Once a wireless terminal has cleared network access control, obtained an IP address on the local subnet, and has routing service for IP packets between the terminal and the network, the terminal has access to the higher-level services available on the global Internet – Web pages, IP telephony, streaming video and the like. From the point of view of routing and packet delivery service, a wireless terminal is no different than a wired terminal. A desktop PC connected to the Internet through DSL must go through a similar process to get Internet access as a wireless terminal and the resulting routing and packet delivery service is basically the same. Unlike the user of a desktop PC, however, the user of a wireless terminal is free to move the terminal to a new location. Such a movement may cross an invisible line in the access network topology between a geographical area where the current IP address continues to provide packet delivery service and where the address stops functioning. In other words, the terminal moves from one IP subnet to another causing IP handover to occur.

If the user's mobility patterns conform to the nomadic usage model discussed in Chapter 4, then starting network access control and local IP subnet configuration from the beginning are adequate for initiating routing and packet delivery service in the new subnet.

Users of wireless Internet services have a reasonable expectation that their activities are protected from eavesdropping and snooping by attackers even when confidentiality protection is not in use. All Internet traffic contains identifiers that allow application, transport, and network protocols to keep track of important entities and interactions. From a technical standpoint, privacy means that these identities are not traceable back to information allowing an eavesdropper to identify the user. If the identities are additionally masked from one or both endpoints in the protocols, then the communication is also anonymous. Privacy and anonymity are important security properties for certain types of transactions, and are different from confidentiality discussed in Chapter 1. The contents of a communication between two hosts can be protected by encryption to provide confidentiality from eavesdropping, while the identities of the two hosts are still exposed through unencrypted information necessary for routing. For wireless Internet communication, location privacy means that the geographic location of a particular wireless terminal cannot be inferred from the contents of the terminal's traffic or from unencrypted identifiers. As for general privacy, location anonymity means that the location is masked from endpoints as well as from eavesdroppers. Location privacy and location anonymity are issues for fixed terminals too, but because users typically carry wireless terminals with them, the risk for users is larger with wireless terminals.

In the next section, we briefly discuss the threat against general privacy of communications on the Internet and specific threats against location privacy for wireless terminals.

Wireless network operators and end users need the ability to utilize equipment from different vendors in their networks and in customer-accessible devices. Left to themselves, vendors of network equipment and of end-user access devices such as wireless terminals tend to produce equipment that is slightly different in various ways, hindering the ability of their customers to build multi-vendor networks from interoperable equipment pieces. The key to ensuring interoperability is to have a standardized system design with clearly specified interfaces between the various network devices and well-designed, standardized protocols on the interfaces. The process of systematically identifying requirements and functionality and mapping that into network entities, interfaces, and standardized protocols is the key to ensuring a design that meets real-world needs and in which the pieces work together well. This requirement is generally true for network systems, but it also applies specifically to security systems.

While standardization is the key to ensuring interoperability in complex multi-vendor systems, system architectures are the principal tool for guiding the design, implementation, and deployment process. In this chapter, we examine the topic of network system architecture. In the next section, we discuss the role of architecture in system standardization in more detail. Following that, we describe a particular approach to developing a system architecture, the functional architectural approach, that is used in some wireless network standardization processes.

Wireless Internet Security: Architecture and Protocols approaches wireless Internet security from the direction of system architecture. A system architecture is essentially a high-level blueprint that guides the detailed design, implementation, and deployment decisions that result in a real, usable system, just like the architectural plans for a building guide its construction. Architectures serve as tools for understanding how to design and evolve a complex information technology system. Architectures are regularly developed by wireless standardization bodies to guide the development of interoperable, standardized protocols on interfaces between equipment provided by multiple vendors, including wireless devices used by consumers. Corporations often provide architectures as guidelines for customers, describing how their products fit together with other equipment to provide solutions for their customers' information technology problems.

In the field of wireless security, the architectural approach has been neglected. This neglect is partially a result of the case-driven nature of network security. Most security systems have been developed in response to specific attacks that surface after the system has been deployed, rather than as a planned part of the initial system development process. Indeed, the original Internet architecture had almost no provisions for security. Internet users were assumed to be members of a co-operative community that would never attempt actions on the Internet harmful to others' interests. This approach is changing slowly, as system designers begin to internalize the disastrous results of grafting security onto a system after a successful attack has compromised the original design.

The Internet was originally developed with little or no security. As a government-run test bed for academic research, the user community was co-operative and nobody considered the possibility that one user or group of users would undertake operations harmful to others. The commercialization of the Internet in the early to mid 1990s resulted in the rise of the potential for adversarial interactions. These interactions are motivated by various harming concerns: the desire for profit at others' expense without providing any offered value, the need to prove technical prowess by disruption, etc. The introduction of widespread, inexpensive wireless links into the Internet in the late 1990s led to additional opportunities for disruption. Unlike wired links, wireless links know no physical boundaries, so physical security measures that are effective for securing the endpoints where terminals plug into wired networks are ineffective for wireless links. Some initial attempts to secure wireless links had the opposite effect: providing the appearance of security while actually exposing the end user to sophisticated attacks. Subsequently, wireless security has become an important technical topic for research, development, and standardization.

In response to the rise of security problems on the Internet, the technical community has developed a collection of basic technologies for addressing network security. While there are special characteristics of wireless systems that in certain cases distinguish wireless network security from general network security, wireless network security is a subtopic of general network security.

What is information?

In this section we are going to try to quantify the notion of information. Before we do this, we should be aware that ‘information’ has a special meaning in probability theory, which is not the same as its use in ordinary language. For example, consider the following two statements:

1. (i) I will eat some food tomorrow.

2. (ii) The prime minister and leader of the opposition will dance naked in the street tomorrow.

If I ask which of these two statements conveys the most information, you will (I hope!) say that it is (ii). Your argument might be that (i) is practically a statement of the obvious (unless I am prone to fasting), whereas (ii) is extremely unlikely. To summarise:

1. (i) has very high probability and so conveys little information,

2. (ii) has very low probability and so conveys much information. Clearly, then, quantity of information is closely related to the element of surprise.

Consider now the following ‘statement’:

1. (iii) XQWQYK VZXPU VVBGXWQ.

Our immediate reaction to (iii) is that it is meaningless and hence conveys no information. However, from the point of view of English language structure we should be aware that (iii) has low probability (e.g. Q is a rarely occurring letter and is generally followed by U, (iii) contains no vowels) and so has a high surprise element.

The above discussion should indicate that the word ‘information’, as it occurs in everyday life, consists of two aspects, ‘surprise’ and ‘meaning’.

When I wrote the first edition of this book in the early 1990s it was designed as an undergraduate text which gave a unified introduction to the mathematics of ‘chance’ and ‘information’. I am delighted that many courses (mainly in Australasia and the USA) have adopted the book as a core text and have been pleased to receive so much positive feedback from both students and instructors since the book first appeared. For this second edition I have resisted the temptation to expand the existing text and most of the changes to the first nine chapters are corrections of errors and typos. The main new ingredient is the addition of a further chapter (Chapter 10) which brings a third important concept, that of ‘time’ into play via an introduction to Markov chains and their entropy. The mathematical device for combining time and chance together is called a ‘stochastic process’ which is playing an increasingly important role in mathematical modelling in such diverse (and important) areas as mathematical finance and climate science. Markov chains form a highly accessible subclass of stochastic (random) processes and nowadays these often appear in first year courses (at least in British universities). From a pedagogic perspective, the early study of Markov chains also gives students an additional insight into the importance of matrices within an applied context and this theme is stressed heavily in the approach presented here, which is based on courses taught at both Nottingham Trent and Sheffield Universities.

Chance and information

Our experience of the world leads us to conclude that many events are unpredictable and sometimes quite unexpected. These may range from the outcome of seemingly simple games such as tossing a coin and trying to guess whether it will be heads or tails to the sudden collapse of governments or the dramatic fall in prices of shares on the stock market. When we try to interpret such events, it is likely that we will take one of two approaches – we will either shrug our shoulders and say it was due to ‘chance’ or we will argue that we might have have been better able to predict, for example, the government's collapse if only we'd had more ‘information’ about the machinations of certain ministers. One of the main aims of this book is to demonstrate that these two concepts of ‘chance’ and ‘information’ are more closely related than you might think. Indeed, when faced with uncertainty our natural tendency is to search for information that will help us to reduce the uncertainty in our own minds; for example, think of the gambler about to bet on the outcome of a race and combing the sporting papers beforehand for hints about the form of the jockeys and the horses.

Before we proceed further, we should clarify our understanding of the concept of chance. It may be argued that the tossing of fair, unbiased coins is an ‘intrinsically random’ procedure in that everyone in the world is equally ignorant of whether the result will be heads or tails.

Counting

This chapter will be devoted to problems involving counting. Of course, everybody knows how to count, but sometimes this can be quite a tricky business. Consider, for example, the following questions:

1. (i) In how many different ways can seven identical objects be arranged in a row?

2. (ii) In how many different ways can a group of three ball bearings be selected from a bag containing eight?

Problems of this type are called combinatorial. If you try to solve them directly by counting all the possible alternatives, you will find this to be a laborious and time-consuming procedure. Fortunately, a number of clever tricks are available which save you from having to do this. The branch of mathematics which develops these is called combinatorics and the purpose of the present chapter is to give a brief introduction to this topic.

A fundamental concept both in this chapter and the subsequent ones on probability theory proper will be that of an ‘experience’ which can result in several possible ‘outcomes’. Examples of such experiences are:

1. (a) throwing a die where the possible outcomes are the six faces which can appear,

2. (b) queueing at a bus-stop where the outcomes consist of the nine different buses, serving different routes, which stop there.

If A and B are two separate experiences, we write A ∘ B to denote the combined experience of A followed by B.

This is designed to be an introductory text for a modern course on the fundamentals of probability and information. It has been written to address the needs of undergraduate mathematics students in the ‘new’ universities and much of it is based on courses developed for the Mathematical Methods for Information Technology degree at the Nottingham Trent University. Bearing in mind that such students do not often have a firm background in traditional mathematics, I have attempted to keep the development of material gently paced and user friendly – at least in the first few chapters. I hope that such an approach will also be of value to mathematics students in ‘old’ universities, as well as students on courses other than honours mathematics who need to understand probabilistic ideas.

I have tried to address in this volume a number of problems which I perceive in the traditional teaching of these subjects. Many students first meet probability theory as part of an introductory course in statistics. As such, they often encounter the subject as a ragbag of different techniques without the same systematic development that they might gain in a course in, say, group theory. Later on, they might have the opportunity to remedy this by taking a final-year course in rigorous measure theoretic probability, but this, if it exists at all, is likely to be an option only. Consequently, many students can graduate with degrees in mathematical sciences, but without a coherent understanding of the mathematics of probability.