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crypto3_new - CIS CIS 5371 Cryptography 3 Probability...

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CIS 5371 Cryptography 3. Probability & Information Theory 1
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B i l f b bilit Basic rules of probability N i Notation Events: S, , E, F , ..., E F, E F, … . Pr[ S ]=1 Pr[ ]=0 0 Pr[ E ] 1 1 ] [ Pr ] Pr[ , \ E E E S E ]=1, Pr[ ]=0, 0 ] Pr[E F] = Pr[E] + Pr[F] - Pr[E F], . ] Pr[ ] Pr[ F E F E ] Pr[ ] | Pr[ F E E F 2 . ] Pr[ E
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B i l f b bilit Basic rules of probability A E i i ld f An Experiment can yield one of n equally probable outcomes. Event E1: One of the n values occurs. Pr[E1] = 1/ n Event E2: m of the n values occur. Pr[E2] = m / n Event E3: An Ace is drawn from a pack of 52 cards Pr[E3] = 4/52 = 1/13 3
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B i l f b bilit Basic rules of probability ) 1 ( ] [ P : n l k on Distributi Binomial k n k : ' Pr Law Bayes p p k trials n in succeses ] Pr[ ] Pr[ ] | Pr[ ] | Pr[ F E E F F E 4
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Bi thd P d Birthday Paradox elements n of set a is Y where Y X f Let : the x x x values distinct pairwise k for E Event k k , , , : 2 1 , least at is j i some for occurs x f x f collision a of y probabilit j i , ), ( ) ( n k then If Paradox Birthday 1774 . 1 2 / 1 : 5
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I f ti Th Information Theory Entropy (Shannon) The entropy of a message source is a measure of the
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