crypto3_new

crypto3_new - CIS CIS 5371 Cryptography 3. Probability...

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Unformatted text preview: CIS CIS 5371 Cryptography 3. Probability & Information Theory 1 Basic rules of probability Notation Events: S, , E, F, ..., EF, EF, … . Pr[S]=1, Pr[]=0, 0 Pr[E] 1 Pr[ Pr[EF] = Pr[E] + Pr[F] - Pr[EF], . . E S \ E , Pr[ E ] Pr [ E ] 1 EF Pr[ E ] Pr[ F ] Pr[ E F ] Pr[ F | E ] Pr[ E ] 2 Basic rules of probability 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 Basic rules of probability Binomial Distributi on : n k Pr [ k succeses in n trials ] p (1 p ) n k k Bayes ' Law : Pr[ E ] Pr[ E | F ] Pr[ F | E ] Pr[ F ] 4 Bi Birthday Paradox Let f : X Y where Y is a set of n elements Event E k , : for k pairwise distinct values x1 , x 2 , , x k the probabilit y of a collision f ( xi ) f ( x j ), occurs for some i j , is at least Birthday Paradox : If 1 / 2 then k 1.1774 n 5 Information Theory Th Entropy (Shannon) The entropy of a message source is a measure of the amount of information the source has Let L = {a1, … , an} be a language with n letters. S is a source that outputs these letters with independent probabilities Prob[a1], … , Prob[an]. The entropy of S is: H (S ) n i 1 1 Pr[ a i ] log 2 Pr[ a ] bits i 6 Information Theory Th Example A source S outputs a random bit. Its entropy is: 1 1 H ( S ) Pr[0] log 2 Pr[0] Pr[1] log 2 Pr[1] 1 1 (1) (1) 1 bit 2 2 7 ...
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This note was uploaded on 12/11/2011 for the course CIS 5371 taught by Professor Mascagni during the Fall '11 term at FSU.

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crypto3_new - CIS CIS 5371 Cryptography 3. Probability...

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