Abstract We establish the randomized distributed function computation (RDFC) framework, in which a sender transmits just enough information for a receiver to generate a randomized function of the input data. Describing RDFC as a form of semantic communication, which can be essentially seen as a generalized remote-source-coding problem, we show that security and privacy constraints naturally fit this model, as they generally require a randomization step. Using strong coordination metrics, we ensure (local differential) privacy for every input sequence and prove that such guarantees can be met even when no common randomness is shared between the transmitter and receiver. This work provides lower bounds on Wyner’s common information (WCI), which is the communication cost when common randomness is absent, and proposes numerical techniques to evaluate the other corner point of the RDFC rate region for continuous-alphabet random variables with unlimited shared randomness. Experiments illustrate that a sufficient amount of common randomness can reduce the semantic communication rate by up to two orders of magnitude compared to the WCI point, while RDFC without any shared randomness still outperforms lossless transmission by a large margin. A finite blocklength analysis further confirms that the privacy parameter gap between the asymptotic and non-asymptotic RDFC methods closes exponentially fast with input length. Our results position RDFC as an energy-efficient semantic communication strategy for privacy-aware distributed computation systems.

Next-generation wireless networks are progressing beyond conventional connectivity to incorporate emerging sensing and computing capabilities. This convergence gives rise to integrated systems that enable not only uninterrupted communication, but also environmental awareness, intelligent decision-making, and novel applications that take advantage of these combined features. At the same time, this integration brings substantial security challenges. As computing, sensing, and communication become more tightly intertwined, the overall complexity of the system increases, creating new vulnerabilities and expanding the attack surface. The widespread deployment of data-heavy artificial intelligence applications further amplifies concerns regarding data security and privacy. This paper presents a comprehensive survey of security and privacy threats, along with potential countermeasures, in integrated wireless systems. We first review physical-layer security techniques for communication networks, and then investigate the security and privacy implications of semantic and pragmatic communications and their associated cross-layer design methodologies. For sensing functionalities, we pinpoint security and privacy risks at the levels of signal sources, propagation channels, and sensing targets, and summarize state-of-the-art defense strategies for each. The growing computational requirements of these applications drive the need for distributed computing over the network, which introduces additional risks such as data leakage, weak authentication, and multiple points of failure. We subsequently discuss secure coded computing approaches that can help overcome several of these challenges. Finally, we introduce unified security frameworks tailored to integrated communication–sensing–computing architectures, offering an end-to-end perspective on protecting future wireless systems.

Distributed computing enables scalable machine learning by distributing tasks across multiple nodes, but ensuring privacy in such systems remains a challenge. This paper introduces a novelprivate coded distributed computingmodel that integrates privacy constraints to keep task assignments hidden. By leveragingplacement delivery arrays(PDAs), we design an extended PDA framework to characterize achievable computation and communication loads under privacy constraints. By constructing two classes of extended PDAs, we explore the trade-offs between computation and communication, showing that although privacy increases communication overhead, it can be significantly alleviated through optimized PDA-based coded strategies.

Secure rate-distortion-perception (RDP) trade-offs arise in critical applications, such as semantic compression and privacy-preserving generative coding, where preserving perceptual quality while minimizing distortion is vital. This paper studies a framework for secure RDP over noiseless and noisy broadcast channels under strong secrecy constraints. We first characterize the exact secure RDP region for noiseless transmission channels. We then develop an inner bound on the secure RDP region for a memoryless broadcast channel with correlated noise components at the receivers' observations and prove its tightness under a more capable broadcast channel assumption. Our results demonstrate how optimized binning schemes simultaneously achieve high perceptual quality, low distortion, and strong secrecy, illuminating fundamental information-theoretic limits for next-generation trustworthy computation systems.

The randomized distributed function computation (RDFC) framework, which unifies many cutting-edge distributed computation and learning applications, is considered. An autoencoder (AE) architecture is proposed to minimize the total variation distance between the probability distribution simulated by the AE outputs and an unknown target distribution, using only data samples. We illustrate significantly high RDFC performance with communication load gains from our AEs compared to data compression methods. Our designs establish deep learning-based RDFC methods and aim to facilitate the use of RDFC methods, especially when the amount of common randomness is limited and strong function computation guarantees are required.

Distributed computing methods play a vital role in scalable machine learning as they divide computations across multiple nodes to handle large-scale tasks efficiently. However, maintaining privacy within such systems is a key challenge, particularly for sensitive use cases like federated learning. This paper presents a private coded distributed computing model that incorporates privacy safeguards into distributed computing processes, ensuring that the task allocation of each node remains undisclosed. By leveraging placement delivery arrays (PDAs), the proposed framework introduces a private coding scheme that achieves a balance between computation and communication loads while preserving privacy. We design an extended PDA merging multiple PDAs to formulate the achievable computation and communication loads under privacy constraints.

Consider the problem of best arm identification with a security constraint. Specifically, assume a setup of stochastic linear bandits with K arms of dimension d. In each arm pull, the player receives a reward that is the sum of the dot product of the arm with an unknown parameter vector and independent noise. The player’s goal is to identify the best arm after T arm pulls. Moreover, assume a copycat Chloe is observing the arm pulls. The player wishes to keep Chloe ignorant of the best arm.While a minimax–optimal algorithm identifies the best arm with an $\Omega \left({\frac{T}{{\log (d)}}}\right)$ error exponent, it easily reveals its best-arm estimate to an outside observer, as the best arms are played more frequently. A naïve secure algorithm that plays all arms equally results in an $\Omega \left({\frac{T}{d}}\right)$ exponent. In this paper, we propose a secure algorithm that plays with coded arms. The algorithm does not require any key or cryptographic primitives, yet achieves an $\Omega \left({\frac{T}{{{{\log }^2}(d)}}}\right)$ exponent while revealing almost no information on the best arm.

This paper addresses the challenge of best arm identification in stochastic multi-armed bandit (MAB) models under privacy-preserving constraints, such as in dynamic spectrum access networks where secondary users must privately detect underutilized channels. While previous network security research has explored securing MAB algorithms through techniques such as homomorphic encryption or differential privacy, these methods often suffer from high computational overhead or introduce noise that strictly decreases accuracy. In contrast, this work focuses on lightweight solutions that ensure data confidentiality without compromising the accuracy of best arm identification. We introduce two secure protocols that leverage additive secret sharing and threshold secret sharing. The proposed model, employing aggregation nodes and a comparator node, securely distributes computations to prevent any entity from accessing complete reward or ranking data. Furthermore, the protocol ensures resistance to collusion and fault tolerance, while maintaining computational efficiency. These contributions establish a scalable and robust framework for privacy-preserving best arm identification, offering practical and secure solutions that use MAB methods for network security.

This paper explores the multi-access distributed computing (MADC) model, a novel distributed computing framework where mapper and reducer nodes are distinct entities. Unlike traditional MapReduce frameworks, MADC leverages coding-theoretic techniques to minimize communication overhead without necessitating file replication across mapper nodes. We introduce a new approach utilizing combinatorial designs, specifically t-designs, to construct efficient coding schemes that achieve a computation load of 1. By establishing a connection between t-designs and MapReduce Arrays, we characterize the achievable communication loads and demonstrate the flexibility of our method in selecting the number of reducer nodes. The proposed scheme significantly reduces the number of reducer nodes relative to existing combinatorial topology schemes, at the expense of increased communication cost.

The wiretap channel is a well-studied problem in the physical layer security literature. Although it is proven that the decoding error probability and information leakage can be made arbitrarily small in the asymptotic regime, further research on finite-blocklength codes is required on the path towards practical, secure communication systems. This work provides the first experimental characterization of a deep learning-based, finite-blocklength code construction for multi-tap fading wiretap channels without channel state information. In addition to the evaluation of the average probability of error and information leakage, we examine the designed codes in the presence of fading in terms of the equivocation rate and illustrate the influence of (i) the number of fading taps, (ii) differing variances of the fading coefficients, and (iii) the seed selection for the hash function-based security layer.

A novel distributed computing model calledMulti-access Distributed Computing (MADC)was recently introduced in the literature. The MADC models with Combinatorial Topology (CT) were studied, where there are A mapper nodes andK= (Λ α) reducer nodes with each reducer node connected to distinct α 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). The connection between MRAs and MRGs is established, thereby exploring new topologies and providing coded shuffling schemes for the MADC models with MRGs using the structure of MRAs. A novelNearest Neighbor Connect-MRG (NNC-MRG)is explored and a coding scheme is provided for MADC models with NNC-MRG. Moreover, CT is generalized to Generalized Combinatorial-MRG (GC-MRG). A set ofg–regular MRAs is provided which corresponds to the existing scheme for MADC models with CT and extended those to generate another set of MRAs to represent MADC models with GC-MRG. One of the major limitations of the existing scheme for CT is that it requires an exponentially large number of reducer nodes and input files for large Λ. 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. Another way of tackling this is by using a different MRG, specifically NNC-MRG, where the number of reducer nodes and files required are significantly smaller compared to CT.

We consider two critical aspects of security in thedistributed computing (DC)model:secure data shufflingandsecure coded computing. It is imperative that any external entity overhearing the communication does not gain any information about theintermediate 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. First, we establish that the computation and communication loads stay the same as for non-secure data shuffling. However, implementing secure data shuffling requires additional overhead for storing secret keys at the nodes. Next, we show that for secure coded computation, both the computation and communication loads increase compared to the non-secure scenario, along with the overhead for storing secret keys. Finally, we extend our security results to a novel distributed computing model known asmulti-access distributed computing (MADC), which was recently introduced. The MADC model features two distinct sets of nodes, namelymapperandreducernodes. Unlike the original setting where mapper and reducer nodes were the same, in this model, they are separate entities, and each reducer node is connected to multiple mapper nodes. We show that, for MADC models also, computation and communication loads remain the same with or without secure data shuffling. However, secure coded computation results in increased computation and communication loads compared to the non-secure case, and both scenarios require overhead for storing secret keys at the reducer nodes.

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.

A novel distributed computing model called Multi-access 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$\dot{K}=\binom{\lambda}{\alpha}$reducer nodes with each reducer node connected to distinct$\alpha$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$g$-regular 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 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.

Small neural networks (NNs) used for error correction were shown to improve on classic channel codes and to address channel model changes. We extend the code dimension of any such structure by using the same NN under one-hot encoding multiple times, then serially-concatenated with an outer classic code. We design NNs with the same network parameters, where each Reed-Solomon codeword symbol is an input to a different NN. Significant improvements in block error probabilities for an additive Gaussian noise channel as compared to the small neural code are illustrated, as well as robustness to channel model changes.

The distributed source coding problem is extended by positing that noisy measurements of a remote source are the correlated random variables that should be reconstructed at another terminal. We consider a secure and private distributed lossy source coding problem with two encoders and one decoder such that (i) all terminals noncausally observe a noisy measurement of the remote source; (ii) a private key is available to each legitimate encoder and all private keys are available to the decoder; (iii) rate-limited noiseless communication links are available between each encoder and the decoder; (iv) the amount of information leakage to an eavesdropper about the correlated random variables is defined assecrecyleakage, andprivacyleakage is measured with respect to the remote source; and (v) two passive attack scenarios are considered, where a strong eavesdropper can access both communication links and a weak eavesdropper can choose only one of the links to access. Inner and outer bounds on the rate regions defined under secrecy, privacy, communication, and distortion constraints are derived for both passive attack scenarios. When one or both sources should be reconstructed reliably, the rate region bounds are simplified.

Federated learning (FL) enables large-scale machine learning with user data privacy due to its decentralized structure. However, the user data can still be inferred via the shared model updates. To strengthen the privacy, we consider FL with local differential privacy (LDP). One of the challenges in FL is its huge communication cost caused by iterative transmissions of model updates. It has been relieved by quantization in the literature, however, there have been not many works that consider its effect on LDP and the unboundedness of the randomized model updates. We propose a communication-efficient FL algorithm with LDP that uses a Gaussian mechanism followed by quantization and the Elias-gamma coding. A novel design of the algorithm guarantees LDP even after the quantization. Under the proposed algorithm, we provide a trade-off analysis of privacy and communication costs theoretically: quantization reduces the communication costs but requires a larger perturbation to enable LDP. Experimental results show that the accuracy is mostly affected by the noise from LDP mechanisms, and it becomes enhanced when the quantization error is larger. Nonetheless, our experimental results enabled LDP with a significant compression ratio and only a slight reduction of accuracy in return. Furthermore, the proposed algorithm outperforms another algorithm with a discrete Gaussian mechanism under the same privacy budget and communication costs constraints in the experiments.

This work considers mitigation of information leakage between communication and sensing operations in joint communication and sensing systems. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to simultaneously achieve reliable communication and channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to a 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 characteristic of the receiver, e.g., its location. For independent and identically distributed (i.i.d.) 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 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 a binary joint communication and sensing model.

We extend a previous framework for designing differentially private (DP) mechanisms via randomized graph colorings that was restricted to binary functions, corresponding to colorings in a graph, to multi-valued functions. As before, datasets are nodes in the graph and any two neighboring datasets are connected by an edge. In our setting, we assume that each dataset has a preferential ordering for the possible outputs of the mechanism, each of which we refer to as a rainbow. Different rainbows partition the graph of datasets into different regions. We show that if the DP mechanism is pre-specified at the boundary of such regions and behaves identically for all same-rainbow boundary datasets, at most one optimal such mechanism can exist and the problem can be solved by means of a morphism to a line graph. We then show closed form expressions for the line graph in the case of ternary functions. Treatment of ternary queries in this paper displays enough richness to be extended to higher-dimensional query spaces with preferential query ordering, but the optimality proof does not seem to follow directly from the ternary proof.

The problem of secure source coding with multiple terminals is extended by considering a remote source whose noisy measurements are the correlated random variables used for secure source reconstruction. The main additions to the problem include 1) all terminals noncausally observe a noisy measurement of the remote source; 2) a private key is available to all legitimate terminals; 3) the public communication link between the encoder and decoder is rate-limited; and 4) the secrecy leakage to the eavesdropper is measured with respect to the encoder input, whereas the privacy leakage is measured with respect to the remote source. Exact rate regions are characterized for a lossy source coding problem with a private key, remote source, and decoder side information under security, privacy, communication, and distortion constraints. By replacing the distortion constraint with a reliability constraint, we obtain the exact rate region also for the lossless case. Furthermore, the lossy rate region for scalar discrete-time Gaussian sources and measurement channels is established.

Consider the identification (ID) via channels problem, where a receiver decides whether the transmitted identifier is its identifier, rather than decoding it. This model allows to transmit identifiers whose size scales doubly-exponentially in the blocklength, unlike common transmission codes with exponential scaling. Binary constant-weight codes (CWCs) suffice to achieve the ID capacity. Relating parameters of a binary CWC to the minimum distance of a code and using higher-order correlation moments, two upper bounds on binary CWC sizes are proposed. These bounds are also upper bounds on identifier sizes for ID codes constructed by using binary CWCs. We propose two constructions based on optical orthogonal codes (OOCs), which are used in optical multiple access schemes, have constant-weight codewords, and satisfy cyclic cross-correlation and auto-correlation constraints. These constructions are modified and concatenated with outer Reed-Solomon codes to propose new binary CWCs being optimal for ID. Improvements to the finite-parameter performance are shown by using outer codes with larger minimum distance vs. blocklength ratios. We illustrate ID regimes for which our ID code constructions perform significantly better than existing constructions.

We consider a set of security and privacy problems under reliability and storage constraints that can be tackled by using codes and particularly focus on the secret-key agreement problem. Polar subcodes (PSCs) are polar codes (PCs) with dynamically-frozen symbols and have a larger code minimum distance than PCs with only statically-frozen symbols. A randomized nested PSC construction, where the low-rate code is a PSC and the high-rate code is a PC, is proposed for successive cancellation list (SCL) and sequential decoders. This code construction aims to perform lossy compression with side information, i.e., Wyner-Ziv (WZ) coding. Nested PSCs are used in the key agreement problem with physical identifiers and two terminals since WZ-coding constructions significantly improve on Slepian-Wolf coding constructions such as fuzzy extractors. Significant gains in terms of the secret-key vs. storage rate ratio as compared to nested PCs with the same list sizes are illustrated to show that nested PSCs significantly improve on all existing code constructions. The performance of the nested PSCs is shown to improve with larger list sizes, unlike the nested PCs considered. A design procedure to efficiently construct nested PSCs and possible improvements to the nested PSC designs are also provided.

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 remainsecretfrom 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 remainprivatefrom 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.

Federated learning (FL) allows to train a massive amount of data privately due to its decentralized structure. Stochastic gradient descent (SGD) is commonly used for FL due to its good empirical performance, but sensitive user information can still be inferred from weight updates shared during FL iterations. We consider Gaussian mechanisms to preserve local differential privacy (LDP) of user data in the FL model with SGD. The trade-offs between user privacy, global utility, and transmission rate are proved by defining appropriate metrics for FL with LDP. Compared to existing results, the query sensitivity used in LDP is defined as a variable, and a tighter privacy accounting method is applied. The proposed utility bound allows heterogeneous parameters over all users. Our bounds characterize how much utility decreases and transmission rate increases if a stronger privacy regime is targeted. Furthermore, given a target privacy level, our results guarantee a significantly larger utility and a smaller transmission rate as compared to existing privacy accounting methods.

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 privacy and secrecy. Specifically, 1) the remote source should remain private from an eavesdropper and the fusion center, measured in terms of the information leaked about the remote source; 2) the function computed should remain secret from the eavesdropper, measured in terms of the information leaked about the arguments of the function, to ensure secrecy regardless of the exact function used. 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 differing only in the Markov chain conditions imposed are characterized.

Consider the identification (ID) via channels problem, where a receiver wants to decide whether the transmitted identifier is its identifier, rather than decoding the identifier. This model allows to transmit identifiers whose size scales doubly-exponentially in the blocklength, unlike common transmission (or channel) codes whose size scales exponentially. It suffices to use binary constant-weight codes (CWCs) to achieve the ID capacity. By relating the parameters of a binary CWC to the minimum distance of a code and using higher-order correlation moments, two upper bounds on the binary CWC size are proposed. These bounds are shown to be upper bounds also on the identifier sizes for ID codes constructed by using binary CWCs. We propose two code constructions based on optical orthogonal codes, which are used in optical multiple access schemes, have constant-weight codewords, and satisfy cyclic cross-correlation and autocorrelation constraints. These constructions are modified and concatenated with outer Reed-Solomon codes to propose new binary CWCs optimal for ID. Improvements to the finite-parameter performance of both our and existing code constructions are shown by using outer codes with larger minimum distance vs. blocklength ratios. We also illustrate ID performance regimes for which our ID code constructions perform significantly better than existing constructions.

A basic model for key agreement with a remote (or hidden) source is extended to a multi-user model with joint secrecy and privacy constraints over all entities that do not trust each other after key agreement. Multiple entities using different measurements of the same source through broadcast channels (BCs) to agree on mutually-independent local secret keys are considered. Our model is the proper multi-user extension of the basic model since the encoder and decoder pairs are not assumed to trust other pairs after key agreement, unlike assumed in the literature. Strong secrecy constraints imposed on all secret keys jointly, which is more stringent than separate secrecy leakage constraints for each secret key considered in the literature, are satisfied. Inner bounds for maximum key rate, and minimum privacy-leakage and database-storage rates are proposed for any finite number of entities. Inner and outer bounds for degraded and less-noisy BCs are given to illustrate cases with strong privacy. A multi-enrollment model that is used for common physical unclonable functions is also considered to establish inner and outer bounds for key-leakage-storage regions that differ only in the Markov chains imposed. For this special case, the encoder and decoder measurement channels have the same channel transition matrix and secrecy leakage is measured for each secret key separately. We illustrate cases for which it is useful to have multiple enrollments as compared to a single enrollment and vice versa.

Noisy measurements of a physical unclonable function (PUF) are used to store secret keys with reliability, security, privacy, and complexity constraints. A new set of low-complexity and orthogonal transforms with no multiplication is proposed to obtain bit-error probability results significantly better than all methods previously proposed for key binding with PUFs. The uniqueness and security performance of a transform selected from the proposed set is shown to be close to optimal. An error-correction code with a low-complexity decoder and a high code rate is shown to provide a block-error probability significantly smaller than provided by previously proposed codes with the same or smaller code rates.

The key agreement problem with biometric or physical identifiers and two terminals for key enrollment and reconstruction is considered. A nested convolutional code construction that performs lossy compression with side information is proposed. Nested convolutional codes are an alternative to nested polar codes and nested random linear codes that achieve all points of the key-leakage-storage regions of the generated-secret and chosen-secret models for long block lengths. Our design uses a convolutional code for vector quantization during enrollment and a subcode of it for error correction during reconstruction. Physical identifiers with small bit error probability are considered to illustrate the gains of the proposed construction. One variant of nested convolutional codes improves on all previous constructions in terms of the key vs. storage rate ratio but it has high complexity. Another variant of nested convolutional codes with lower complexity performs similarly to previously designed nested polar codes. The results suggest that the choice of convolutional or polar codes for key agreement with identifiers depends on the complexity constraints.

The problem of secret-key based authentication under privacy and storage constraints on the source sequence is considered. The identifier measurement channels during authentication are assumed to be controllable via a cost-constrained action sequence. Single-letter inner and outer bounds for the keyleakage-storage-cost regions are derived for a generalization of a classic two-terminal key agreement model with an eavesdropper that observes a sequence that is correlated with the sequences observed by the legitimate terminals. The additions to the model are that the encoder observes a noisy version of a remote source, and the noisy output and the remote source output together with an action sequence are given as inputs to the measurement channel at the decoder. Thus, correlation is introduced between the noise components on the encoder and decoder measurements. The model with a secret key generated by an encoder is extended to the randomized models, where a secret-key is embedded to the encoder. The results are relevant for several user and device authentication scenarios including physical and biometric identifiers with multiple measurements that provide diversity and multiplexing gains. To illustrate the behavior of the rate region, achievable (secret-key rate, storage-rate, cost) tuples are given for binary identifiers and measurement channels that can be represented as a mixture of binary symmetric subchannels. The gains from using an action sequence such as a large secret-key rate at a significantly small hardware cost, are illustrated to motivate the use of low-complexity transform-coding algorithms with cost-constrained actions.

Two new classes of skew codes over a finite field F are proposed, called skew convolutional codes and skew trellis codes. These two classes are defined by, respectively, left or right sub-modules over the skew fields of fractions of skew polynomials over $\mathbb{F}$. The skew convolutional codes can be represented as periodic time-varying ordinary convolutional codes. The skew trellis codes are in general nonlinear over $\mathbb{F}$. Every code from both classes has a code trellis and can be decoded by Viterbi or BCJR algorithms.

A two-party key agreement problem with public discussion, known as the source model problem, is considered. By relating key agreement to hypothesis testing, a new coding scheme is developed that yields a sufficient condition to achieve a positive secret-key (SK) rate in terms of Rényi divergence. The merits of this coding scheme are illustrated by applying it to an erasure model for Eve's side information and by deriving an upper bound on Eve's erasure probabilities for which the SK capacity is zero. This bound strictly improves on the best known single-letter lower bound on the SK capacity. Moreover, the bound is tight when Alice's or Bob's source is binary, which extends a previous result for a doubly symmetric binary source. The results motivate a new measure for the correlation between two random variables which is of independent interest.

A basic model for key agreement with biometric or physical identifiers is extended to include measurements of a hidden source through a general broadcast channel (BC). An inner bound for strong secrecy, maximum key rate, and minimum privacy-leakage and database-storage rates is proposed. The inner bound is shown to be tight for physically-degraded and less-noisy BCs.

The two-terminal key agreement problem with biometric or physical identifiers is considered. Two linear code constructions based on Wyner-Ziv coding are developed. The first construction uses random linear codes and achieves all points of the key-leakage-storage regions of the generated-secret and chosen-secret models. The second construction uses nested polar codes for vector quantization during enrollment and for error correction during reconstruction. The simulation results show that the nested polar codes achieve privacy leakage and storage rates that improve on existing code designs. One proposed code achieves a rate tuple that cannot be achieved by existing methods.

The two-party key agreement problem with public discussion, known as the source model problem, is considered for an erasure model for Eve's side information. By relating the key agreement problem to hypothesis testing, a new coding scheme is developed that yields an upper bound on the maximum erasure probability for which the secret-key (SK) capacity is zero. The bound is shown to be tight when Alice's or Bob's source is binary, and this shows that the new code achieves larger SK rates than the best known coding scheme. A full version of this paper with extensions to general models for Eve's side information is available in [1].

The key-leakage-storage region is derived for a generalization of a classic two-terminal key agreement model. The additions to the model are that the encoder observes a hidden, or noisy, version of the identifier, and that the encoder and decoder can perform multiple measurements. To illustrate the behavior of the region, the theory is applied to binary identifiers and noise modeled via binary symmetric channels. In particular, the key-leakage-storage region is simplified by applying Mrs. Gerber's lemma twice in different directions to a Markov chain. The growth in the region as the number of measurements increases is quantified. The amount by which the privacy-leakage rate reduces for a hidden identifier as compared to a noise-free (visible) identifier at the encoder is also given. If the encoder incorrectly models the source as visible, it is shown that substantial secrecy leakage may occur and the reliability of the reconstructed key might decrease.

The problem of secret-key based authentication under a privacy constraint on the source sequence is considered. The identifier measurements during authentication are assumed to be controllable via a cost-constrained “action” sequence. Single-letter characterizations of the optimal trade-off among the secret-key rate, storage rate, privacy-leakage rate, and action cost are given for the four problems where noisy or noiseless measurements of the source are enrolled to generate or embed secret keys. The results are relevant for several user-authentication scenarios, including physical and biometric authentications with multiple measurements. Our results include, as special cases, new results for secret-key generation and embedding with action-dependent side information without any privacy constraint on the enrolled source sequence.

A joint quantizer and code design is proposed to store secret keys by using fuzzy commitment. Ring oscillators (RO) are used as physical identifiers and transform-coding algorithms to decorrelate the RO outputs. The transform codes are combined with scalar quantizers to satisfy a small block-error probability constraint. The proposed designs are shown to provide perfect secrecy, and smaller privacy-leakage and greater secret-key rates than previously proposed codes.

A new post-processing scheme is proposed for Physical Unclonable Functions (PUFs) based on Ring Oscillators (ROs). The scheme uses the Discrete Cosine Transform (DCT) to decorrelate the RO outputs and improves on existing RO PUFs in terms of uniqueness and the number of extracted bits.