We generalize secret-sharing models that rely on correlated randomness and public communication, originally designed for a fixed access structure, to support a sequence of dynamic access structures, which we term an Additive Access Structure. Specifically, the access structure is allowed to monotonically grow by having any subset of participants added to it at a given time step, and the dealer only learns of these changes to the access structure on the time step that they occur. For this model, we prove the existence of a secret sharing strategy that achieves the same secret rate at each time step as the best known strategy for the fixed access structure version of this model. We also prove that there exists a strategy that is capacity-achieving at any time step where the access structure is a threshold access structure.

Information-theoretically secure Symmetric Private Information Retrieval (SPIR) from a single server is known to be infeasible over noiseless channels. Known solutions to overcome this infeasibility involve additional resources such as database replication, shared randomness, or noisy channels. In this paper, we propose an alternative approach for achieving SPIR with information-theoretic security guarantees, without relying on shared randomness, noisy channels, or data replication. Specifically, we demonstrate that it is sufficient to use a noiseless binary adder multiple-access channel, where inputs are controlled by two non-colluding servers and the output is observed by the client, alongside a public noiseless communication channel between the client and the servers. Furthermore, in this setting, we characterize the optimal file rates, i.e., the file lengths normalized by the number of channel uses, that can be transferred.

The reconstruction of sparse signals from a limited set of measurements poses a significant challenge as it necessitates a solution to an underdetermined system of linear equations. Compressed sensing (CS) deals with sparse signal reconstruction using techniques such as linear programming (LP) and iterative message passing schemes. The interval passing algorithm (IPA) is an attractive CS approach due to its low complexity when compared to LP. In this paper, we propose a sequential IPA that is inspired by sequential belief propagation decoding of low-density-parity-check (LDPC) codes used for forward error correction in channel coding. In the sequential setting, each check node (CN) in the Tanner graph of an LDPC measurement matrix is scheduled one at a time in every iteration, as opposed to the standard “flooding” interval passing approach in which all CNs are scheduled at once per iteration. The sequential scheme offers a significantly lower message passing complexity compared to flooding IPA on average, and for some measurement matrix and signal sparsity, a complexity reduction of 36% is achieved. We show both analytically and numerically that the reconstruction accuracy of the IPA is not compromised by adopting our sequential scheduling approach.

For uniform secret sharing, the access function takes as input, an integer$i$and returns as output the fraction of information leaked about the secret by$i$shares. Most previous works aimed to characterize the minimum share size, considering a fixed access function with all outputs predefined. By contrast, in this paper, we consider uniform secret sharing where not all outputs of the access function are predefined, instead, only upper bounds are specified for some outputs. These constraints define a set of access functions, and our goal is to find the access function in this set that minimizes the share sizes. We (i) determine the optimal access function that leads to minimum share sizes by optimizing over this set of access functions. We show that it is a convex function expressed as a combination of piece-wise linear functions. Additionally, we (ii) characterize a closed-form expression of the optimal share sizes.

This work considers a secret sharing problem where the dealer uses a classical-quantum channel to divide and distribute shares to two users by encoding the secret so that the channel observation of each user is their share. The channel observations of a single user contains very little information about the secret, but the two users together can recover the secret. We derive a one-shot and an asymptotic achievability result for secret sharing over a quantum broadcast channel. Additionally, our achievability results coincide with the secret sharing capacity for the classical broadcast channel.

Consider lossy function computation in distributed databases that contain both sensitive (private) and non-sensitive (public) attributes. A user aims to compute a function of the public attributes and side information and interacts with the databases to download a response from each for computing the function. In this paper, we are interested in quantifying the optimal download cost and the minimum information leakage about the private attributes that the user can learn. Our main contributions include complete characterizations of the optimal trade-offs among download cost, leakage, and distortion in a single database for both discrete and Gaussian sources, as well as inner and outer bounds of the tradeoffs for distributed databases.

We study covert classical communication over a quantum multiple-access channel (MAC) with a helper. Specifically, we consider three transmitters, where one transmitter helps the other two transmitters communicate covertly with a receiver. We demonstrate the feasibility of achieving a positive covert rate over this channel and establish an achievable rate region. Our result recovers as a special case known results for classical communication over classical MACs with a degraded message set, classical communication over quantum MACs, and classical communication over MACs with a helper. To the best of our knowledge, our result is the first to achieve covert communication with positive rates over both classical and quantum MACs.

We study covert communication and covert secret key generation with positive rates over channels with causal Channel State Information (CSI) at the transmitter. Specifically, we consider a state-dependent Discrete Memoryless Channel (DMC) where the transmitter has causal access to the CSI, and aims to communicate covertly with the receiver while simultaneously generating a covert secret key shared with the receiver. We derive an achievable rate region for this problem, which recovers as a special case the best-known results for covert communication over channels with CSI. To the best of our knowledge, our results are the first instance of achieving a positive rate for covert secret key generation.

We study a privacy-preserving data-sharing setting where a privatizer transforms private data into a sanitized version observed by an authorized reconstructor and two unauthorized adversaries, each with access to side information correlated with the private data.The reconstructor is evaluated under a distortion function, while each adversary is evaluated using a separate loss function. The privatizer ensures the reconstructor distortion remains below a fixed threshold while maximizing the minimum loss across the two adversaries. This two-adversary setting models cases where individual users cannot reconstruct the data accurately, but their combined side information enables estimation within the distortion threshold. The privatizer maximizes individual loss while permitting accurate reconstruction only through collaboration. This echoes secret-sharing principles, but with lossy rather than perfect recovery. We frame this as a constrained data-driven minimax optimization problem and propose a data-driven training procedure that alternately updates the privatizer, reconstructor, and adversaries. We also analyze the Gaussian and binary cases as special scenarios where optimal solutions can be obtained. These theoretical optimal results are benchmarks for evaluating the proposed minimax training approach.

Consider the Gaussian wiretap channel, where a transmitter wishes to send a confidential message to a legitimate receiver in the presence of an eavesdropper. It is well known that if the eavesdropper experiences less channel noise than the legitimate receiver, then it is impossible for the transmitter to achieve positive secrecy rates. A known solution to this issue consists in involving a second transmitter, referred to as a helper, to help the first transmitter to achieve security. While such a solution has been studied for the asymptotic blocklength regime and via non-constructive coding schemes, in this paper, for the first time, we design explicit and short blocklength codes using deep learning and cryptographic tools to demonstrate the benefit and practicality of cooperation between two transmitters over the wiretap channel. Specifically, our proposed codes show strict improvement in terms of information leakage compared to existing codes that do not consider a helper. Our code design approach relies on a reliability layer, implemented with an autoencoder architecture based on the successive interference cancellation method, and a security layer implemented with universal hash functions. We also propose an alternative autoencoder architecture that significantly reduces training time by allowing the decoders to independently estimate messages without successively canceling interference by the receiver during training. Additionally, we show that our code design is also applicable to the multiple access wiretap channel with helpers, where two transmitters send confidential messages to the legitimate receiver.

This study investigates secret-key generation for device authentication using physical identifiers, such as responses from physical unclonable functions (PUFs). The system includes two legitimate terminals (encoder and decoder) and an eavesdropper (Eve), each with access to different measurements of the identifier. From the device identifier, the encoder generates a secret key, which is securely stored in a private database, along with helper data that is saved in a public database accessible by the decoder for key reconstruction. Eve, who also has access to the public database, may use both her own measurements and the helper data to attempt to estimate the secret key and identifier. Our setup focuses on authentication scenarios where channel statistics are uncertain, with the involved parties employing multiple antennas to enhance signal reception. Our contributions include deriving inner and outer bounds on the optimal trade-off among secret-key, storage, and privacy-leakage rates for general discrete sources, and showing that these bounds are tight for Gaussian sources.

We consider multi-user commitment models that capture the problem of enabling multiple bidders to simultaneously submit auctions to verifiers while ensuring that i) verifiers do not obtain information on the auctions until bidders reveal them at a later stage; and, ii) bidders cannot change their auction once committed. Specifically, we assume that bidders and verifiers have access to a noiseless channel as well as a noisy multiple-access channel or broadcast channel, where inputs are controlled by the bidders and outputs are observed by verifiers. In the case of multiple bidders and a single verifier connected by a non-redundant multiple-access channel, we characterize the commitment capacity region when bidders are not colluding. When the bidders are colluding, we derive an achievable region and a tight converse for the sum rate. In both cases our proposed achievable commitment schemes are constructive. In the case of a single bidder and multiple verifiers connected by a non-redundant broadcast channel, in which verifiers could drop out of the network after auctions are committed, we also characterize the commitment capacity. Our results demonstrate how commitment schemes can benefit from multi-user protocols, and develop resilience when some verifiers may become unavailable.

ConsiderLusers, who each hold private data, and one fusion center who must compute a function of the private data of theLusers. To accomplish this task, each user may utilize a public and noiseless broadcast channel in a non-interactive manner. In this setting, and in the absence of any additional resources such as secure links, we study the optimal communication rates and minimum information leakages on the private user data that are achievable. Specifically, we study the information leakage of the user data at the fusion center (beyond the knowledge of the function output), as well as at predefined groups of colluding users who eavesdrop one another. We derive the capacity region when the user data is independent, and inner and outer regions for the capacity region when the user data is correlated.

The reconstruction of sparse signals from a limited set of measurements poses a significant challenge as it necessitates a solution to an underdetermined system of linear equations. Compressed sensing (CS) deals with sparse signal reconstruction using techniques such as linear programming (LP) and iterative message passing schemes. The interval passing algorithm (IPA) is an attractive CS approach due to its low complexity when compared to LP. In this paper, we propose a sequential IPA that is inspired by sequential belief propagation decoding of low-density-parity-check (LDPC) codes used for forward error correction in channel coding. In the sequential setting, each check node (CN) in the Tanner graph of an LDPC measurement matrix is scheduled one at a time in every iteration, as opposed to the standard “flooding” interval passing approach in which all CNs are scheduled at once per iteration. The sequential scheme offers a significantly lower message passing complexity compared to flooding IPA on average, and for some measurement matrix and signal sparsity, a complexity reduction of approximately 36% is achieved. We show both analytically and numerically that the reconstruction accuracy of the IPA is not compromised by adopting our sequential scheduling approach.

Noiseless private side information does not reduce the download cost in Symmetric Private Information Retrieval (SPIR) unless the client knows all but one file. While this is a pessimistic result, we explore in this paper whether noisy client side information available at the client helps decrease the download cost in the context of SPIR with colluding and replicated servers. Specifically, we assume that the client possesses noisy side information about each stored file, which is obtained by passing each file through one of D possible discrete memoryless test channels. The statistics of the test channels are known by the client and by all the servers, but the mapping$\boldsymbol {\mathcal {M}}$between the files and the test channels is unknown to the servers. We study this problem under two privacy metrics. Under the first metric, the client wants to preserve the privacy of its file selection and the mapping$\boldsymbol {\mathcal {M}}$, and the servers want to preserve the privacy of all the non-selected files. Under the second metric, the client is willing to reveal the index of the test channel that is associated with its desired file. For both privacy metrics, we derive the optimal common randomness and download cost. Our setup generalizes SPIR with colluding servers and SPIR with private noiseless side information. Unlike noiseless side information, our results demonstrate that noisy side information can reduce the download cost, even when the client does not have noiseless knowledge of all but one file.

We study covert communication and covert secret key generation with positive rates over quantum state-dependent channels. Specifically, we consider fully quantum state-dependent channels when the transmitter shares an entangled state with the channel. We study this problem setting under two security metrics. For the first security metric, the transmitter aims to communicate covertly with the receiver while simultaneously generating a covert secret key, and for the second security metric, the transmitter aims to transmit a secure message covertly and generate a covert secret key with the receiver simultaneously. Our main results include one-shot and asymptotic achievable positive covert-secret key rate pairs for both security metrics. Our results recover as a special case the best-known results for covert communication over state-dependent classical channels. To the best of our knowledge, our results are the first instance of achieving a positive rate for covert secret key generation and the first instance of achieving a positive covert rate over a quantum channel. Additionally, we show that our results are optimal when the channel is classical and the state is available non-causally at both the transmitter and the receiver.

Consider the Gaussian wiretap channel, where a legitimate transmitter wishes to send a confidential message to a legitimate receiver in the presence of an eavesdropper. Unfortunately, in this setting, it is well known that if the eavesdropper experiences less channel noise than the legitimate receiver, then it is impossible for the transmitter to achieve positive secrecy rates. A known solution to this issue consists in involving a second transmitter, referred to as a helper, to help the first transmitter to achieve security. While such a solution has been studied for the asymptotic blocklength regime and via non-constructive coding schemes, in this paper, for the first time, we design explicit and short blocklength codes using deep learning and cryptographic tools to demonstrate the benefit and practicality of cooperation between two transmitters over the wiretap channel. Specifically, our proposed codes show strict improvement in terms of information leakage compared to existing point-to-point codes that do not consider a helper, even when the transmitter has adverse channel conditions, in the sense that the eavesdropper experiences less channel noise than the legitimate receiver. Our code design approach relies on a reliability layer, implemented with an autoencoder architecture inspired by the successive interference cancellation method developed for broadcast channels, and a security layer implemented with universal hash functions.

Information-theoretically secure Symmetric Private Information Retrieval (SPIR) is known to be infeasible over noiseless channels with a single server. Previous solutions in-volved additional resources such as database replication, shared randomness, or noisy channels. This paper demonstrates that, using a noiseless multiple access channel, SPIR with information-theoretic security guarantees is feasible without shared random-ness, a noisy channel, or data replication. Specifically, we leverage a noiseless binary adder channel and employ two non-colluding servers with independent content. Furthermore, we characterize the optimal file rates, i.e., the file lengths normalized by the number of channel uses, that can be transferred.

Consider a scenario involving multiple users and a fusion center. Each user possesses a sequence of bits and can communicate with the fusion center through a one-way public channel. The fusion center's task is to compute the sum of all the sequences under the privacy requirement that a set of colluding users, along with the fusion center, cannot gain more than a predetermined amount$\delta$of information, measured through mutual information, about the sequences of other users. Our first contribution is to characterize the minimum amount of necessary communication between the users and the fusion center, as well as the minimum amount of necessary shared randomness at the users. Our second contribution is to establish a connection between secure summation and secret sharing by showing that secret sharing is necessary to generate the local randomness needed for private summation, and prove that it holds true for any$\delta\geqslant 0$.

Noiseless private side information does not reduce the download cost in Symmetric Private Information Retrieval (SPIR) unless the client knows all but one file. While this is a pessimistic result, we explore in this paper whether noisy private side information available at the client helps decrease the download cost in the context of SPIR with colluding and replicated servers. Specifically, we assume that the client possesses noisy side information about each stored file, which is obtained by passing each file through one of$D$possible discrete memoryless test channels. The statistics of the test channels are known by the client and by all the servers, but the mapping$\mathcal{M}$between the files and the test channels is unknown to the servers. We study this problem under two privacy metrics. Under the first metric, the client wants to preserve the privacy of its file selection and the mapping$\mathcal{M}$, and the servers want to preserve the privacy of all the non-selected files. Under the second metric, the client is willing to reveal the index of the test channel that is associated with its desired file. For both privacy metrics, we derive the optimal common randomness and download cost. Our setup generalizes SPIR with colluding servers and SPIR with private noiseless side information. Unlike noiseless side information, our results demonstrate that noisy side information can reduce the download cost, even when the client does not have noiseless knowledge of all but one file.

In this study, we investigate the fundamental limits of secret-key generation with physical identifiers for compound authentication channels. Our contributions in this paper are the derivations of inner and outer bounds on the optimal tradeoff of secret-key, storage, and privacy-leakage rates for general discrete sources, and we show that these bounds are tight for Gaussian sources. In special cases, our characterizations reduce to existing results derived in previous works.

We show that it is possible to achieve a positive covert communication rate over state-dependent quantum channels. Specifically, we consider fully quantum state-dependent channels when the transmitter shares an entangled state with the channel. To the best of our knowledge, this is the first instance of achieving a positive covert rate over a quantum channel. Our main results include a one-shot achievable covert rate and asymptotic achievable covert rates that recover, as a special case, known results for classical channels.

We consider a secret-sharing model where a dealer distributes the shares of a secret among a set of participants with the constraint that only predetermined subsets of participants must be able to reconstruct the secret by pooling their shares. Our study generalizes Shamir’s secret-sharing model in three directions. First, we allow a joint design of the protocols for the creation of the shares and the distribution of the shares, instead of constraining the model to independent designs. Second, instead of assuming that the participants and the dealer have access to information-theoretically secure channels at no cost, we assume that they have access to a public channel and correlated randomness. Third, motivated by a wireless network setting where the correlated randomness is obtained from channel gain measurements, we explore a distributed setting where the dealer is an entity made of multiple sub-dealers. Our main results are inner and outer regions for the achievable secret rates that the dealer and the participants can obtain in this model. To this end, we develop two new achievability techniques, a first one to successively handle reliability and security constraints in a distributed setting, and a second one to reduce a multi-dealer setting to multiple single-user dealer settings. Our results yield the capacity region for threshold access structures when the correlated randomness corresponds to pairwise secret keys shared between each sub-dealer and each participant, and the capacity for the all-or-nothing access structure in the presence of a single dealer and arbitrarily correlated randomness.

Consider the problem of storing data in a distributed manner over T servers. Specifically, the data needs to (i) be recoverable from any$\tau $servers, and (ii) remain private from any z colluding servers, where privacy is quantified in terms of mutual information between the data and all the information available at any z colluding servers. For this model, our main results are (i) the fundamental trade-off between storage size and the level of desired privacy, and (ii) the optimal amount of local randomness necessary at the encoder. As a byproduct, our results provide an optimal lower bound on the individual share size of ramp secret sharing schemes under a more general leakage symmetry condition than the ones previously considered in the literature.

This paper considers the Gaussian multiple access wiretap channel (GMAC-WT) with selfish transmitters, i.e., who are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective, i.e, multiple access, protocol instead of operating on their own. If yes, the question arises whether there is a protocol that satisfies all the participating transmitters simultaneously, in the sense that no transmitter has an incentive to deviate from the protocol. Utilizing coalitional game theory, these questions are addressed for the degraded GMAC-WT with an arbitrary number of transmitters and for the non-degraded GMAC-WT with two transmitters. In particular, for the degraded GMAC-WT, cooperation is shown to be in the best interest of all transmitters, and the existence of protocols that incentivize all transmitters to participate is established. Furthermore, a unique, fair, stable, and achievable secrecy rate allocation is determined. For the non-degraded GMAC-WT, depending on the channel parameters, there are cases where cooperation is not in the best interest of all transmitters, and cases where it is. In the latter cases, a unique, fair, stable, and achievable secrecy rate allocation is determined.

Consider Private Information Retrieval (PIR), where a client wants to retrieve one file out of$K$files that are replicated in$N$different servers and the client selection must remain private when up to$T$servers may collude. Additionally, suppose that the client has noisy side information about each of the$K$files, and the side information about a specific file is obtained by passing this file through one of$D$possible discrete memoryless test channels, where$D\le K$. While the statistics of the test channels are known by the client and by all the servers, the specific mapping$\boldsymbol { \mathcal {M}}$between the files and the test channels is unknown to the servers. We study this problem under two different privacy metrics. Under the first privacy metric, the client wants to preserve the privacy of its desired file selection and the mapping$\boldsymbol { \mathcal {M}}$. Under the second privacy metric, the client wants to preserve the privacy of its desired file and the mapping$\boldsymbol { \mathcal {M}}$but is willing to reveal the index of the test channel that is associated to its desired file. For both of these two privacy metrics, we derive the optimal normalized download cost. Our problem setup generalizes PIR with colluding servers, PIR with private noiseless side information, and PIR with private side information under storage constraints.

Consider the problem of storing data in a distributed manner over T servers. Specifically, the data needs to (i) be recoverable from any τ servers, and (ii) remain private from any z colluding servers, where privacy is quantified in terms of mutual information between the data and all the information available at any z colluding servers. For this model and under a leakage symmetry requirement at the servers, our main results are (i) the fundamental trade-off between storage size and the level of desired privacy, and (ii) the optimal amount of local randomness necessary at the encoder. As a byproduct, our results provide an optimal lower bound on the individual share size of ramp secret sharing schemes under a more general leakage symmetry condition than the ones previously considered in the literature.

Consider a secret sharing model where a dealer shares a secret with several participants through a Gaussian broadcast channel such that predefined subsets of participants can reconstruct the secret and all other subsets of participants cannot learn any information about the secret. Our first contribution is to show that, in the asymptotic blocklength regime, it is optimal to consider coding schemes that rely on two coding layers, namely, a reliability layer and a secrecy layer, where the reliability layer is a channel code for a compound channel without any security constraint. Our second contribution is to design such a two-layer coding scheme at short blocklength. Specifically, we design the reliability layer via an autoencoder, and implement the secrecy layer with hash functions. To evaluate the performance of our coding scheme, we empirically evaluate the probability of error and information leakage, which is defined as the mutual information between the secret and the unauthorized sets of users channel outputs. We empirically evaluate this information leakage via a neural network-based mutual information estimator. Our simulation results demonstrate a precise control of the probability of error and leakage thanks to the two-layer coding design.

Consider Private Information Retrieval (PIR), where a client wants to retrieve one file out of K files that are replicated in N different servers and the client selection must remain private when up to T servers may collude. Additionally, suppose that the client has noisy side information about each of the K files, and the side information about a specific file is obtained by passing this file through one of D possible discrete memoryless test channels, where D≤K. While the statistics of the test channels are known by the client and by all the servers, the specific mapping ${\mathcal{M}}$ between the files and the test channels is unknown to the servers. We study this problem when the client wants to preserve the privacy of its desired file selection and the mapping ${\mathcal{M}}$. For this problem setup, we derive the optimal download rate. Our problem setup generalizes PIR with private noiseless side information and PIR with private side information under storage constraints.

Consider a commitment protocol between two parties, Alice and Bob, in which Alice may (i) commit to a message using a non-redundant discrete memoryless channel whose outputs are observed by Bob; and (ii) later reveal her committed message to Bob who must decide whether Alice is revealing the message she actually committed to. A commitment protocol should meet three standard requirements: concealment, bindingness, and soundness, to ensure that no party may act dishonestly. Our objective is to study whether one can enforce a fourth requirement that would allow Alice to retract a commitment before the reveal phase starts without Bob detecting that she ever participated in the commit phase of the protocol. We positively answer this question and characterize the commitment capacity for such a setting by relying on tools developed for covert communication.A full version of the paper is available at https://bloch.ece.gatech.edu/ITWretractablecommitment.pdf.

We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint with hash functions. For blocklengths smaller than or equal to 128, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper for our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper’s channel observations, and is empirically measured via a neural network-based mutual information estimator. Our simulation results provide examples of codes with positive secrecy rates that outperform the best known achievable secrecy rates obtained non-constructively for the Gaussian wiretap channel. Additionally, we show that our code design is suitable for the compound and arbitrarily varying Gaussian wiretap channels, for which the channel statistics are not perfectly known but only known to belong to a pre-specified uncertainty set. These models not only capture uncertainty related to channel statistics estimation, but also scenarios where the eavesdropper jams the legitimate transmission or influences its own channel statistics by changing its location.

We consider wiretap channels with uncertainty on the eavesdropper channel under (i) noisy blockwise type II, (ii) compound, or (iii) arbitrarily varying models. We present explicit wiretap codes that can handle these models in a unified manner and only rely on three primitives, namely source coding with side information, universal hashing, and distribution approximation. Our explicit wiretap codes achieve the best known single-letter achievable rates, previously obtained non-constructively, for the models considered. Our results are obtained for strong secrecy, do not require a pre-shared secret between the legitimate users, and do not require any symmetry properties on the channel. An extension of our results to compound main channels is also derived via new capacity-achieving polar coding schemes for compound settings.

Consider a user who wishes to store a file in multiple servers such that at least t servers are needed to reconstruct the files, and z colluding servers cannot learn any information about the file. Unlike traditional models, where perfectly secure channels are assumed to be available at no cost between the user and each server, we assume that the user can only send data to the servers via public channels, and that the user and each server share an individual secret key with length n. For a given n, we determine the maximal length of the file that the user can store, and thus quantify the necessary cost to store a file with a certain length, in terms of the length of the secret that the user needs to share with the servers. Additionally, for this maximal file length, we determine (i) the optimal amount of local randomness needed at the user, (ii) the optimal amount of public communication from the user to the servers, and (iii) the optimal amount of storage requirement at the servers.

Consider L users, who each holds private data, and one fusion center who must compute a function of the private data of the L users. To accomplish this task, each user can make a single use of a public and noiseless broadcast channel. In this setting, and in the absence of any additional resources such as secure links, we study the optimal communication rates and minimum information leakages on the private user data that are achievable. Specifically, we study the information leakage of the user data at the fusion center (beyond the knowledge of the function output), as well as at predefined groups of colluding users who eavesdrop one another. We derive the capacity region when the user data is independent, and inner and outer regions for the capacity region when the user data is correlated.

Consider a source and multiple users who observe the independent and identically distributed (i.i.d.) copies of correlated Gaussian random variables. The source wishes to compress and store its observation in a public database such that (i) authorized sets of users can reconstruct the source with some distortion level, and (ii) information leakage to non-authorized sets of colluding users is minimized. In other words, the recovery of the data is restricted to a predefined access structure of the users. One of the main results of this paper is a closed-form characterization of the fundamental trade-off between source coding rate and the information leakage rate when any authorized set of users has "better" side information than any set of unauthorized users.

We study private classical communication over quantum multiple-access channels. For an arbitrary number of transmitters, we derive a regularized expression of the capacity region. In the case of degradable channels, we establish a single-letter expression for the best achievable sum-rate and prove that this quantity also corresponds to the best achievable sum-rate for quantum communication over degradable quantum multiple-access channels. In our achievability result, we decouple the reliability and privacy constraints, which are handled via source coding with quantum side information and universal hashing, respectively. Hence, we also establish that the multi-user coding problem under consideration can be handled solely via point-to-point coding techniques. As a by-product of independent interest, we derive a distributed leftover hash lemma against quantum side information that ensures privacy in our achievability result.

Consider a user who wishes to store a file in multiple servers such that at least$t$servers are needed to reconstruct the file, and$z$colluding servers cannot learn any information about the file. Unlike traditional secret-sharing models, where perfectly secure channels are assumed to be available at no cost between the user and each server, we assume that the user can only send data to the servers via a public channel, and that the user and each server share an individual secret key with length$n$. For a given$n$, we determine the maximal length of the file that the user can store, and thus quantify the necessary cost to store a file of a certain length, in terms of the length of the secret keys that the user needs to share with the servers. Additionally, for this maximal file length, we determine (i) the optimal amount of local randomness needed at the user, (ii) the optimal amount of public communication from the user to the servers, and (iii) the optimal amount of storage requirement at the servers.

In this paper, we study an information-theoretic secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the following constraints: (i) authorized sets of users can recover the secret by pooling their shares, and (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with participants through a one-way, authenticated, rate-limited, and public channel. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants. Our main result is a closed-form characterization of the fundamental trade-off between secret rate and public communication rate.

We show that the problem of code construction for multiple access channel (MAC) resolvability can be reduced to the simpler problem of code construction for source resolvability. Specifically, we propose a MAC resolvability code construction that relies on a combination of multiple source resolvability codes, used in a black-box manner, and leverages randomness recycling implemented via distributed hashing and block-Markov coding. Since explicit source resolvability codes are known, our results also yield the first explicit coding schemes that achieve the entire MAC resolvability region for any discrete memoryless multiple-access channel with binary input alphabets.

We study private classical communication over quantum multiple-access channels. For an arbitrary number of transmitters, we derive a regularized expression of the capacity region. In the case of degradable channels, we establish a single-letter expression for the best achievable sum-rate and prove that this quantity also corresponds to the best achievable sum-rate for quantum communication over degradable quantum multiple-access channels. Our achievability result decouples the reliability and privacy constraints, which are handled via distributed source coding with quantum side information at the receiver and distributed hashing, respectively. As a by-product of independent interest, we derive a distributed leftover hash lemma against quantum side information that ensures privacy in our achievability result.

We consider secret sharing where a dealer wants to share a secret with several participants such that predefined subsets of participants can reconstruct the secret and all other subsets of participants cannot learn any information about the secret. To this end, the dealer and the participants have access to samples of correlated random variables and a one-way (from the dealer to the participants), authenticated, public, and rate-limited communication channel. For this problem, we propose the first constructive and low-complexity coding scheme able to handle arbitrary access structures. Our construction relies on a vector quantization coupled with distribution approximations with polar codes to handle the reliability constraints, followed by universal hashing to handle the security constraints. We stress that our coding scheme does not require symmetry or degradation assumptions on the correlated random variables, and does not need a pre-shared secret among the participants and dealer. Our result is also optimal in the special case of rate-unlimited public communication when all the participants are needed to reconstruct the secret.

We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint via hash functions. For blocklengths smaller than 16, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper of our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper’s channel observations, and is empirically measured via a recent mutual information neural estimator. Simulation results provide examples of codes with positive rates that achieve a leakage inferior to one percent of the message length.

We consider the problem of storing data in a distributed manner over T servers. We require the data (i) to be recoverable from the T servers, and (ii) to remain private from any T -1 colluding servers, where privacy is quantified in terms of mutual information between the data and all the information available at the T -1 colluding servers. For this model, we determine (i) the fundamental trade-off between storage size and the level of desired privacy, (ii) the optimal amount of local randomness necessary at the encoder, and (iii) an explicit low-complexity coding scheme that solely relies on XOR operations and that asymptotically (with the data size) matches the fundamental limits found.

We show that the problem of code construction for multiple access channel resolvability can be reduced to the simpler problem of code construction for source resolvability. Specifically, we propose a multiple access channel resolvability coding scheme that involves randomness recycling, implemented via distributed hashing, and block-Markov encoding, where each encoding block is obtained as a combination of several source resolvability codes. Our construction is independent of the way the source resolvability codes are implemented and yields explicit coding schemes that achieve the multiple access channel resolvability region for an arbitrary discrete memoryless multiple access channel whose input alphabets are binary.

We consider oblivious transfer between one client and two non-colluding servers that store independent contents. The client requests one file from each server such that (i) the servers do not learn the file selection of the client, and (ii) the client does not learn information about the non-selected files. We show under the honest-but-curious assumption that oblivious transfer with non-zero rates can be achieved with a multiuser protocol between the client and the servers. This contrasts with the case where the client engages in independent protocols with each of the two servers, for which it is known that oblivious transfer with information-theoretic security is impossible in the absence of additional resources. Furthermore, we derive a capacity result for the proposed setting.

We study a secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the constraints that (i) authorized sets of users can recover the secret by pooling their shares, (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and the participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with the participants through a one-way, authenticated, rate-limited, and public channel. Our main result is a closed-form characterization of the trade-off between secret rate and public communication rate. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants, and the size of the shares does not depend exponentially but rather linearly on the number of participants and the size of the secret for arbitrary access structures.

We consider authentication of messages sent from transmitters to a receiver over a multiple access channel, where each transmitter shares a secret key with the legitimate receiver. Additionally, there exists a computationally unbounded opponent who has access to noisy observations of the messages transmitted and can initiate impersonation or substitution attacks. We require that the legitimate receiver must be able to authenticate the messages he receives with respect to predetermined groups of transmitters, but at the same time must be kept ignorant of the transmitter's identity of a given message in a given group. We propose an information-theoretic formulation of these anonymity constraints as well as an authentication coding scheme for which the asymptotic probability of successful attack is shown to optimally scale with the length of the secret keys shared between each transmitter and the legitimate receiver. Our results quantify the positive impact of the multiple access setting compared to the single-user setting on the probability of successful attack.

We propose a model for biometric systems with a multiuser access structure, where after enrollment only predefined authorized sets of participants are allowed to access the system upon presenting their biometrics. Two types of system design are considered for the enrollment. In the first one, the participants must simultaneously present their biometrics to enroll in the system. In the second one, each participant can individually enroll in the system, which is more convenient for systems with a large number of participants. For these two types of enrollment and the presence of a multiuser access structure, the fundamental trade-off between security and privacy leakage is studied.

The Gaussian multiple-access wiretap channel when the number of transmitters grows unbounded and at most linearly with the blocklength is studied. Its capacity region is characterized when the eavesdropper channel is degraded and when the transmitters' activities are random. Unlike the conventional Gaussian multiple-access wiretap channel, the capacity region is independent of the power of the transmitters and depends only on the sum of the message lengths of the transmitters.

This paper considers secret-key generation between several agents and a base station that observe independent and identically distributed realizations of correlated random variables. Each agent wishes to generate the longest possible individual key with the base station by means of public communication. All keys must be jointly kept secret from all external entities. In this many-to-one secret-key generation setting, it can be shown that the agents can take advantage of a collective protocol to increase the sum rate of their generated keys. However, when each agent is only interested in maximizing its own secret-key rate, agents may be unwilling to participate in a collective protocol. Furthermore, when such a collective protocol is employed, how to fairly allocate individual key rates arises as a valid issue. This paper studies the tension between cooperation and self-interest with a game-theoretic treatment. This paper establishes that cooperation is in the best interest of all individualistic agents and that there exist individual secret-key rate allocations that incentivize the agents to follow the protocol. In addition, an explicit coding scheme that achieves such allocations is proposed.

We develop explicit codes for the wiretap channel when uncertainties hold on the eavesdropper's channel statistics. We do not require any symmetry or degradation assumptions on the channel and we do not require a pre-shared secret between the legitimate users. Our code construction achieves the best known achievable communication rate derived with nonconstructive proofs. The underlying idea of our code design is an efficient emulation of random binning via polar codes to obtain reliability, along with an appropriate combination of universal hashing implemented via invertible extractors to ensure secrecy. Our code construction does not follow from previous constructions with polar codes that cannot support uncertainties on the eavesdropper's channel and require a pre-shared secret, and conceptually differs from known explicit codes relying on invertible extractors that are not optimal for asymmetric or non-degraded channels.

We consider a model for secret sharing, where a dealer distributes the shares of a secret among a set of participants with the constraint that only predetermined subsets of participants must be able to reconstruct the secret by pooling their shares. Unlike traditional secret sharing models, no secure channels are available between the dealer and the participants. Additionally, we assume that the dealer is an abstract entity made of several sub-dealers able to communicate with the participants through a noiseless and authenticated public channel. In this setting, we assume that the sub-dealers and the participants observe realizations of independently and identically distributed random variables. Our main results are inner and outer bounds on the rate of the secret that the dealer can distribute to the participants via its sub-dealers.

We design polar codes for empirical coordination and strong coordination in two-node networks. Our constructions hinge on the fact that polar codes enable explicit low-complexity schemes for soft covering. We leverage this property to propose explicit and low-complexity coding schemes that achieve the capacity regions of both empirical coordination and strong coordination for sequences of actions taking value in an alphabet of prime cardinality. Our results improve previously known polar coding schemes, which (i) were restricted to uniform distributions and to actions obtained via binary symmetric channels for strong coordination, (ii) required a non-negligible amount of common randomness for empirical coordination, and (iii) assumed that the simulation of discrete memoryless channels could be perfectly implemented. As a by-product of our results, we obtain a polar coding scheme that achieves channel resolvability for an arbitrary discrete memoryless channel whose input alphabet has prime cardinality.

We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters. No degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with an explicit and low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting, which introduces two virtual transmitters, and cooperative jamming strategies implemented by these virtual transmitters. Specifically, our coding scheme combines point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on block Markov encoding to be able to deal with an arbitrary channel and strong secrecy. Consequently, our coding scheme is the combination of inter-dependent block Markov constructions. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.

We consider secret-key generation between several agents and a base station that observe independent and identically distributed (i.i.d.) realizations of correlated random variables. Each agent wishes to generate the longest possible individual key with the base station by means of public communication. All keys must be jointly kept secret from all external entities. We do not require them to be kept secret among the agents. In this many-to-one secret-key generation setting, it can be shown that the agents can take advantage of a collective protocol to increase the sum-rate of all the generated keys. However, when each agent is only interested in maximizing its own secret-key rate, agents may be unwilling to participate in a collective protocol. Furthermore, when such a collective protocol is employed, how to fairly allocate individual key rates arises as a valid issue. We study this tension between cooperation and self-interest with a game-theoretic treatment. We establish that cooperation is in the best interest of all agents and that there exists individual secret-key rate allocations that incentivize the agents to follow the protocol. Additionally, we propose an explicit and low-complexity coding scheme based on polar codes and hash functions that achieves such allocations.

We study the degraded Gaussian multiple access wiretap channel with selfish transmitters, i.e., they are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective, i.e, multiple access, protocol instead of operating on their own. If yes, the question arises if there is a protocol that satisfies all the participating transmitters, in the sense that no transmitter has an incentive to deviate from the protocol. We answer these questions in the positive utilizing coalitional game theory. In particular, we show that cooperation is in the best interest of all transmitters and that there exist protocols that incentivize all transmitters to participate. Furthermore, we determine a unique, fair, and stable achievable secrecy rate allocation.

We study the Gaussian multiple access channel in presence of an adversary, who is simultaneously able to eavesdrop and jam, i.e., an active wiretapper. We assume that the adversary has a power constraint, which she can utilize to have any arbitrary jamming strategy. The multiple access channel between the legitimate transmitters and the receiver thus becomes arbitrarily varying. We derive inner and outer bounds on the secrecy rate region of our model. In the case of a degraded channel, we characterize the optimal secrecy sum-rate, and within 0.5 bits per channel use the optimal individual rate constraints. As a special case, we obtain the secrecy capacity of the point-to-point Gaussian wiretap channel when the eavesdropper is able to arbitrarily jam.

We study the problem of achieving strong secrecy over wiretap channels at negligible cost, in the sense of maintaining the overall communication rate of the same channel without secrecy constraints. Specifically, we propose and analyze two source-channel coding architectures, in which secrecy is achieved by multiplexing public and confidential messages. In both cases, our main contribution is to show that secrecy can be achieved without compromising communication rate and by requiring only randomness of asymptotically vanishing rate. Our first source-channel coding architecture relies on a modified wiretap channel code, in which randomization is performed using the output of a source code. In contrast, our second architecture relies on a standard wiretap code combined with a modified source code termed uniform compression code, in which a small shared secret seed is used to enhance the uniformity of the source code output. We carry out a detailed analysis of uniform compression codes and characterize the optimal size of the shared seed.

We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters - no degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with a low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting and different cooperative jamming strategies. Specifically, our coding scheme combines several point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on a chaining construction to be able to deal with an arbitrary channel and strong secrecy. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.

We consider authentication of messages sent by L legitimate transmitters to a legitimate receiver over a noisy multiple access channel. We assume the presence of a computationally unbounded opponent who has access to noisy observations of the messages transmitted, and can perform impersonation or substitution attacks. In addition, we consider anonymity constraints where the legitimate receiver must be able to authenticate the messages he receives with respect to predetermined groups of transmitters, but must be kept ignorant of the transmitter's identity of a given message in a given group. Our main result is an authentication coding scheme for which asymptotically matching upper and lower bounds on the probability of successful attack are derived. Our result analytically quantifies the impact of a multiuser setting compared to a single-user setting, as well as the negative impact of anonymity constraints on the probability of successful attack.

We develop a low-complexity polar coding scheme for the discrete memoryless broadcast channel with confidential messages under strong secrecy and randomness constraints. Our scheme extends previous work by using an optimal rate of uniform randomness in the stochastic encoder, and avoiding assumptions regarding the symmetry or degraded nature of the channels. The price paid for these extensions is that the encoder and the decoders are required to share a secret seed of negligible size and to increase the block length through chaining. We also highlight a close conceptual connection between the proposed polar coding scheme and a random binning proof of the secrecy capacity region.

We design low-complexity polar codes for empirical and strong coordination in two-node network. Our constructions hinge on the observation that polar codes may be used to approximate distribution; which we leverage to prove that nested polar codes achieve the capacity region of empirical coordination and strong coordination.

It is known that a sub-linear rate of source-independent random seed (common randomness) can enable the construction of lossless compression codes whose output is nearly uniform under the variational distance (Chou-Bloch-ISIT'13). This work uses finite-blocklength techniques to present an alternate proof that for near-uniform lossless compression, the seed length has to grow strictly larger than √n, where n represents the blocklength of the lossless compression code. In the lossy setting, we show the surprising result that a seed is not required to make the encoder output nearly uniform.

We develop a low-complexity and secrecy capacity achieving polar coding scheme for the discrete memoryless wiretap channel. Our scheme extends previous work by using a nearly optimal amount of uniform randomness in the stochastic encoder, and avoiding assumptions regarding the symmetry or degraded nature of the channels. The price paid for these extensions is that the encoder and decoder are required to share a secret seed of negligible size. We also highlight a close conceptual connection between the proposed polar coding scheme and a random binning proof of the secrecy capacity.

We investigate channel resolvability for the l-user multiple-access channel (MAC) with two different families of encoders. The first family consists of invertible extractors, while the second one consists of injective group homomorphisms, and was introduced by Hayashi for the point-to-point channel resolvability. The main benefit of these two families is to provide explicit low-complexity channel resolvability codes in the case of symmetric MACs. Specifically, we provide two examples of families of invertible extractors suitable for MAC resolvability with uniform input distributions, one based on finite-field multiplication, which can be implemented in O(n log n) for a limited range of values of the encoding blocklength n, and a second based on modified Toeplitz matrices, which can be implemented in O(n log n) for a wider range of values of n. We also provide an example of family of injective group homomorphisms based on finite-field multiplication suitable for MAC resolvability with uniform input distributions, which can be implemented in O(n log n) for some values of n.

For a discrete or a continuous source model, we study the problem of secret-key generation with one round of rate-limited public communication between two legitimate users. Although we do not provide new bounds on the wiretap secret-key (WSK) capacity for the discrete source model, we use an alternative achievability scheme that may be useful for practical applications. As a side result, we conveniently extend known bounds to the case of a continuous source model. Specifically, we consider a sequential key-generation strategy, that implements a rate-limited reconciliation step to handle reliability, followed by a privacy amplification step performed with extractors to handle secrecy. We prove that such a sequential strategy achieves the best known bounds for the rate-limited WSK capacity (under the assumption of degraded sources in the case of two-way communication). However, we show that, unlike the case of rate-unlimited public communication, achieving the reconciliation capacity in a sequential strategy does not necessarily lead to achieving the best known bounds for the WSK capacity. Consequently, reliability and secrecy can be treated successively but not independently, thereby exhibiting a limitation of sequential strategies for rate-limited public communication. Nevertheless, we provide scenarios for which reliability and secrecy can be treated successively and independently, such as the two-way rate-limited SK capacity, the one-way rate-limited WSK capacity for degraded binary symmetric sources, and the one-way rate-limited WSK capacity for Gaussian degraded sources.

For any lossless fixed-length compression scheme operating at the optimal coding rate, it is known that the encoder output is not uniform in variational distance, which yet might be desirable in some security schemes. In the case of independent and identically distributed (i.i.d.) sources, uniformity in divergence might be achieved if a uniformly distributed sequence, called seed, of length dnnegligible compared to the message length n, is shared between the encoder and the decoder. We show that the optimal scaling of dnthat jointly ensures an optimal coding rate and a uniform encoder output in divergence, is roughly on the order of √n. We also develop a near optimal achievability scheme using invertible extractors.

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).

We study the problem of key-distillation for a source model, with a one-way and rate-limited public communication between two legitimate users. Although, the secret-key capacity is already known, we provide an alternative achievability scheme, that directly translates into practical designs. We consider a sequential key-distillation strategy, which consists of a reconciliation phase followed by a privacy amplification phase performed with extractors. We determine the reconciliation capacity and show that, for a degraded source, such a sequential strategy leads to an optimal key-distillation strategy that achieves the secret-key capacity. We illustrate our results in the case of a binary source model.