meaningful privacy measure called pointwise maximal cost (PMC) and demonstrate that imposing an upper bound on PMC is equivalent to enforcing a lower bound on the information density. PMC quantifies the information leakage about a secret to adversaries who aim to minimize non-negative cost functions after observing the outcome of a privacy mechanism. When restricted to finite alphabets, PMC can equivalently be defined as the information leakage to adversaries aiming to minimize the probability of incorrectly guessing randomized functions of the secret. We study the properties of PMC and apply it to standard privacy mechanisms to demonstrate its practical relevance. Through a detailed examination, we connect PMC with other privacy measures that impose upper or lower bounds on the information density. These are pointwise maximal leakage (PML), local differential privacy (LDP), and (asymmetric) local information privacy. In particular, we show that a mechanism satisfies LDP if and only if it has both bounded PMC and bounded PML. Overall, our work fills a conceptual and operational gap in the taxonomy of privacy measures, bridges existing disconnects between different frameworks, and offers insights for selecting a suitable notion of privacy in a given application.

cs.IT↗

arXiv2026

How Entanglement Reshapes the Geometry of Quantum Differential Privacy

Quantum differential privacy provides a rigorous framework for quantifying privacy guarantees in quantum information processing. While classical correlations are typically regarded as adversarial to privacy, the role of their quantum analogue, entanglement, is not well understood. In this work, we investigate how quantum entanglement fundamentally shapes quantum local differential privacy (QLDP). We consider a bipartite quantum system whose input state has a prescribed level of entanglement, characterized by a lower bound on the entanglement entropy. Each subsystem is then processed by a local quantum mechanism and measured using local operations only, ensuring that no additional entanglement is generated during the process. Our main result reveals a sharp phase-transition phenomenon in the relation between entanglement and QLDP: below a mechanism-dependent entropy threshold, the optimal privacy leakage level mirrors that of unentangled inputs; beyond this threshold, the exact privacy leakage is strictly smaller than its unentangled value and admits an explicitly computable upper bound that strictly decreases with the entropy. This bound can also certify that some non-private mechanisms become private under sufficiently strong entanglement constraints. The phase-transition phenomenon gives rise to a nonlinear dependence of the certified privacy-leakage upper bound on the entanglement entropy, even though the underlying quantum mechanisms and measurements are linear. We show that the transition is governed by the intrinsic non-convex geometry of the set of entanglement-constrained quantum states, which we parametrize as a smooth manifold and analyze via Riemannian optimization. Our findings demonstrate that entanglement serves as a genuine privacy-enhancing resource, offering a geometric and operational foundation for designing robust privacy-preserving quantum protocols.

cs.IT↗

arXiv2026

Sparse Point-wise Privacy Leakage: Mechanism Design and Fundamental Limits

We study an information-theoretic privacy mechanism design problem, where an agent observes useful data $Y$ that is arbitrarily correlated with sensitive data $X$, and design disclosed data $U$ generated from $Y$ (the agent has no direct access to $X$). We introduce \emph{sparse point-wise privacy leakage}, a worst-case privacy criterion that enforces two simultaneous constraints for every disclosed symbol $u\in\mathcal{U}$: (i) $u$ may be correlated with at most $N$ realizations of $X$, and (ii) the total leakage toward those realizations is bounded. In the high-privacy regime, we use concepts from information geometry to obtain a local quadratic approximation of mutual information which measures utility between $U$ and $Y$. When the leakage matrix $P_{X|Y}$ is invertible, this approximation reduces the design problem to a sparse quadratic maximization, known as the Rayleigh-quotient problem, with an $\ell_0$ constraint. We further show that, for the approximated problem, one can without loss of optimality restrict attention to a binary released variable $U$ with a uniform distribution. For small alphabet sizes, the exact sparsity-constrained optimum can be computed via combinatorial support enumeration, which quickly becomes intractable as the dimension grows. For general dimensions, the resulting sparse Rayleigh-quotient maximization is NP-hard and closely related to sparse principal component analysis (PCA). We propose a convex semidefinite programming (SDP) relaxation that is solvable in polynomial time and provides a tractable surrogate for the NP-hard design, together with a simple rounding procedure to recover a feasible leakage direction. We also identify a sparsity threshold beyond which the sparse optimum saturates at the unconstrained spectral value and the SDP relaxation becomes tight.

cs.IT↗

arXiv2026

Privacy-Utility Trade-offs Under Multi-Level Point-Wise Leakage Constraints

An information-theoretic privacy mechanism design is studied, where an agent observes useful data $Y$ which is correlated with the private data $X$. The agent wants to reveal the information to a user, hence, the agent utilizes a privacy mechanism to produce disclosed data $U$ that can be revealed. We assume that the agent has no direct access to $X$, i.e., the private data is hidden. We study privacy mechanism design that maximizes the disclosed information about $Y$, measured by the mutual information between $Y$ and $U$, while satisfying a point-wise constraint with different privacy leakage budgets. We introduce a new measure, called the \emph{multi-level point-wise leakage}, which allows us to impose different leakage levels for different realizations of $U$. In contrast to previous studies on point-wise measures, which use the same leakage level for each realization, we consider a more general scenario in which each data point can leak information up to a different threshold. As a result, this concept also covers cases in which some data points should not leak any information about the private data, i.e., they must satisfy perfect privacy. In other words, a combination of perfect privacy and non-zero leakage can be considered. When the leakage is sufficiently small, concepts from information geometry allow us to locally approximate the mutual information. We show that when the leakage matrix $P_{X|Y}$ is invertible, utilizing this approximation leads to a quadratic optimization problem that has closed-form solution under some constraints. In particular, we show that it is sufficient to consider only binary $U$ to attain the optimal utility. This leads to simple privacy designs with low complexity which are based on finding the maximum singular value and singular vector of a matrix.

cs.IT↗

arXiv2025

Composition Theorems for f-Differential Privacy

"f differential privacy" (fDP) is a recent definition for privacy privacy which can offer improved predictions of "privacy loss". It has been used to analyse specific privacy mechanisms, such as the popular Gaussian mechanism. In this paper we show how fDP's foundation in statistical hypothesis testing implies equivalence to the channel model of Quantitative Information Flow. We demonstrate this equivalence by a Galois connection between two partially ordered sets. This equivalence enables novel general composition theorems for fDP, supporting improved analysis for complex privacy designs.

cs.CR↗

arXiv2025

Performance Bounds on Pliable Index Coding Using Absent Receivers

We characterise bounds on the optimal broadcast rate for a few classes of pliable-index-coding instances. Unlike the majority of currently solved instances, which belong to a special class where all receivers with a certain side-information cardinality are either present or absent, we consider more general instances without this constraint. We devise a novel algorithm that constructs a decoding chain by iteratively adding a message that can be decoded by a receiver whose side information is already in the chain. If the decoding chain cannot proceed due to the absence of a receiver with the required messages, we skip a message by adding it to the chain regardless. We prove that a lower bound on the optimal broadcast rate is a function of the number of skipped messages, across all possible decoding choices of the receivers and any realisation of the algorithm for each decoding choice. While this result is not computationally feasible in isolation, it serves as a basis for deriving explicit lower bounds on the broadcast rate for specific classes of pliable-index-coding instances. These lower bounds depend on the number of absent receivers or the pattern of their side-information sets. Specifically, we explicitly characterise the optimal broadcast rate for instances with up to and including four absent receivers with any side-information pattern, as well as instances where the side-information sets are nested in particular ways.

cs.IT↗

arXiv2025

An Extension of the Adversarial Threat Model in Quantitative Information Flow

In this paper, we propose an extended framework for quantitative information flow (QIF), aligned with the previously proposed core-concave generalization of entropy measures, to include adversaries that use Kolmogorov-Nagumo $f$-mean to infer secrets in a private system. Specifically, in our setting, an adversary uses Kolmogorov-Nagumo $f$-mean to compute its best actions before and after observing the system's randomized outputs. This leads to generalized notions of prior and posterior vulnerability and generalized axiomatic relations that we will derive to elucidate how these $f$-mean based vulnerabilities interact with each other. We demonstrate the usefulness of this framework by showing how some notions of leakage that had been derived outside of the QIF framework and so far seemed incompatible with it are indeed explainable via such an extension of QIF. These leakage measures include $α$-leakage, which is the same as Arimoto mutual information of order $α$, maximal $α$-leakage, which is the $α$-leakage capacity, and maximal $(α,β)$-leakage, which is a generalization of the above and captures local differential privacy as a special case. We define the notion of generalized capacity and provide partial results for special classes of functions used in the Kolmogorov-Nagumo mean. We also propose a new pointwise notion of gain function, which we coin pointwise information gain. We show that this pointwise information gain can explain R{é}yni divergence and Sibson mutual information of order $α\in [0,\infty]$ as the Kolmogorov-Nagumo average of the gain with a proper choice of function $f$.

cs.IT↗

arXiv2025

Comparing privacy notions for protection against reconstruction attacks in machine learning

Within the machine learning community, reconstruction attacks are a principal concern and have been identified even in federated learning (FL), which was designed with privacy preservation in mind. In response to these threats, the privacy community recommends the use of differential privacy (DP) in the stochastic gradient descent algorithm, termed DP-SGD. However, the proliferation of variants of DP in recent years\textemdash such as metric privacy\textemdash has made it challenging to conduct a fair comparison between different mechanisms due to the different meanings of the privacy parameters $ε$ and $δ$ across different variants. Thus, interpreting the practical implications of $ε$ and $δ$ in the FL context and amongst variants of DP remains ambiguous. In this paper, we lay a foundational framework for comparing mechanisms with differing notions of privacy guarantees, namely $(ε,δ)$-DP and metric privacy. We provide two foundational means of comparison: firstly, via the well-established $(ε,δ)$-DP guarantees, made possible through the Rényi differential privacy framework; and secondly, via Bayes' capacity, which we identify as an appropriate measure for reconstruction threats.

cs.LG↗

arXiv2025

An Information Geometric Approach to Local Information Privacy with Applications to Max-lift and Local Differential Privacy

We study an information-theoretic privacy mechanism design, where an agent observes useful data $Y$ and wants to reveal the information to a user. Since the useful data is correlated with the private data $X$, the agent uses a privacy mechanism to produce disclosed data $U$ that can be released. We assume that the agent observes $Y$ and has no direct access to $X$, i.e., the private data is hidden. We study the privacy mechanism design that maximizes the revealed information about $Y$ while satisfying a bounded Local Information Privacy (LIP) criterion. When the leakage is sufficiently small, concepts from information geometry allow us to locally approximate the mutual information. By utilizing this approximation the main privacy-utility trade-off problem can be rewritten as a quadratic optimization problem that has closed-form solution under some constraints. For the cases where the closed-form solution is not obtained we provide lower bounds on it. In contrast to the previous works that have complexity issues, here, we provide simple privacy designs with low complexity which are based on finding the maximum singular value and singular vector of a matrix. To do so, we follow two approaches where in the first one we find a lower bound on the main problem and then approximate it, however, in the second approach we approximate the main problem directly. In this work, we present geometrical interpretations of the proposed methods and in a numerical example we compare our results considering both approaches with the optimal solution and the previous methods. Furthermore, we discuss how our method can be generalized considering larger amounts for the privacy leakage. Finally, we discuss how the proposed methods can be applied to deal with differential privacy.

cs.IT↗

arXiv2024

An Algorithm for Enhancing Privacy-Utility Tradeoff in the Privacy Funnel and Other Lift-based Measures

This paper investigates the privacy funnel, a privacy-utility tradeoff problem in which mutual information quantifies both privacy and utility. The objective is to maximize utility while adhering to a specified privacy budget. However, the privacy funnel represents a non-convex optimization problem, making it challenging to achieve an optimal solution. An existing proposed approach to this problem involves substituting the mutual information with the lift (the exponent of information density) and then solving the optimization. Since mutual information is the expectation of the information density, this substitution overestimates the privacy loss and results in a final smaller bound on the privacy of mutual information than what is allowed in the budget. This significantly compromises the utility. To overcome this limitation, we propose using a privacy measure that is more relaxed than the lift but stricter than mutual information while still allowing the optimization to be efficiently solved. Instead of directly using information density, our proposed measure is the average of information density over the sensitive data distribution for each observed data realization. We then introduce a heuristic algorithm capable of achieving solutions that produce extreme privacy values, which enhances utility. The numerical results confirm improved utility at the same privacy budget compared to existing solutions in the literature. Additionally, we explore two other privacy measures, $\ell_{1}$-norm and strong $χ^2$-divergence, demonstrating the applicability of our algorithm to these lift-based measures. We evaluate the performance of our method by comparing its output with previous works. Finally, we validate our heuristic approach with a theoretical framework that estimates the optimal utility for strong $χ^2$-divergence, numerically showing a perfect match.

cs.IT↗

arXiv2024

Generalization of the Fano and Non-Fano Index Coding Instances

Matroid theory is fundamentally connected with index coding and network coding problems. In fact, the reliance of linear index coding and network coding rates on the characteristic of a field has been demonstrated by using the two well-known matroid instances, namely the Fano and non-Fano matroids. This established the insufficiency of linear coding, one of the fundamental theorems in both index coding and network coding. While the Fano matroid is linearly representable only over fields with characteristic two, the non-Fano instance is linearly representable only over fields with odd characteristic. For fields with arbitrary characteristic $p$, the Fano and non-Fano matroids were extended to new classes of matroid instances whose linear representations are dependent on fields with characteristic $p$. However, these matroids have not been well appreciated nor cited in the fields of network coding and index coding. In this paper, we first reintroduce these matroids in a more structured way. Then, we provide a completely independent alternative proof with the main advantage of using only matrix manipulation rather than complex concepts in number theory and matroid theory. In this new proof, it is shown that while the class $p$-Fano matroid instances are linearly representable only over fields with characteristic $p$, the class $p$-non-Fano instances are representable over fields with any characteristic other than characteristic $p$. Finally, following the properties of the class $p$-Fano and $p$-non-Fano matroid instances, we characterize two new classes of index coding instances, respectively, referred to as the class $p$-Fano and $p$-non-Fano index coding, each with a size of $p^2 + 4p + 3$.

cs.IT↗

arXiv2024

$α$-leakage by Rényi Divergence and Sibson Mutual Information

For $\tilde{f}(t) = \exp(\frac{α-1}αt)$, this paper proposes a $\tilde{f}$-mean information gain measure. Rényi divergence is shown to be the maximum $\tilde{f}$-mean information gain incurred at each elementary event $y$ of channel output $Y$ and Sibson mutual information is the $\tilde{f}$-mean of this $Y$-elementary information gain. Both are proposed as $α$-leakage measures, indicating the most information an adversary can obtain on sensitive data. It is shown that the existing $α$-leakage by Arimoto mutual information can be expressed as $\tilde{f}$-mean measures by a scaled probability. Further, Sibson mutual information is interpreted as the maximum $\tilde{f}$-mean information gain over all estimation decisions applied to channel output.

cs.IT↗

arXiv2024

Privacy-Utility Tradeoff Based on $α$-lift

Information density and its exponential form, known as lift, play a central role in information privacy leakage measures. $α$-lift is the power-mean of lift, which is tunable between the worst-case measure max-lift ($α=\infty$) and more relaxed versions ($α<\infty$). This paper investigates the optimization problem of the privacy-utility tradeoff (PUT) where $α$-lift and mutual information are privacy and utility measures, respectively. Due to the nonlinear nature of $α$-lift for $α<\infty$, finding the optimal solution is challenging. Therefore, we propose a heuristic algorithm to estimate the optimal utility for each value of $α$, inspired by the optimal solution for $α=\infty$ and the convexity of $α$-lift with respect to the lift, which we prove. The numerical results show the efficacy of the algorithm and indicate the effective range of $α$ and privacy budget $\varepsilon$ with good PUT performance.

cs.IT↗

arXiv2024

Bayes' capacity as a measure for reconstruction attacks in federated learning

Within the machine learning community, reconstruction attacks are a principal attack of concern and have been identified even in federated learning, which was designed with privacy preservation in mind. In federated learning, it has been shown that an adversary with knowledge of the machine learning architecture is able to infer the exact value of a training element given an observation of the weight updates performed during stochastic gradient descent. In response to these threats, the privacy community recommends the use of differential privacy in the stochastic gradient descent algorithm, termed DP-SGD. However, DP has not yet been formally established as an effective countermeasure against reconstruction attacks. In this paper, we formalise the reconstruction threat model using the information-theoretic framework of quantitative information flow. We show that the Bayes' capacity, related to the Sibson mutual information of order infinity, represents a tight upper bound on the leakage of the DP-SGD algorithm to an adversary interested in performing a reconstruction attack. We provide empirical results demonstrating the effectiveness of this measure for comparing mechanisms against reconstruction threats.

cs.LG↗

arXiv2024

Group Complete-$\{s\}$ Pliable Index Coding

This paper introduces a novel class of PICOD($t$) problems referred to as $g$-group complete-$S$ PICOD($t$) problems. It constructs a multi-stage achievability scheme to generate pliable index codes for group complete PICOD problems when $S = \{s\}$ is a singleton set. Using the maximum acyclic induced subgraph bound, lower bounds on the broadcast rate are derived for singleton $S$, which establishes the optimality of the achievability scheme for a range of values for $t$ and for any $g$ and $s$. For all other values, it is shown that the achievability scheme is optimal among the restricted class of broadcast codes.

cs.IT↗

arXiv2024

Generalized Rainbow Differential Privacy

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.

cs.CR↗

arXiv2024

Cooperative Jamming for Physical Layer Security Enhancement Using Deep Reinforcement Learning

Wireless data communications are always facing the risk of eavesdropping and interception. Conventional protection solutions which are based on encryption may not always be practical as is the case for wireless IoT networks or may soon become ineffective against quantum computers. In this regard, Physical Layer Security (PLS) presents a promising approach to secure wireless communications through the exploitation of the physical properties of the wireless channel. Cooperative Friendly Jamming (CFJ) is among the PLS techniques that have received attention in recent years. However, finding an optimal transmit power allocation that results in the highest secrecy is a complex problem that becomes more difficult to address as the size of the wireless network increases. In this paper, we propose an optimization approach to achieve CFJ in large Wi-Fi networks by using a Reinforcement Learning Algorithm. Obtained results show that our optimization approach offers better secrecy results and becomes more effective as the network size and the density of Wi-Fi access points increase.

cs.NI↗