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# lecture4 - Lecture4:HashFunctions,Message...

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Lecture 4: Hash Functions, Message  Authentication and Key Distribution CS 392/6813: Computer Security  Fall 2008 Nitesh Saxena     * Adopted from Previous Lectures by Nasir Memon

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1/23/2006 Lecture 4: Hash Functions and Key Distribution 2 Course Admin HW#3 to be posted very soon Sorry for the delay Solutions will be posted soon Regarding programming portions of the homework Submit the whole modified code that you used to measure  timings Comment the portions in the code where you modified the  code Include a small “readme” for us to understand this If you did not submit the code for HW#2, do so now Upload it on MyPoly Break during the lecture?
1/23/2006 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

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1/23/2006 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. Infeasible to get x, given h(x).                        One- wayness property Given x, infeasible to find y such that h(x) = h(y).  Weak collision property . Infeasible to find any pair x and y such that h(x) =  h(y).  Strong collision property
1/23/2006 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

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1/23/2006 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: ( 29 ( 29 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
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lecture4 - Lecture4:HashFunctions,Message...

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