Contemporary techniques of data security are primarily based on computational complexity, typically on the infeasibility of inverting certain functions using currently available mathematical techniques and computing power. Among the various protocols based on such ideas, those approved by the cryptography community appear secure enough, but mathematical and technological progress may render them insecure in the future. Indeed, past experience suggests that this is likely to happen. Information-theoretic secrecy offers provable security even against an adversary with unlimited computing power. This chapter provides a glimpse into the substantial progress that has been made towards clarifying the theoretical possibilities in this direction. Practical applications are reasonably expected within a much shorter time than capacity-achieving coding techniques have followed Shannon's discovery of the noisy channel coding theorem. Two kinds of problems will be addressed: secure transmission over insecure channels and secret key generation taking advantage of public communication. After introducing necessary concepts and tools in Section 17.1, these problems will be treated in Sections 17.2 and 17.3. Let us emphasize that the mathematical models and techniques will be similar to those in previous chapters. These models, however, are now studied from a non-cooperative aspect: a major goal is to keep (at least) one party ignorant of (at least part of) the information exchanged.
Contemporary techniques of data security are primarily based on computational complexity, typically on the infeasibility of inverting certain functions using currently available mathematical techniques and computing power. Among the various protocols based on such ideas, those approved by the cryptography community appear secure enough, but mathematical and technological progress may render them insecure in the future. Indeed, past experience suggests that this is likely to happen. Information-theoretic secrecy offers provable security even against an adversary with unlimited computing power. This chapter provides a glimpse into the substantial progress that has been made towards clarifying the theoretical possibilities in this direction. Practical applications are reasonably expected within a much shorter time than capacity-achieving coding techniques have followed Shannon's discovery of the noisy channel coding theorem. Two kinds of problems will be addressed: secure transmission over insecure channels and secret key generation taking advantage of public communication. After introducing necessary concepts and tools in Section 17.1, these problems will be treated in Sections 17.2 and 17.3. Let us emphasize that the mathematical models and techniques will be similar to those in previous chapters. These models, however, are now studied from a non-cooperative aspect: a major goal is to keep (at least) one party ignorant of (at least part of) the information exchanged.
Secure communication ensures the integrity and confidentiality of communication between connected devices. An information-theoretic approach to secure communication gives the strongest confidentiality guarantee by assuming that the attacker has unlimited computing power. The earliest formal model and definition of information-theoretic secure communication is by Shannon, who employed a secret key shared between communicating parties to provide confidentiality. An alternative elegant information-theoretic approach to secure communication views the natural characteristics of the environment (i.e., channel’s noise) as a resource to build security functionalities. This approach was first proposed by Wyner, and the corresponding secure communication model is called the wiretap channel model. These two approaches introduce two primary resources for providing information-theoretic secure communication: the shared secret key and physical properties of the communication medium. In this thesis, we study how to employ the above two resources for secure message transmission. We study this by using channel’s noise in the wiretap channel model. In this model, a sender is connected to the receiver and the adversary through two noisy channels. We propose a new wiretap encoding scheme with strong secrecy that provides perfect secrecy and reliability, asymptotically. The construction treats the noise in the adversary’s channel as a source of randomness that is extracted and used to hide the message from the adversary. We realize the wiretap channel model using cooperative jamming to evaluate the performance of wiretap codes in practice. We consider a model called keyed wiretap channel that unifies Wyner’s model with Shannon’s model of perfect secrecy for information systems, and propose a keyed encoding schemes with strong secrecy and other properties that are attractive in practice. We also study two-party information-theoretic secret key agreement when the two parties have access to samples of a common source of randomness and use a single message transmission to arrive at a shared random key. We propose a secret key agreement protocol in this setting, prove its security, and show its superior performance compared to other known protocols with the same properties. Finally, we propose an information-theoretic secret key agreement over a virtual wiretap channel created by cooperative jamming.
In this chapter, we discuss the construction of practical codes for secrecy. The design of codes for the wiretap channel turns out to be surprisingly difficult, and this area of information-theoretic security is still largely in its infancy. To some extent, the major obstacles in the road to secrecy capacity are similar to those that lay in the path to channel capacity: the random-coding arguments used to establish the secrecy capacity do not provide explicit code constructions. However, the design of wiretap codes is further impaired by the absence of a simple metric, such as a bit error rate, which could be evaluated numerically. Unlike codes designed for reliable communication, whose performance is eventually assessed by plotting a bit-error-rate curve, we cannot simulate an eavesdropper with unlimited computational power; hence, wiretap codes must possess enough structure to be provably secure. For certain channels, such as binary erasure wiretap channels, the information-theoretic secrecy constraint can be recast in terms of an algebraic property for a code-generator matrix. Most of the chapter focuses on such cases since this algebraic view of secrecy simplifies the analysis considerably. As seen in Chapter 4, the design of secret-key distillation strategies is a somewhat easier problem insofar as reliability and security can be handled separately by means of information reconciliation and privacy amplification. Essentially, the construction of coding schemes for key agreement reduces to the design of Slepian–Wolf-like codes for information reconciliation, which can be done efficiently with low-density parity-check (LDPC) codes or turbo-codes.
Most of themainstream cryptographic protocols that are used today rely on the assumption that the adversary has limited computational power, and that a given set of mathematical problems is hard to solve (on average), i.e. that there is no polynomial time algorithm that solves these problems. While these assumptions are reasonable for now they might not be as relevant for long termsecurity. Indeed, all the communication that happens today can be recorded by an adversary who can later – when the technology allows it – break security. There are good reasons to think that technological progress may lead to break the assumptions made today. For example the rapidly increasing computational power of our computer already allows one to break anything that has been encrypted using DES in the 70s and 80s in few days using regular desktop type devices. There is also the constant improvement of the efficiency of the known algorithms that solve a class of problems. Note that, even though the discovery of a polynomial algorithm for a problem we believe to be hard is still possible, much weaker improvements on current algorithms that solve these hard problems, can already be a threat for security.
In Chapter 3, we considered the transmission of information over a noisy broadcast channel subject to reliability and security constraints; we showed that appropriate coding schemes can exploit the presence of noise to confuse the eavesdropper and guarantee some amount of information-theoretic security. It is important to note that the wiretap channel model assumes that all communications occur over the channel, hence communications are inherently rate-limited and one-way. Consequently, the results obtained do not fully capture the role of noise for secrecy; in particular, for situations in which the secrecy capacity is zero, it is not entirely clear whether this stems from the lack of any “physical advantage” over the eavesdropper or the restrictions imposed on the communication schemes. The objective of this chapter is to study more precisely the fundamental role of noise in information-theoretic security. Instead of studying how we can communicate messages securely over a noisy channel, we now analyze how much secrecy we can extract from the noise itself in the form of a secret key. Specifically, we assume that the legitimate parties and the eavesdropper observe the realizations of correlated random variables and that the legitimate parties attempt to agree on a secret key unknown to the eavesdropper. To isolate the role played by noise, we remove restrictions on communication schemes and we assume that the legitimate parties can distill their key by communicating over a two-way, public, noiseless , and authenticated channel at no cost.
In this chapter, we develop the notion of secrecy capacity , which plays a central role in physical-layer security. The secrecy capacity characterizes the fundamental limit of secure communications over noisy channels, and it is essentially the counterpart to the usual point-to-point channel capacity when communications are subject not only to reliability constraints but also to an information-theoretic secrecy requirement. It is inherently associated with a channel model called the wiretap channel , which is a broadcast channel in which one of the receivers is treated as an adversary. This adversarial receiver, which we call the eavesdropper to emphasize its passiveness, should remain ignorant of the messages transmitted over the channel. The mathematical tools, and especially the random-coding argument, presented in this chapter are the basis for most of the theoretical research in physical-layer security, and we use them extensively in subsequent chapters. We start with a review of Shannon's model of secure communications (Section 3.1), and then we informally discuss the problem of secure communications over noisy channels (Section 3.2). The intuition we develop from loose arguments is useful to grasp the concepts underlying the proofs of the secrecy capacity and motivates a discussion of the choice of an information-theoretic secrecy metric (Section 3.3). We then study in detail the fundamental limits of secure communication over degraded wiretap channels (Section 3.4) and broadcast channels with confidential messages (Section 3.5).
Security is one of the most important issues in communications. Security issues arising in communication networks include confidentiality, integrity, authentication and non-repudiation. Attacks on the security of communication networks can be divided into two basic types: passive attacks and active attacks. An active attack corresponds to the situation in which a malicious actor intentionally disrupts the system. A passive attack corresponds to the situation in which a malicious actor attempts to interpret source information without injecting any information or trying to modify the information; i.e., passive attackers listen to the transmission without modifying it. Information Theoretic Security focuses on confidentiality issues, in which passive attacks are of primary concern. The information theoretic approach to achieving secure communication opens a promising new direction toward solving wireless networking security problems. Compared to contemporary cryptosystems, information theoretic approaches offer advantages such as eliminating the key management issue; are less vulnerable to the man-in-the-middle and achieve provable security that is robust to powerful eavesdroppers possessing unlimited computational resources, knowledge of the communication strategy employed including coding and decoding algorithms, and access to communication systems either through perfect or noisy channels. Information Theoretic Security surveys the research dating back to the 1970s which forms the basis of applying this technique in modern systems. It proceeds to provide an overview of how information theoretic approaches are developed to achieve secrecy for a basic wire-tap channel model as well as for its extensions to multiuser networks. It is an invaluable resource for students and researchers working in network security, information theory and communications.