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Unformatted text preview: Solutions for HW 5 From 8.7 Exercise 3 Onetime pads are rarely used in practise because of the problem of key distribution. As the key must be completely random, it must be generated and distributed using some secure medium (usually by courier). Further, the sender and receiver must ensure they stay synchronized, so the recipient knows where in the key sequence the senders key begins. Exercise 10 Prove the following: a) If p is a prime, (p) = p1. The residue set Z p = {0, 1, , p1} Note that except for 0, p is relatively prime to each element in Z p . Hence ( p ) = p 1 b) If p and q are primes, (pq) = (p1)(q1). The residue set is Z pq = {0, 1, , pq1} A number that is a multiple of p or q is not relatively prime to pq . Hence, elements of sets { p , 2 p , 3 p , .., ( q1) p } and { q , 2 q , 3 q , , ( p1) q } are not relatively prime to pq . Also note that 0 is not relatively prime to pq )....
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This note was uploaded on 11/02/2009 for the course SIS 2150 taught by Professor Joshi during the Spring '09 term at Philadelphia.
 Spring '09
 joshi

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