Information-theoretic Physical Layer Security for Satellite Channels

Shannon introduced the classic model of a cryptosystem in 1949, where Eve has access to an identical copy of the cyphertext that Alice sends to Bob. Shannon defined perfect secrecy to be the case when the mutual information between the plaintext and the cyphertext is zero. Perfect secrecy is motivated by error-free transmission and requires that Bob and Alice share a secret key. Wyner in 1975 and later I.~Csisz\'ar and J.~K\"orner in 1978 modified the Shannon model assuming that the channels are noisy and proved that secrecy can be achieved without sharing a secret key. This model is called wiretap channel model and secrecy capacity is known when Eve's channel is noisier than Bob's channel. In this paper we review the concept of wiretap coding from the satellite channel viewpoint. We also review subsequently introduced stronger secrecy levels which can be numerically quantified and are keyless unconditionally secure under certain assumptions. We introduce the general construction of wiretap coding and analyse its applicability for a typical satellite channel. From our analysis we discuss the potential of keyless information theoretic physical layer security for satellite channels based on wiretap coding. We also identify system design implications for enabling simultaneous operation with additional information theoretic security protocols

A Classification of Unimodular Lattice Wiretap Codes in Small Dimensions

Lattice coding over a Gaussian wiretap channel, where an eavesdropper listens to transmissions between a transmitter and a legitimate receiver, is considered. A new lattice invariant called the secrecy gain is used as a code design criterion for wiretap lattice codes since it was shown to characterize the confusion that a chosen lattice can cause at the eavesdropper: the higher the secrecy gain of the lattice, the more confusion. In this paper, a formula for the secrecy gain of unimodular lattices is derived. Secrecy gains of extremal odd unimodular lattices as well as unimodular lattices in dimension n, 16 \leq n \leq 23 are computed, covering the 4 extremal odd unimodular lattices and all the 111 nonextremal unimodular lattices (both odd and even) providing thus a classification of the best wiretap lattice codes coming from unimodular lattices in dimension n, 8 < n \leq 23. Finally, to permit lattice encoding via Construction A, the corresponding error correction codes are determined.Comment: 10 page

Formally Unimodular Packings for the Gaussian Wiretap Channel

This paper introduces the family of lattice-like packings, which generalizes lattices, consisting of packings possessing periodicity and geometric uniformity. The subfamily of formally unimodular (lattice-like) packings is further investigated. It can be seen as a generalization of the unimodular and isodual lattices, and the Construction A formally unimodular packings obtained from formally self-dual codes are presented. Recently, lattice coding for the Gaussian wiretap channel has been considered. A measure called secrecy function was proposed to characterize the eavesdropper's probability of correctly decoding. The aim is to determine the global maximum value of the secrecy function, called (strong) secrecy gain. We further apply lattice-like packings to coset coding for the Gaussian wiretap channel and show that the family of formally unimodular packings shares the same secrecy function behavior as unimodular and isodual lattices. We propose a universal approach to determine the secrecy gain of a Construction A formally unimodular packing obtained from a formally self-dual code. From the weight distribution of a code, we provide a necessary condition for a formally self-dual code such that its Construction A formally unimodular packing is secrecy-optimal. Finally, we demonstrate that formally unimodular packings/lattices can achieve higher secrecy gain than the best-known unimodular lattices.Comment: Accepted for publication in IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:2111.0143

Applications of Derandomization Theory in Coding

Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory is to eliminate or reduce the need for randomness in such randomized constructions. In this thesis, we explore some applications of the fundamental notions in derandomization theory to problems outside the core of theoretical computer science, and in particular, certain problems related to coding theory. First, we consider the wiretap channel problem which involves a communication system in which an intruder can eavesdrop a limited portion of the transmissions, and construct efficient and information-theoretically optimal communication protocols for this model. Then we consider the combinatorial group testing problem. In this classical problem, one aims to determine a set of defective items within a large population by asking a number of queries, where each query reveals whether a defective item is present within a specified group of items. We use randomness condensers to explicitly construct optimal, or nearly optimal, group testing schemes for a setting where the query outcomes can be highly unreliable, as well as the threshold model where a query returns positive if the number of defectives pass a certain threshold. Finally, we design ensembles of error-correcting codes that achieve the information-theoretic capacity of a large class of communication channels, and then use the obtained ensembles for construction of explicit capacity achieving codes. [This is a shortened version of the actual abstract in the thesis.]Comment: EPFL Phd Thesi

A Cryptographic Treatment of the Wiretap Channel

The wiretap channel is a setting where one aims to provide information-theoretic privacy of communicated data based solely on the assumption that the channel from sender to adversary is ``noisier\u27\u27 than the channel from sender to receiver. It has been the subject of decades of work in the information and coding (I&C) community. This paper bridges the gap between this body of work and modern cryptography with contributions along two fronts, namely METRICS (definitions) of security, and SCHEMES. We explain that the metric currently in use is weak and insufficient to guarantee security of applications and propose two replacements. One, that we call mis-security, is a mutual-information based metric in the I&C style. The other, semantic security, adapts to this setting a cryptographic metric that, in the cryptography community, has been vetted by decades of evaluation and endorsed as the target for standards and implementations. We show that they are equivalent (any scheme secure under one is secure under the other), thereby connecting two fundamentally different ways of defining security and providing a strong, unified and well-founded target for designs. Moving on to schemes, results from the wiretap community are mostly non-constructive, proving the existence of schemes without necessarily yielding ones that are explicit, let alone efficient, and only meeting their weak notion of security. We apply cryptographic methods based on extractors to produce explicit, polynomial-time and even practical encryption schemes that meet our new and stronger security target

Security performance and protocol consideration in optical communication system with optical layer security enabled by optical coding techniques

With the fast development of communication systems, network security issues have more and more impact on daily life. It is essential to construct a high degree of optical layer security to resolve the security problem once and for all. Three different techniques which can provide optical layer security are introduced and compared. Optical chaos can be used for fast random number generation. Quantum cryptography is the most promising technique for key distribution. And the optical coding techniques can be deployed to encrypt the modulated signal in the optical layer. A mathematical equation has been derived from information theory to evaluate the information-theoretic security level of the wiretap channel in optical coding schemes. And the merits and limitation of two coherent optical coding schemes, temporal phase coding and spectral phase coding, have been analysed. The security scheme based on a reconfigurable optical coding device has been introduced, and the corresponding security protocol has been developed. By moving the encryption operation from the electronic layer to the optical layer, the modulated signals become opaque to the unauthorised users. Optical code distribution and authentication is the one of the major challenges for our proposed scheme. In our proposed protocol, both of the operations are covered and defined in detail. As a preliminary draft of the optical code security protocol, it could be a useful guidance for further research

Semantic and effective communications

Shannon and Weaver categorized communications into three levels of problems: the technical problem, which tries to answer the question "how accurately can the symbols of communication be transmitted?"; the semantic problem, which asks the question "how precisely do the transmitted symbols convey the desired meaning?"; the effectiveness problem, which strives to answer the question "how effectively does the received meaning affect conduct in the desired way?". Traditionally, communication technologies mainly addressed the technical problem, ignoring the semantics or the effectiveness problems. Recently, there has been increasing interest to address the higher level semantic and effectiveness problems, with proposals ranging from semantic to goal oriented communications. In this thesis, we propose to formulate the semantic problem as a joint source-channel coding (JSCC) problem and the effectiveness problem as a multi-agent partially observable Markov decision process (MA-POMDP). As such, for the semantic problem, we propose DeepWiVe, the first-ever end-to-end JSCC video transmission scheme that leverages the power of deep neural networks (DNNs) to directly map video signals to channel symbols, combining video compression, channel coding, and modulation steps into a single neural transform. We also further show that it is possible to use predefined constellation designs as well as secure the physical layer communication against eavesdroppers for deep learning (DL) driven JSCC schemes, making such schemes much more viable for deployment in the real world. For the effectiveness problem, we propose a novel formulation by considering multiple agents communicating over a noisy channel in order to achieve better coordination and cooperation in a multi-agent reinforcement learning (MARL) framework. Specifically, we consider a MA-POMDP, in which the agents, in addition to interacting with the environment, can also communicate with each other over a noisy communication channel. The noisy communication channel is considered explicitly as part of the dynamics of the environment, and the message each agent sends is part of the action that the agent can take. As a result, the agents learn not only to collaborate with each other but also to communicate "effectively'' over a noisy channel. Moreover, we show that this framework generalizes both the semantic and technical problems. In both instances, we show that the resultant communication scheme is superior to one where the communication is considered separately from the underlying semantic or goal of the problem.Open Acces