Secure Communication

Wireless sensor networks will be widely deployed in the near future. While much research has focused on making these networks feasible and useful, security has received little attention. We present a suite of security protocols optimized for sensor networks: SPINS. SPINS has two secure building blocks: SNEP and µTESLA. SNEP includes: data confidentiality, two-party data authentication, and evidence of data freshness. µTESLA provides authenticated broadcast for severely resource-constrained environments. We implemented the above protocols, and show that they are practical even on minimal hardware: the performance of the protocol suite easily matches the data rate of our network. Additionally, we demonstrate that the suite can be used for building higher level protocols.

In recent years, a large amount of work on chaos-based cryptosystems have been published. However many of the proposed schemes fail to explain or do not possess a number of features that are fundamentally important to all kind of cryptosystems. As a result, many proposed systems are difficult to implement in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a thorough security analysis. Consequently, it is difficult for other researchers and end users to evaluate their security and performance. This work is intended to provide a common framework of basic guidelines that, if followed, every new cryptosystem would benefit from. The suggested guidelines address three main issues: implementation, key management, and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements. Meanwhile, several recommendations are made regarding some practical aspects of analog chaos-based secure communications, such as channel noise, limited bandwith, and attenuation.

Abstruct-A circuit implementation of the chaotic Lorenz system is described. The chaotic behavior of the circuit closely matches the results predicted by numerical experiments. Using the concept of synchronized chaotic systems (SCS's), two possible approaches to secure communications are demonstrated with the Lorenz circuit implemented in both the transmitter and receiver. In the first approach, a chaotic masking signal is added at the transmitter to the message, and at the receiver, the masking is regenerated and subtracted from the received signal. The second approach utilizes modulation of the coefficients of the chaotic system in the transmitter and corresponding detection of synchronization error in the receiver to transmit binary-valued bit streams.

Under the sole assumption that Alice and Bob are connected by a classical authentic communication channel, secret communication-and thus also the generation of a secret key-is impossible . This changes dramatically when quantum mechanics comes into the game. Bennett and Brassard [BB84] (see also ) were the first to propose a quantum key distribution (QKD) scheme which uses communication over a (completely insecure) quantum channel (in addition to the classical authentic channel). The scheme is commonly known as the BB84 protocol.

Role-based access control (RBAC) models have generated a great interest in the security community as a powerful and generalized approach to security management. In many practical scenarios, users may be restricted to assume roles only at predefined time periods. Furthermore, roles may only be invoked on prespecified intervals of time depending upon when certain actions are permitted. To capture such dynamic aspects of a role, a temporal RBAC (TRBAC) model has been recently proposed. However, the TRBAC model addresses the role enabling constraints only. In this paper, we propose a Generalized Temporal Role-Based Access Control (GTRBAC) model capable of expressing a wider range of temporal constraints. In particular, the model allows expressing periodic as well as duration constraints on roles, user-role assignments, and role-permission assignments. In an interval, activation of a role can further be restricted as a result of numerous activation constraints including cardinality constraints and maximum active duration constraints. The GTRBAC model extends the syntactic structure of the TRBAC model and its event and trigger expressions subsume those of TRBAC. Furthermore, GTRBAC allows expressing role hierarchies and separation of duty (SoD) constraints for specifying fine-grained temporal semantics.

The development of the wireless body area sensor network (BASN) is imperative for modern telemedicine and m-health, but security remains a formidable challenge yet to be resolved. As nodes of BASN are expected to be interconnected on or in the human body, the body itself can form an inherently secure communication pathway that is unavailable to all other kinds of wireless networks. This article explores the use of this conduit in the security mechanism of BASN; that is, by a biometrics approach that uses an intrinsic characteristic of the human body as the authentication identity or the means of securing the distribution of a cipher key to secure inter-BASN communications. The method was tested on 99 subjects with 838 segments of simultaneous recordings of electrocardiogram and photoplethysmogram. By using the interpulse interval (IPI) as the biometric trait, the system achieved a minimum half total error rate of 2.58 percent when the IPIs measured from signals, which were sampled at 1000 Hz, were coded into 128-bit binary sequences. The study opens up a few key issues for future investigation, including compensation schemes for the asynchrony of different channels, coding schemes, and other suitable biometric traits.

E S O F T W A R E J a n u a r y / F e b r u a r y 2 0 0 2 0 7 4 0 -7 4 5 9 / 0 2 / $ 1 7 . 0 0 © 2 0 0 2 I E E E J a n u a r y I E E E S O F T W A R E 4 3 Malformed input 16% Resource leaks 6% Format bugs 6% Buffer overflows 19% Access 16% Pathnames 10% Other 16% Symbolic links 11%

This paper deals with the problem of synchronization of a class of continuous-time chaotic systems using the driveresponse concept. An adaptive observer-based response system is designed to synchronize with a given chaotic drive system whose dynamical model is subjected to unknown parameters. Using the Lyapunov stability theory an adaptation law is derived to estimate the unknown parameters. We show that synchronization is achieved asymptotically. The approach is next applied to chaos-based secure communication. To demonstrate the efficiency of the proposed scheme numerical simulations are presented.

This paper deals with relay selection in cooperative networks with secrecy constraints. The proposed scheme enables an opportunistic selection of two relay nodes to increase security against eavesdroppers. The first relay operates as a conventional mode and assists a source to deliver its data to a destination via a Decode-and-Forward strategy. The second relay is used in order to create intentional interference at the eavesdropper nodes. The proposed selection technique jointly protects the primary destination against interference and eavesdropping and jams the reception of the eavesdropper. The new approach is analyzed for different complexity requirements based on instantaneous and average knowledge of the eavesdropper channels. In addition an investigation of an hybrid security scheme which switches between jamming and non-jamming protection is discussed in the paper. It is proven that an appropriate application of these two modes further improves security. The enhancements of the proposed selection techniques are demonstrated analytically and with simulation results.

A working free-space quantum key distribution (QKD) system has been developed and tested over an outdoor optical path of ∼ 1 km at Los Alamos National Laboratory under nighttime conditions. Results show that QKD can provide secure real-time key distribution between parties who have a need to communicate secretly. Finally, we examine the feasibility of surface to satellite QKD.

Devices that harness the laws of quantum physics hold the promise for information processing that outperforms their classical counterparts, and for unconditionally secure communication 1 . However, in particular, implementations based on condensed-matter systems face the challenge of short coherence times. Carbon materials 2,3 , particularly diamond 4-6 , however, are suitable for hosting robust solid-state quantum registers, owing to their spin-free lattice and weak spin-orbit coupling. Here we show that quantum logic elements can be realized by exploring long-range magnetic dipolar coupling between individually addressable single electron spins associated with separate colour centres in diamond. The strong distance dependence of this coupling was used to characterize the separation of single qubits (98±3 Å) with an accuracy close to the value of the crystal-lattice spacing. Our demonstration of coherent control over both electron spins, conditional dynamics, selective readout as well as switchable interaction should open the way towards a viable room-temperature solid-state quantum register. As both electron spins are optically addressable, this solid-state quantum device operating at ambient conditions provides a degree of control that is at present available only for a few systems at low temperature.

The goal of the Advanced Encryption Standard (AES) is to achieve secure communication. The use of AES does not, however, guarantee reliable communication. Prior work has shown that even a single transient error occurring during the AES encryption (or decryption) process will very likely result in a large number of errors in the encrypted/decrypted data. Such faults must be detected before sending to avoid the transmission and use of erroneous data. Concurrent fault detection is important not only to protect the encryption/decryption process from random faults. It will also protect the encryption/decryption circuitry from an attacker who may maliciously inject faults in order to find the encryption secret key. In this paper, we first describe some studies of the effects that faults may have on a hardware implementation of AES by analyzing the propagation of such faults to the outputs. We then present two fault detection schemes: The first is a redundancy-based scheme while the second uses an error detecting code. The latter is a novel scheme which leads to very efficient and high coverage fault detection. Finally, the hardware costs and detection latencies of both schemes are estimated.

The generation of random bit sequences based on non-deterministic physical mechanisms is of paramount importance for cryptography and secure communications. High data rates also require extremely fast generation rates and robustness to external perturbations. Physical generators based on stochastic noise sources have been limited in bandwidth to 100 Mbit s 21 generation rates. We present a physical random bit generator, based on a chaotic semiconductor laser, having time-delayed self-feedback, which operates reliably at rates up to 300 Gbit s 21 . The method uses a high derivative of the digitized chaotic laser intensity and generates the random sequence by retaining a number of the least significant bits of the high derivative value. The method is insensitive to laser operational parameters and eliminates the necessity for all external constraints such as incommensurate sampling rates and laser external cavity round trip time. The randomness of long bit strings is verified by standard statistical tests.

Modern industrial communication networks are increasingly based on open protocols and platforms that are also used in the office IT and Internet environment. This reuse facilitates development and deployment of highly connected systems, but also makes the communication system vulnerable to electronic attacks. This paper gives an overview of IT security issues in industrial automation systems which are based on open communication systems. First, security objectives, electronic attack methods, and the available countermeasures for general IT systems are described. General security objectives and best practices are listed. Particularly for the TCP/IP protocol suite, a wide range of cryptography-based secure communication protocols is available. The paper describes their principles and scope of application. Next, we focus on industrial communication systems, which have a number of security-relevant characteristics distinct from the office IT systems. Confidentiality of transmitted data may not be required; however, data and user authentication, as well as access control are crucial for the mission critical and safety critical operation of the automation system. As a result, modern industrial automation systems, if they include security measures at all, emphasize various forms of access control. The paper describes the status of relevant specifications and implementations for a number of standardized automation protocols. Finally, we illustrate the application of security concepts and tools by brief case studies describing security issues in the configuration and operation of substations, plants, or for remote access.

In this paper, control theory is used to formalize finite-time chaos synchronization as a nonlinear finite-time observer design issue. This paper introduces a finite-time observer for nonlinear systems that can be put into a linear canonical form up to an output injection. The finite-time convergence relies on the homogeneity properties of nonlinear systems. The observer is then applied to the

Advances in microelectronics, material science and wireless technology have led to the development of sensors that can be used for accurate monitoring of inaccessible environments. Health monitoring, telemedicine, military and environmental monitoring are some of the applications where sensors can be used. The sensors implanted inside the human body to monitor parts of the body are called biosensors. These biosensors form a network and collectively monitor the health condition of their carrier or host.

A fundamental problem in designing secure multi-party protocols is how to deal with adaptive adversaries i.e., adversaries that may c hoose the corrupted parties during the course of the computation, in a setting where the channels are insecure and secure communication is achieved by cryptographic primitives based on the computational limitations of the adversary.

A Body Area Network (BAN) is a wireless network of health monitoring sensors designed to deliver personalized health-care. Securing inter-sensor communications within BANs is essential for preserving not only the privacy of health data but also for ensuring safety of healthcare-delivery. This paper presents Physiological Signal based Key Agreement (PSKA), a scheme for enabling secure inter-sensor communication within a BAN in a usable (plug-n-play, transparent) manner. PSKA allows neighboring nodes in a BAN to agree to a symmetric (shared) cryptographic key, in an authenticated manner, using physiological signals obtained from the subject. No initialization or pre-deployment is required; simply deploying sensors in BAN is enough to make them communicate securely. Contributions of the paper are as follows: 1) description of PSKA key agreement protocol, 2) analysis of its security characteristics, 3) validation of PSKA utilizing two of the most commonly collected physiological signals photoplethysmogram (PPG) and electrocardiogram (EKG), and 4) cost analysis of executing PSKA, based on a prototype VHDL implementation, and its comparison with Diffie-Hellman key agreement protocol. Our analysis and prototyping shows that PSKA is a viable inter-sensor key agreement protocol for BANs.

The fluctuating intensity of a chaotic semiconductor laser is used for generating random sequences at rates up to 12:5 Gbits=s. The conversion of the fluctuating intensity to a random bit sequence can be implemented in either software or hardware and the overall rate of generation is much faster than any previously reported random number generator based on a physical mechanism. The generator's simplicity, robustness, and insensitivity to control parameters should enable its application to tasks of secure communication and calculation procedures requiring ultrahigh-speed generation of random bit sequences.

We propose a novel algorithm for detecting wormhole attacks in wireless multi-hop networks. The algorithm uses only connectivity information to look for forbidden substructures in the connectivity graph. The proposed approach is completely localized and, unlike many techniques proposed in literature, does not use any special hardware artifact or location information, making the technique universally applicable. The algorithm is independent of wireless communication models. However, knowledge of the model and node distribution helps estimate a parameter used in the algorithm. We present simulation results for three different communication models and two different node distributions, and show that the algorithm is able to detect wormhole attacks with a 100% detection and 0% false alarm probabilities whenever the network is connected with high probability. Even for very low density networks where chances of disconnection is very high, the detection probability remains very high.

Secure communication is very important in computer networks and authentication is one of the most eminent preconditions. However, common authentication schemes are not applicable in ad hoc networks because public key infrastructures with a centralized certification authority are hard to deploy there. We propose and evaluate a security concept based on a distributed certification facility. A network is divided into clusters with one special head node each. These cluster head nodes execute administrative functions and hold shares of a network key used for certification. New nodes start to participate in the network as guests; they can only become full members with a networksigned certificate after their authenticity has been warranted by some other members. The feasibility of this concept was verified by simulation. Three different models for node mobility were used in order to include realistic scenarios as well as make the results comparable to other work. The simulation results include an evaluation of the log-on times, availability, and communication overhead.

Research on the secure communication applications of chaotic synchronization is reviewed. A number of secure communication methods and devices using different types of synchronous behavior are examined. For the purpose of comparing existing methods, quantitative characteristics of operating capacity of various schemes are introduced and estimated. An extremely noise-stable secure information transmission method, based on the phenomenon of generalized chaos synchronization, is proposed. All of the methods considered are systematically checked for efficiency for the first time by numerically simulating unidirectionally coupled chaotic R ossler systems selected for transmitting and receiving oscillators. The key advantages and disadvantages of secure information transmission schemes using synchronized chaotic oscillations are discussed. The experimental data gathered in this field are also reviewed.

Real-world deployments of wireless sensor networks (WSNs) require secure communication. It is important that a receiver is able to verify that sensor data was generated by trusted nodes. It may also be necessary to encrypt sensor data in transit. Recently, WSNs and traditional IP networks are more tightly integrated using IPv6 and 6LoWPAN. Available IPv6 protocol stacks can use IPsec to secure data exchange. Thus, it is desirable to extend 6LoWPAN such that IPsec communication with IPv6 nodes is possible. It is beneficial to use IPsec because the existing end-points on the Internet do not need to be modified to communicate securely with the WSN. Moreover, using IPsec, true end-to-end security is implemented and the need for a trustworthy gateway is removed.

In this paper, the issues of lag synchronization of coupled time-delayed systems with chaos are investigated in detail. Two different systems are considered, namely, neural and Mackey-Glass systems. Some sufficient conditions for determining the lag synchronization between the drive and corresponding coupling systems are derived. Moreover, synchronization attributes, such as the relationship among the speed that lag synchronization can achieve, the time delays in the involved systems and the synchronization lag, are analyzed. By using the proposed lag synchronization technique with the chaotic masking strategy, the application towards a secure communication scheme is also discussed. The effectiveness of the proposed approach is illustrated by computer simulations.

A continuous-variable quantum key distribution protocol based on squeezed states and heterodyne detection is introduced and shown to attain higher secret key rates over a noisy line than any other oneway Gaussian protocol. This increased resistance to channel noise can be understood as resulting from purposely adding noise to the signal that is converted into the secret key. This notion of noise-enhanced tolerance to noise also provides a better physical insight into the poorly understood discrepancies between the previously defined families of Gaussian protocols.

Synchronization of fractional order chaotic dynamical systems is receiving increasing attention owing to its interesting applications in secure communications of analog and digital signals and cryptographic systems. In this article we utilize active control technique to synchronize different fractional order chaotic dynamical systems. Further we investigate the interrelationship between the (fractional) order and synchronization in different chaotic dynamical systems. It is observed that synchronization is faster as the order tends to one.

Wireless networks are being driven by the need for providing network access to mobile or nomadic computing devices. Although the need for wireless access to a network is evident, new problems are inherent in the wireless medium itself. Specifically, the wireless medium introduces new opportunities for eavesdropping on wireless data communications. Anyone with an appropriate wireless receiver can eavesdrop, and this kind of eavesdropping is virtually undetectable. Furthermore, since the wireless medium cannot be contained by the usual physical constraints of walls and doors, active intrusions through the wireless medium are also made easier. In order to prevent this unauthorized access to the network, the authors present the design of a secure communication protocol that provides for both the privacy of wireless data communications and the authenticity of communicating parties. The placement of the protocol in the overall protocol stack and issues relevant to wireless links and mobile computing devices are discussed. They also present proof of the security of the protocol using the logic of authentication formalism developed by Burrows, Abadi, and Needham (1990).>

The detection of covert timing channels is of increasing interest in light of recent practice on the exploitation of covert timing channels over the Internet. However, due to the high variation in legitimate network traffic, detecting covert timing channels is a challenging task. The existing detection schemes are ineffective to detect most of the covert timing channels known to the security community. In this paper, we introduce a new entropy-based approach to detecting various covert timing channels. Our new approach is based on the observation that the creation of a covert timing channel has certain effects on the entropy of the original process, and hence, a change in the entropy of a process provides a critical clue for covert timing channel detection. Exploiting this observation, we investigate the use of entropy and conditional entropy in detecting covert timing channels. Our experimental results show that our entropy-based approach is sensitive to the current covert timing channels, and is capable of detecting them in an accurate manner.

We present an entangled-state quantum cryptography system that operated for the first time in a real world application scenario. The full key generation protocol was performed in real time between two distributed embedded hardware devices, which were connected by 1.45 km of optical fiber, installed for this experiment in the Vienna sewage system. The generated quantum key was immediately handed over and used by a secure communication application.

Clustered sensor networks have been shown to increase system throughput, decrease system delay, and save energy. While those with rotating cluster heads, such as LEACH, have also advantages in terms of security, the dynamic nature of their communication makes most existing security solutions inadequate for them. In this paper, we show how random key predistribution, widely studied in the context of flat networks, can be used to secure communication in hierarchical (cluster-based) protocols such as LEACH. To our knowledge, it is the first work that investigates random key predistribution as applied to hierarchical WSNs.

Clustered sensor networks have recently been shown to increase system throughput, decrease system delay, and save energy while performing data aggregation. Whereas those with rotating cluster heads, such as LEACH (low-energy adaptive clustering hierarchy), have also advantages in terms of security, the dynamic nature of their communication makes most existing security solutions inadequate for them. In this paper, we investigate the problem of adding security to hierarchical (cluster-based) sensor networks where clusters are formed dynamically and periodically, such as LEACH. For this purpose, we show how random key predistribution, widely studied in the context of flat networks, and mTESLA, a building block from SPINS, can be both used to secure communications in this type of network. We present our solution, and provide a detailed analysis of how different values for the various parameters in such a system impact a hierarchical network in terms of security and energy efficiency. To the best of our knowledge, ours is the first that investigates security in hierarchical WSNs with dynamic cluster formation. r

We demonstrate theoretically and experimentally that secure communication using intermediate-energy (mesoscopic) coherent states is possible. Our scheme is different from previous quantum cryptographic schemes in that a short secret key is explicitly used and in which ...

It is important to design cryptographically strong S-Boxes in order to design secure systems. In this study, a strong, chaos-based S-Box design is proposed. Continuous-time Lorenz system is chosen as the chaotic system. Proposed methodology is analyzed and tested for the following criteria: Bijective property, nonlinearity, strict avalanche criterion, output bits independence criterion and equiprobable input/output XOR distribution. The results of the analysis show that the proposed cryptosystem is a highly reliable system suitable for secure communication.

In this paper, we propose a method of robust nonlinear H 1 master-slave synchronization for chaotic Lur'e systems with applications to secure communication. The scheme makes use of vector field modulation and either full static state or linear dynamic output error feedback control. The master-slave systems are assumed to be nonidentical and channel noise is taken into account. Binary valued continuous time message signals are recovered by minimizing the L 2 -gain from the exogenous input to the tracking error for the standard plant representation of the scheme. The exogenous input takes into account the message signal, channel noise and parameter mismatch. Matrix inequality conditions for dissipativity with finite L 2 -gain of the standard plant form are derived based on a quadratic storage function. The controllers are designed by solving a nonlinear optimization problem which takes into account both channel noise and parameter mismatch. The method is illustrated on Chua's circuit.

A delay tolerant network (DTN) is a store and forward network where end-to-end connectivity is not assumed and where opportunistic links between nodes are used to transfer data. An emerging application of DTNs are rural area DTNs, which provide Internet connectivity to rural areas in developing regions using conventional transportation mediums, like buses. Potential applications of these rural area DTNs are e-governance, telemedicine and citizen journalism. Therefore, security and privacy are critical for DTNs. Traditional cryptographic techniques based on PKI-certified public keys assume continuous network access, which makes these techniques inapplicable to DTNs. We present the first anonymous communication solution for DTNs and introduce a new anonymous authentication protocol as a part of it. Furthermore, we present a security infrastructure for DTNs to provide efficient secure communication based on identity-based cryptography. We show that our solutions have better performance than existing security infrastructures for DTNs.

Gaining access to sensitive resources on the Web usually involves an explicit registration step, where the client has to provide a predetermined set of information to the server. The registration process yields a login/password combination, a cookie, or something similar that can be used to access the sensitive resources. In this paper we show how an explicit registration step can be avoided on the Semantic Web by using appropriate semantic annotations, rule-oriented access control policies, and automated trust negotiation. After presenting the PeerTrust language for policies and trust negotiation, we describe our implementation of implicit registration and authentication that runs under the Java-based MINERVA Prolog engine. The implementation includes a PeerTrust policy applet and evaluator, facilities to import local metadata, policies and credentials, and secure communication channels between all parties.

This paper presents synthesis approaches for synchronization and secure communications of chaotic systems by using fuzzy model-based design methods. Many well-known continuous and discrete chaotic systems can be exactly represented by T-S fuzzy models with only one premise variable. According to the applications on synchronization and signal modulation, the general fuzzy models may have either i) common bias terms; or ii) the same premise variable and driving signal. Then we propose two types of driving signals, namely, fuzzy driving signal and crisp driving signal, to deal with the asymptotical synchronization and secure communication problems for cases i) and ii), respectively. Based on these driving signals, the solutions are found by solving LMI problems. It is worthy to note that many well-known chaotic systems, such as Duffing system, Chua's circuit, Rössler's system, Lorenz system, Henon map, and Lozi map can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either the fuzzy driving signal or the crisp driving signal. Finally, several numerical simulations are shown to verify the results.

Recommender systems are widely used to help deal with the problem of information overload. However, recommenders raise serious privacy and security issues. The personal information collected by recommenders raises the risk of unwanted exposure of that information. Also, malicious users can bias or sabotage the recommendations that are provided to other users. This paper raises important research questions in three topics relating to exposure and bias in recommender systems: the value and risks of the preference information shared with a recommender, the effectiveness of shilling attacks designed to bias a recommender, and the issues involved in distributed or peer-to-peer recommenders. The goal of the paper is to bring these questions to the attention of the information and communication security community, to invite their expertise in addressing them.

Preserving a person's privacy in an efficient manner is very important for critical, life-saving infrastructures like Body Sensor Networks (BSN). This paper presents a novel key agreement scheme which allows two sensors in a BSN to agree to a common key generated using electrocardiogram (EKG) signals. This EKG-based Key Agreement (EKA) scheme aims to bring the "plug-n-play" paradigm to BSN security whereby simply deploying sensors on the subject can enable secure communication, without requiring any form of initialization such as pre-deployment. Analysis of the scheme based on real EKG data (obtained from MIT PhysioBank database) shows that keys resulting from EKA are: random, time variant, can be generated based on short-duration EKG measurements, identical for a given subject and different for separate individuals.

In this paper, the synchronization problem of coupled Chua's circuits generator of n-scroll chaotic attractors in master-slave configuration is numerically studied. In particular, we consider a modified Chua's circuit generator of 5-scroll chaotic attractors by using Hamiltonian systems and state observer approach. A potential application to transmit encrypted audio and image information is also given.

In this paper the key storage problem associated with the provision of secure communications between every pair of users in a large network is described, and a possible method of alleviating the problem is discussed. This method, based on the use of finite incidence structures with special properties called key distribution patterns, is shown to generalize earlier work in the area. The more general formulation of the storage saving scheme contained here enables use to be made of the extensive body of knowledge already existing on the theory of block designs. From this theory we are able to extract a number of new families of examples of potentially useful key distribution systems.

A new random geometric graph model, the so-called secrecy graph, is introduced and studied. The graph represents a wireless network and includes only edges over which secure communication in the presence of eavesdroppers is possible. The underlying point process models considered are Poisson point processes. In the Poisson case, the node degrees are determined and percolation is studied using analytical bounds and simulations. It turns out that a small density of eavesdroppers already has a drastic impact on the connectivity of the secrecy graph.

The emergence of the Internet as a trusted medium for commerce and communication has made cryptography an essential component of modern information systems. Cryptography provides the mechanisms necessary to implement accountability, accuracy, and confidentiality in communication. As demands for secure communication bandwidth grow, efficient cryptographic processing will become increasingly vital to good system performance.