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CS361: Introduction to Computer Security Information Theory Dr. Bill Young Department of Computer Sciences University of Texas at Austin Last updated: October 5, 2010 at 12:51 CS361 Slideset 4: 1 Information Theory

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What is Information Just what is information? The following is the fundamental paradigm of information theory: Sender Receiver a45 Transmission Medium Information is any content to be conveyed from the sender to receiver. It is sent in the form of one or more messages . Our goal is to quantify this sitution. CS361 Slideset 4: 2 Information Theory
Some Information Theory Information theory is the field of study that quantifies the content of messages and the capacity of channels on which information may flow. It asks questions such as the following: 1 How much information is encoded in a particular message? 2 How efficiently can a given alphabet/language be transmitted? 3 What is the maximum capacity of a given transmission medium? 4 How is that capacity or efficiency reduced by interference /noise? These questions all have very precise and deep answers, that are beyond the scope of this course. We’ll only scratch the surface. CS361 Slideset 4: 3 Information Theory

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Why Do We Care? Information theory is very important in computer science. It affects all communication, hardware design, protocol design, cryptography, fault-tolerance, etc. For example, in our current context it is useful to know how much information can be transmitted over a specific covert channel. This is the “bandwidth” of the channel. If the bandwidth is sufficiently small, perhaps we want to ignore it, but if it’s large that suggests a potential problem. CS361 Slideset 4: 4 Information Theory
Quantifying Information: Thought Experiment How much information is contained in each of the following messages? How do you judge? A 1-bit binary number. An n -bit binary number. A single decimal digit. A two digit decimal number. “The attack will come at dawn.” “One if by land; two if by sea.” The King James Bible or the Collected Works of Poe. CS361 Slideset 4: 5 Information Theory

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Information as Uncertainty “The concept in this theory at first seems disappointing and bizarre—disappointing because it has nothing to do with meaning, and bizarre because it deals not with a single message, but with the statistical character of a whole ensemble of messages.” –Warren Weaver “The word ‘information’ relates not so much to what you do say, as to what you could say. The mathematical theory of communication deals with the carriers of information, symbols and signals, not with information itself. That is, information is the measure of your freedom of choice when you select a message.” –Warren Weaver CS361 Slideset 4: 6 Information Theory
Quantifying Information If you have n bits, you have 2 n possible messages. Why?

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