Tutorial 3 -InfoTheory - Math 2 Information Theory...

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Math 2 Information Theory Sebastian Lindner CPSC418- UCalgary FALL2014
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What we are going to learn: - Probability Theory - Prefect Secrecy - Information Theory
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Quick Terms - Computational Security: Oscar must use computational effort to break a cryptosystem. - Provable Security: Malory must solve an underlying difficult (math) problem. - Unconditional Security: Malory can do what ever she wants, as much as she wants (Unlimited Computational Power). Still Secure!
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Probability Review - A random variable (event) X is an experiment whose outcomes are mapped to real numbers. - Probability: We denote p x ( x ) = Pr ( X = x ) the probability that that a random variable X has the outcome x - Joint Probability: Study of probability given two random variables X and Y lumped together into a joint random variable. p X , Y (( X , Y ) = ( x , y )) = Pr (( X = x ) , ( Y = y ))
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Probability Review Joint Probability Example: Consider the roll of a fair die and let X = if the number is even and X = otherwise. Furthermore, let Y = if the number is prime and Y = otherwise. Then the joint distribution of X and Y is P X , Y ( X = , Y = ) = Pr ( ) = P X , Y ( X = , Y = ) = Pr ( , ) = P X , Y ( X = , Y = ) = Pr ( , ) = P X , Y ( X = , Y = ) = Pr ( ) = The probabilities necessarily add up to 1 since the probability that some combination of X and Y occurring is 1.
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Probability Review - Independence: Two events X and Y are independent if p X , Y ( X , Y = x , y ) = p X ( x ) p Y ( y ) . Notice this is not the same as joint probability. Joint can be thought of as two random variables combined with an ’OR’.
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