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# lecture4 - Lecture 4 Hash Functions Message Authentication...

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Lecture 4: Hash Functions, Message Authentication and Key Distribution CS 392/6813: Computer Security Fall 2009 Nitesh Saxena * Adopted from Previous Lectures by Nasir Memon 10/8/2009 Lecture 4: Hash Functions and Key Distribution 2 Course Administration HW3 was posted – due next Monday HW2 has been graded HW2 solution was provided Mid-Term on 10/29 Closed-books/closed-notes In-class Would cover lecture material until 10/22

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10/8/2009 Lecture 4: Hash Functions and Key Distribution 3 Outline of Today’s lecture Hash Functions Properties Known Hash Function SHA-1 Message Authentication using hash fns: HMAC “Private Key” Distribution “Public Key” Distribution: PKI Certification Revocation 10/8/2009 Lecture 4: Hash Functions and Key Distribution 4 Cryptographic Hash Functions Requirements of cryptographic hash functions: Can be applied to data of any length. Output is fixed length Relatively easy to compute h(x), given x and deterministic Infeasible to get x, given h(x). One-wayness property Given x, infeasible to find y such that h(x) = h(y). Weak-collision resistance property . Infeasible to find any pair x and y such that h(x) = h(y). Strong-collision resistance property .
10/8/2009 Lecture 4: Hash Functions and Key Distribution 5 Hash Output Length How long should be the output (n bits) of a cryptographic hash function? To find collision - randomly select messages and check if hash matches any that we know. Throwing k balls in N = 2 n bins. How large should k be, before probability of landing two balls in the same becomes greater than ½? Birthday paradox - a collision can be found in roughly sqrt(N) = 2 (n/2) trials for an n bit hash In a group of 23 )(~ sqrt(365)) people, at least two of them will have the same birthday (with a probability > ½) Hence n should be at least 160 10/8/2009 Lecture 4: Hash Functions and Key Distribution 6 Birthday Paradox Probability that hash values of k random messages are distinct is (that is, no collisions) is: ( ) ( ) 1 1 2 3 1 / 1 ( 1)/2 ( 1)/2 1 2 1 1 1 1 1 (as for small , 1 ,as 1 ) 2! 3! = So for at least one collision we have probability of whose va 1 k i k i n x x i k k N k k N k i N N N n x x x x x e e e e e = =  = =   ≅ − = − + K L lue is above 0.5 when 1.17 k N =

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10/8/2009 Lecture 4: Hash Functions and Key Distribution 7 Generic Hash Function 10/8/2009 Lecture 4: Hash Functions and Key Distribution 8
10/8/2009 Lecture 4: Hash Functions and Key Distribution 9 10/8/2009 Lecture 4: Hash Functions and Key Distribution 10

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10/8/2009 Lecture 4: Hash Functions and Key Distribution 11 10/8/2009 Lecture 4: Hash Functions and Key Distribution 12
10/8/2009 Lecture 4: Hash Functions and Key Distribution 13 10/8/2009 Lecture 4: Hash Functions and Key Distribution 14

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10/8/2009 Lecture 4: Hash Functions and Key Distribution 15 10/8/2009 Lecture 4: Hash Functions and Key Distribution 16
10/8/2009 Lecture 4: Hash Functions and Key Distribution 17 Other Hash Functions Many other hash functions SHA-2 (SHA-256)

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lecture4 - Lecture 4 Hash Functions Message Authentication...

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