We propose a novel hybrid universal network-coding cryptosystem (HUNCC) to obtain secure post-quantum cryptography at high communication rates. The secure network-coding scheme we offer is hybrid in the sense that it combines information-theoretic security with public-key cryptography. In addition, the scheme is general and can be applied to any communication network, and to any public-key cryptosystem.

When there exists a malicious attacker in the network, we need to consider the possibilities of eavesdropping and the contamination simultaneously. Under an acyclic broadcast network, the optimality of linear codes was shown when Eve is allowed to attack any r edges. The optimality of linear codes is not shown under a different assumption for Eve. As a typical example of an acyclic unicast network, we focus on the one-hop relay network under the single transmission scheme by assuming that Eve attacks only one edge in each level.

The Private Information Retrieval (PIR) problem has recently attracted a significant interest in the information-theory community. In this problem, a client wants to download one or more messages belonging to a database while protecting the identity of the downloaded message(s). In this article, we focus on the scenarios in which (i) the entire database is stored on a single server and (ii) the client has prior side information, namely a subset of messages unknown to the server.

This paper introduces the notion of cache-tapping into the information theoretic models of coded caching. The wiretap channel II in the presence of multiple receivers equipped with fixed-size cache memories, and an adversary which selects symbols to tap into from cache placement and/or delivery is introduced. The legitimate terminals know neither whether placement, delivery, or both are tapped, nor the positions in which they are tapped. Only the size of the overall tapped set is known.

We discuss secure transmission via an untrusted relay when we have a multiple access phase from two nodes to the relay and a broadcast phase from the relay to the two nodes. To realize the security, we construct a code that securely transmits the modulo sum of the messages of two nodes via a multiple access channel. In this code, the relay cannot obtain any information with respect to the message of each node, and can decode only the modulo-sum of the messages of the two nodes.

We consider covert communication, i.e., hiding the presence of communication from an adversary for multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) channels. We characterize the maximum covert coding rate under a variety of settings, including different regimes where either the number of transmit antennas or the blocklength is scaled up. We show that a non-zero covert capacity can be achieved in the massive MIMO regime in which the number of transmit antennas scales up but under specific conditions.

The problem of private data disclosure is studied from an information theoretic perspective. Considering a pair of dependent random variables (X, Y), where X and Y denote the private and useful data, respectively, the following problem is addressed: What is the maximum information that can be revealed about Y, measured by mutual information I(Y; U), in which U denotes the revealed data, while disclosing no information about X, captured by the condition of statistical independence, i.e., X ⊥ U, and henceforth called perfect privacy)?

Federated learning is a distributed framework for training machine learning models over the data residing at mobile devices, while protecting the privacy of individual users. A major bottleneck in scaling federated learning to a large number of users is the overhead of secure model aggregation across many users. In particular, the overhead of the state-of-the-art protocols for secure model aggregation grows quadratically with the number of users.

We consider three different variants of differential privacy (DP), namely approximate DP, Rényi DP (RDP), and hypothesis test DP. In the first part, we develop a machinery for optimally relating approximate DP to RDP based on the joint range of two $f$ -divergences that underlie the approximate DP and RDP. In particular, this enables us to derive the optimal approximate DP parameters of a mechanism that satisfies a given level of RDP.

Establishing code equivalences between index coding and network coding provides important insights for code design. Previous works showed an equivalence relation between any index-coding instance and a network-coding instance, for which a code for one instance can be translated to a code for the other instance with the same decoding-error performance. The equivalence also showed a surprising result that any network-coding instance can be mapped to an index-coding instance with a properly designed code translation.