Shannon showed that to achieve perfect secrecy in point-to-point communication, the message rate cannot exceed the shared secret key rate giving rise to the simple one-time pad encryption scheme. In this paper, we extend this work from point-to-point to networks. We consider a connected network with pairwise communication between the nodes. We assume that each node is provided with a certain amount of secret bits before communication commences. An eavesdropper with unlimited computing power has access to all communication and can hack a subset of the nodes not known to the rest of the nodes. We investigate the limits on information-theoretic secure communication for this network. We establish a tradeoff between the secure channel rate (for a node pair) and the secure network rate (sum over all node pair rates) and show that perfect secrecy can be achieved if and only if the sum rate of any subset of unhacked channels does not exceed the shared unhacked-secret-bit rate of these channels. We also propose two practical and efficient schemes that achieve a good balance of network and channel rates with perfect secrecy guarantee. This work has a wide range of potential applications for which perfect secrecy is desired, such as cyber-physical systems, distributed-control systems, and ad-hoc networks.
Shannon showed that to achieve perfect secrecy in point-to-point communication, the message rate cannot exceed the shared secret key rate giving rise to the simple one-time pad encryption scheme. In this paper, we extend this work from point-to-point to networks. We consider a connected network with pairwise communication between the nodes. We assume that each node is provided with a certain amount of secret bits before communication commences. An eavesdropper with unlimited computing power has access to all communication and can hack a subset of the nodes not known to the rest of the nodes. We investigate the limits on information-theoretic secure communication for this network. We establish a tradeoff between the secure channel rate (for a node pair) and the secure network rate (sum over all node pair rates) and show that perfect secrecy can be achieved if and only if the sum rate of any subset of unhacked channels does not exceed the shared unhacked-secret-bit rate of these channels. We also propose two practical and efficient schemes that achieve a good balance of network and channel rates with perfect secrecy guarantee. This work has a wide range of potential applications for which perfect secrecy is desired, such as cyber-physical systems, distributed-control systems, and ad-hoc networks.
Shannon showed that to achieve perfect secrecy in point-to-point communication, the message rate cannot exceed the shared secret key rate giving rise to the simple one-time pad encryption scheme. In this paper, we extend this work from point-to-point to networks. We consider a connected network with pairwise communication between the nodes and assume that each node is provided with a certain amount of secret bits before communication commences. An eavesdropper with unlimited computing power has access to all communication and can hack a subset of the nodes not known to the rest of the nodes. We investigate the limits on information-theoretic secure communication with end-to-end encryption for this network. We establish a tradeoff between the secure channel rate (for a node pair) and the secure network rate (sum over all node pair rates) and show that information-theoretic secrecy can be achieved asymptotically if and only if the sum rate of any subset of unhacked channels does not exceed the shared unhacked-secret-bit rate of these channels. We also propose a practical scheme that achieves a good balance of network and channel rates with information-theoretic secrecy guarantee. This work has a wide range of potential applications for which strong secrecy is desired, such as cyber-physical systems, distributed-control systems, and ad-hoc networks.
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.
The aim of information-theoretic secrecy is to ensure that an eavesdropper who listens to the wireless transmission of a message can only collect an arbitrarily small number of information bits about this message. In contrast to cryptography, there are no assumptions on the computational power of the eavesdropper. Information-theoretically secret communication has been studied for many particular wireless network topologies. In the main part of this thesis, we consider such communication for arbitrary acyclic wireless network topologies. We provide lower and upper bounds on the strong perfect secrecy capacity for the case when the channels of the network are either Gaussian or deterministic. These results are based on the recent understanding of the capacity of wireless networks (without secrecy constraints) by Avestimehr, Diggavi and Tse. As a side result, we give inner and outer bounds on the capacity region for the multisource problem in arbitrary wireless networks with Gaussian or deterministic signal interaction. For linear deterministic signal interaction, we find the exact capacity region. For Gaussian signal interaction, we are able to bound the gap between the two bounds on the capacity region. This gap depends only on the network topology, but not on the signal-to-noise ratio (SNR), which leads to an approximation of the capacity region for the high SNR regime. We further consider a particular network topology, called the fan-network, in which we assume that an eavesdropper has physical access to every node in a subset of the relay nodes. We give a general upper bound on the perfect secrecy capacity, and we characterize the perfect secrecy capacity for two special cases. In the second part of the thesis, we consider interactive secrecy, i.e., secrecy in the presence of a public feedback link from the destination to the source. We focus on the problem of secret key generation rather than secret communication. The benefit of public discussion for secret key generation in a broadcast channel was first shown by Maurer. We extend his ideas to a relay network called the line network, leading to a lower bound on the strongly secret key capacity for this network topology. Finally, we introduce a new channel coding setup called the interference-multiple access (IMA) channel. This channel is a variant of the interference channel where one of the receivers is required to decode the messages from both transmitters. We derive an inner bound on the capacity region of the IMA channel, as well as an outer bound for the so-called structured IMA channel. In a semi-deterministic version of the structured IMA channel, the bounds match, providing a characterization of the capacity region. In the Gaussian case, we obtain a 1 bit-approximation of the capacity region. We also show an inner bound on the equivocation-capacity region for the IMA channel, where we require that part of the private message for one receiver is kept information-theoretically secret from the other receiver.
In this thesis, a new practical method to realize one-time pad perfect secrecy for wireless \ncommunication is presented. Most commonly used security methods are based on cryp- tographic \ntechniques employed at the upper layers of a wireless network. These methods basically rely on the \ncomputational hardness of some mathematical problems. This com- putational complexity is vulnerable \nin nature due to fast-growing computational power of hardware technology, yet not taking into \naccount the revolution of Quantum computing in further future. Another core problematic issue \nexists in symmetric security systems; there is a deadlock between securing the channel and \nestablishing the shared key. We need the key for securing the channel, on the other hand, for \nsharing the key we need a secure channel. \n \nTo address such vulnerabilities, Physical Layer Security (PLS) has been widely studied in recent \nyears. PLS schemes build on the idea of turning unpredictable and random wire- less channel \ncharacteristics into a source for information-theoretic security. Information- theoretic security \nitself, relies on Shannon’s pioneer work . Shannon, inspired by one-time pad, also known as Vernam \ncipher, theoretically showed that the only unconditional per- fect secrecy system is a one-time pad \nwith a key at least as random as the plaintext, i.e., a system that uses a different random key to \ncipher any new plaintext. In PLS key genera- tion methods, legitimate parties alternately send \nprobe signals and estimate Channel State Information (CSI) of common random channel and then \nconvert enough amount of these estimates to secure shared keys. To achieve perfect secrecy, the key \ngeneration methods must meet the key randomness and Key Generation Rate (KGR) requirements of \ntheir specific cryptographic applications. \n \nIn this research a new practical system for achieving unconditional perfect secrecy is presented. \nOur system uses channel phase as the probing parameter to fully benefit from its uniform \ndistribution over [0, 2π]. It also uses an encryption method based on modulo- \n2π addition of phase values which is the perfect counterpart of XOR addition in binary one-time \npad. Moreover, by intentionally perturbing the wireless channel in vicinity of the transceiver \nantenna based on RF-mirrors structure, it produces different random phase values in each channel \nprobing, much faster than the inherent channel variation would do, resulting in dramatically higher \nKGR than any wide-band PLS scheme presented so far and realizing true perfect secrecy. Most \nimportantly, the focus of this research is a detailed practical algorithm for implementing the \nsystem as well as empirical results which makes \nour system the first channel-phase-based PLS scheme implementation, reported so far.
Confidentiality of information is a key consideration in many networking applications, including e-commerce, online banking, and intelligence operations. How can information be communicated reliably to the legitimate users, while keeping it secret from eavesdroppers? How does such a secrecy constraint on communication affect the limits on information flow in the network? In this chapter, we study these questions under the information theoretic notion of secrecy, which requires each eavesdropper to obtain essentially no information about the messages sent from knowledge of its received sequence, the channel statistics, and the codebooks used. We investigate two approaches to achieve secure communication. The first is to exploit the statistics of the channel from the sender to the legitimate receivers and the eavesdroppers. We introduce the wiretap channel as a 2-receiver broadcast channel with a legitimate receiver and an eavesdropper, and establish its secrecy capacity, which is the highest achievable secret communication rate. The idea is to design the encoder so that the channel from the sender to the receiver becomes effectively stronger than the channel to the eavesdropper; hence the receiver can recover the message but the eavesdropper cannot. This wiretap coding scheme involves multicoding and randomized encoding. If the channel from the sender to the receiver is weaker than that to the eavesdropper, however, secret communication at a positive rate is not possible. This brings us to the second approach to achieve secret communication, which is to use a secret key shared between the sender and the receiver but unknown to the eavesdropper. We show that the rate of such secret key must be at least as high as the rate of the confidential message. This raises the question of how the sender and the receiver can agree on such a long secret key in the first place. After all, if they had a confidential channel with sufficiently high capacity to communicate the key, then why not use it to communicate the message itself! We show that if the sender and the receiver have access to correlated sources (e.g., through a satellite beaming common randomness to them), then they can still agree on a secret key even when the channel has zero secrecy capacity. We first consider the source model for key agreement, where the sender communicates with the receiver over a noiseless public broadcast channel to generate a secret key from their correlated sources.
Introduction Future communication systems will be decentralized and ad-hoc, hence allowing various types of network mobile terminals to join and leave. This makes the whole system vulnerable and susceptible to attacks. Anyone within communication range can listen to and possibly extract information. While these days we have numerous cryptographic methods to ensure high-level security, there is no system with perfect security on the physical layer. Therefore, the physical layer security is attracting renewed attention. Of special interest is so-called information-theoretic security since it concerns the ability of the physical layer to provide perfect secrecy of the transmitted data. In this chapter, we present different scenarios of a decentralized system that protects the broadcasted data on the physical layer and makes it impossible for the eavesdropper to receive the packets no matter how computationally powerful the eavesdropper is. In approaches where information-theoretic security is applied, the main objective is to maximize the rate of reliable information from the source to the intended destination, while all malicious nodes are kept ignorant of that information. This maximum reliable rate under which a perfectly secret communication is possible is known as the secrecy capacity . This line of work was pioneered by Aaron Wyner, who defined the wiretap channel and established the possibility of secure communication links without relying on private (secret) keys.