Characterization of the secrecy region of a single relay cooperative system

Security is an important aspect for the future wire- less networks. Since the number of network nodes increases con- stantly, and, in addition, the networks are decentralized and ad- hoc in nature, it becomes more challenging to apply the current cryptographic methods that require exchange of keys between the communicating parties. Information-theoretic secrecy is an emerging security field that explores the possibility of achieving perfect secrecy data transmission between the intended network nodes, while possible malicious nodes (also called eavesdroppers) are kept ignorant of the transmitted information. In other words, that is the ability of the physical layer to provide security (beside the reliability) of the transmitted (broadcasted) data. For that reason, it is often called physical layer security. In this paper we observe how a simple cooperative network with one relay node can improve the physical layer security by decreasing the area in which the eavesdropper can reside and listen to the information transmitted to the destination. This region is called vulnerability region and we provide its characterization. Under certain conditions, the vulnerability region vanishes, which makes our wireless system perfectly secure for any position of the eavesdropper within the wireless network.

A Mobile World of Security

Christine Neuberg

Security in mobile communications is a topic of increasing relevance in everyday life. We all use mobile devices for everyday communications, maybe even for exchanging confidential information with the work place. This requires security systems that are reliable and stable even though mobility and number of users are increasing. An established solution in today's systems is to use symmetric cryptographic systems by relying on pre-established secrets. There are a few drawbacks. The first problem is that all security information is stored in one central storage place. This implies that users are required to trust this storage place. They need to trust that data is properly handled and well protected. The mechanism of storing pre-established long-term secrets at a central storage also makes it vulnerable to adversaries. As soon as someone gains access to it, he automatically has access to all secret information necessary to capture communications. A second problem is that security mechanisms implemented in today's mobile communication systems were designed for a moderate number of users. Since then, the number of users has grown significantly and continues to do so. It would thus be desirable to have a system that is flexible in terms of the number of users it can handle. The third and maybe the most crucial problem is the fact that today's security systems rely on computational cryptography. This means that the security mechanisms in cellular communication systems were designed with limited computational power of the adversary in mind. However, the computational power of computers is growing and systems might be breakable in the near future. A complementary notion of security is information-theoretic security. Systems built in this spirit are unbreakable even with unlimited computational power. These systems exploit the knowledge of statistical properties of the environment. This means mainly that security systems can be proved to be secure with respect to assumptions on the correlated sources and with respect to the nature of the knowledge the adversary can gain. The main idea of information-theoretic security is that two communication partners have access to correlated random sources. An adversary being potentially present in the system, has only degraded access to the source. The common knowledge can be used in order to generate sequences that are very similar among each other. Because the adversary has access to the random source, he is able to generate his own version of the sequence. It is fundamental that the sequences of the communicationpartners are stronger correlated among each other than with respect to the adversary. This advantage in knowledge can be interpreted as a secret among the communication partners to the adversary. In communicating over an authenticated but public channel, this secret can be extracted from the original sequence by both parties. In order for both keys to be equal, the original sequences need to coincide. This is not necessarily the case, but can be achieved by discussion over the public channel. In the first part of this thesis, we propose a security system that relies on information-theoretic security. We will demonstrate how this system can be implemented in cellular communication systems. The movement of the users is random and we want to use it as a random source. We assume that users are moving along a random itinerary while visiting a random sequence of cells. Users not only visit cells in a random order, they also stay for a random time in each cells. It turns out that it is the sequence of durations that contributes most to the randomness of the sequence. We call the sequence of durations timing. This sequence is known to users and to the infrastructure, but only parts of it are known to potential adversaries. By recording the sequence of cells along with the time of residence, both the user and the infrastructure will be able to acquire very similar sequences. After the collection process, a procedure for key agreement is applied. Due to the underlying process, the key will not be uniformly distributed. As this is a requirement for perfect secret keys, a final part of the protocol is privacy amplification, where the perfectly secret bits will be extracted. This system is lightweight as it is based on readily available information and only a small amount of post-processing is required. In the second part of this thesis, we analyze the performance of the system. For this, we demonstrate how the process of bit collection can be analytically modeled. Our analysis leads to two conclusions. It gives us intuition about how to choose parameters such that the scheme performs optimally. Our scheme can be applied to settings that fulfill certain conditions. Conclusions from analysis allow to specify such conditions. We will show the implication of this conclusion in sketching some alternative applications of our scheme.

EPFL2011

Creating Secrets out of Erasures

Suhas Diggavi, Christina Fragouli, Panagiotis Kostopoulos

Current security systems often rely on the adversary's computational limitations. Wireless networks offer the opportunity for a different, complementary kind of security, which relies on the adversary's limited network presence (i.e., that the adversary cannot be located at many different points in the network at the same time). We present a system that leverages this opportunity to enable N wireless nodes to create a shared secret S, in a way that an eavesdropper, Eve, obtains very little information on S. Our system consists of two steps: (1) The nodes transmit packets following a special pattern, such that Eve learns very little about a given fraction of the transmitted packets. This is achieved through a combination of beam forming (from many different sources) and wiretap codes. (2) The nodes participate in a protocol that reshuffles the information known to each node, such that the nodes end up sharing a secret that Eve knows very little about. Our protocol is easily implementable in existing wireless devices and scales well with the number of nodes; these properties are achieved through a combination of public feedback, broadcasting, and network coding. We evaluate our system through a 5-node testbed. We demonstrate that a group of wireless nodes can generate thousands of new shared secret bits per second, with their secrecy being independent of the adversary's computational capabilities.

2013

Function Computation over Networks

Chien-Yi Wang

This thesis looks at efficient information processing for two network applications: content delivery with caching and collecting summary statistics in wireless sensor networks. Both applications are studied under the same paradigm: function computation over networks, where distributed source nodes cooperatively communicate some functions of individual observations to one or multiple destinations. One approach that always works is to convey all observations and then let the destinations compute the desired functions by themselves. However, if the available communication resources are limited, then revealing less unwanted information becomes critical. Centered on this goal, this thesis develops new coding schemes using information-theoretic tools. The first part of this thesis focuses on content delivery with caching. Caching is a technique that facilitates reallocation of communication resources in order to avoid network congestion during peak-traffic times. An information-theoretic model, termed sequential coding for computing, is proposed to analyze the potential gains offered by the caching technique. For the single-user case, the proposed framework succeeds in verifying the optimality of some simple caching strategies and in providing guidance towards optimal caching strategies. For the two-user case, five representative subproblems are considered, which draw connections with classic source coding problems including the Gray-Wyner system, successive refinement, and the Kaspi/Heegard-Berger problem. Afterwards, the problem of distributed computing with successive refinement is considered. It is shown that if full data recovery is required in the second stage of successive refinement, then any information acquired in the first stage will be useful later in the second stage. The second part of this thesis looks at the collection of summary statistics in wireless sensor networks. Summary statistics include arithmetic mean, median, standard deviation, etc, and they belong to the class of symmetric functions. This thesis develops arithmetic computation coding in order to efficiently perform in-network computation for weighted arithmetic sums and symmetric functions. The developed arithmetic computation coding increases the achievable computation rate from

\Theta((\log L)/L)

\Theta(1/\log L)

, where

L

is the number of sensors. Finally, this thesis demonstrates that interaction among sensors is beneficial for computation of type-threshold functions, e.g., the maximum and the indicator function, and that a non-vanishing computation rate is achievable.

EPFL2015