# 32 - Chapter 32 Entropy and Uncertainty Conditional joint...

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June 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #32-1 Chapter 32: Entropy and Uncertainty Conditional, joint probability Entropy and uncertainty Joint entropy Conditional entropy Perfect secrecy

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June 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #32-2 Overview Random variables Joint probability Conditional probability Entropy (or uncertainty in bits) Joint entropy Conditional entropy Applying it to secrecy of ciphers
June 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #32-3 Random Variable Variable that represents outcome of an event X represents value from roll of a fair die; probability for rolling n : p ( X = n ) = 1/6 If die is loaded so 2 appears twice as often as other numbers, p ( X = 2) = 2/7 and, for n 2, p ( X = n ) = 1/7 Note: p ( X ) means specific value for X doesn’t matter Example: all values of X are equiprobable

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June 1, 2004 Computer Security: Art and Science ©2002-2004 Matt Bishop Slide #32-4 Joint Probability Joint probability of X and Y , p ( X , Y ), is probability that X and Y simultaneously assume particular values If X , Y independent, p ( X , Y ) = p ( X ) p ( Y ) Roll die, toss coin p ( X = 3, Y = heads) = p ( X = 3) p ( Y = heads) = 1/6 × 1/2 = 1/12
June 1, 2004

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