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Denial of service (DoS) attacks are launched specifically against WLAN networks at layer 1 (physical) and layer 2 (data link) A denial of service attack is a category of attack that includes any actions resulting in the inability of users or systems to access needed resources DoS attacks can be simple to implement or very complex For this reason, they can be launched by attackers with little skill as well as attackers with in-depth knowledge of IEEE 80211 networks In 2008, I had the opportunity to interview several security professionals at the DefCon hackers conference One individual represented an organization that provides network offloading for DoS protection He stated that a large distributed DoS (DDoS) attack was launched against a client using more than one million nodes from around the world This information shows how serious DoS attacks have become The layer 1, or Physical layer, attacks are also known as RF jamming attacks This attack is done using devices that output RF energy, usually across the entire 24 GHz spectrum used by IEEE 80211 devices When these intentional radiators put out the RF energy at the power levels they support, it drowns out the RF energy being transmitted by valid devices on your WLAN Since the device (called a signal generator) puts out a signal that drowns out the signals of the WLAN, it effectively causes a DoS scenario The interference can also be narrowband and still cause problems on your WLAN if the band fits nicely in the center of your configured 80211 channel Since the AP will not likely be configured to automatically adjust its channel in the face of interference (though some APs do have this capability), a DoS scenario can even be caused by narrowband signal generators



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4 Explain why every nonzero complex number C has two distinct square roots in C 5 An Argand diagram is a device for sketching a complex number in the plane If x + i y is a complex number then we depict it in the cartesian plane as the point (x, y) Sketch the complex numbers 3 2i, 4i + 7, i + e, 6 i 6 The complex number 1 = 1 + 0i has three cube roots Use any means to nd them, and sketch them on an Argand diagram 7 Let p be a polynomial and assume that C is a root of p Prove that (z ) evenly divides p(z) with no remainder 8 Determine whether 2 + 3 is rational or irrational 9 Find all square roots in the quaternions of the number 1 + i + j 10 Explain why subtraction in the integers is well de ned 11 Explain why multiplication in the integers is well de ned 12 Explain why division makes no sense in the integers 13 Prove that addition in the integers is commutative 14 Show that addition of rational numbers is well de ned 15 Show that the complex numbers cannot be ordered as a eld 16 Follow the outline in the text to show that the real numbers form a sub eld of the complex numbers





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80211i

This section will discuss the different network architectures that are popular in today s networking environments This section is very important from an exam point of view as well, so be sure to understand how the different architectures are pieced together

Although everybody knows how to count in the sense of 1 2 3 4 5 the fact is that counting is one of the most important techniques of modern mathematics And counting can be quite sophisticated Imagine counting the number of ways that one can get a straight ush in a hand of seven-card-stud poker This is by no means a trivial counting problem In the present chapter we shall learn some important counting techniques that can be used to attack a variety of problems

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June 24 is an important day for two reasons The first reason is that it is my birthday, and the second, and most likely more important to you, is that on this day in 2004 the 80211i draft standard was ratified by the IEEE, making it official The intent of this supplement is to provide security standards to the 80211 Wi-Fi worlds This is an extremely important supplement because it provides a standard that can be followed going forward instead of having every vendor implement security in a different way This new standard is intended to replace the weak Wired Equivalent Privacy (WEP) security protocol Because of the great need for security solutions in wireless networks, the Wi-Fi Alliance released the Wi-Fi Protected Access (WPA) standard before 80211i was completed WPA is a subset of the 80211i specification In order to reduce confusion, the Wi-Fi Alliance refers to the full implementation of 80211i, in their certifications, as WPA2

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Also known as the Dirichletscher Schubfachschluss ( Dirichlet s drawer-shutting principle ), this is one of the key ideas in all of counting theory And the idea is simplicity itself: Pigeonhole principle: Let k be a positive integer Imagine that you are delivering k + 1 letters to k mailboxes Then it must be that some mailbox will receive two letters

80211r

Before we can discuss the different network architectures, we need to start our discussions by defining two terms: broadband and baseband transmissions

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