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Unformatted text preview: MATH S-104 Lecture 8 In-class Problem Solutions July 16, 2009 Problem 1 : A key exchange protocol allows Alice and Bob to send messages across an insecure channel, and eventually arrive at a secret key that they both know. To be secure, it must be that Eve the eavesdropper, who sees all the messages sent across the insecure channel, is not able to figure out the key that Alice and Bob both know. Given that modular exponentiation is tractable and modular discrete log is not, arrive at a secure key exchange protocol. A solution is the Diffie-Hellman key exchange protocol. Alice chooses g , p , and x . Alice sends g , p , and g x ( mod p ) to Bob. Bob chooses y and sends g y ( mod p ) to Alice. Now Bob computes ( g x ) y ≡ g xy ( mod p ) and Alice computes ( g y ) x ≡ g xy ( mod p ) , which is the shared key. Eve can’t compute the key because she has seen only g x and g y , and can’t compute the discrete log in a reasonable amount of time, so she has neither x nor y . Problem 2 † : Suppose that all license plates have four uppercase letters followed by three digits. a)How many different license plates are possible? ( 26 4 )( 10 3 ) b)How many license plates begin with A and end in 0? ( 26 3 )( 10 2 ) c)How many license plates are possible in which all the letters and digits are distinct? 26 * 25 * 24 * 23 * 10 * 9 * 8 Problem 3 ‡ : Let S be the set of all 4-digit base-10 numbers that contain the digit 7 somewhere. (Number can start with a 0, thus 0007 ∈ S .) a)The cardinality of S can be determined in several ways. Choose at least one of the following and compute S ....
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This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.
- Spring '10