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hmk4 - prime factorization 3 We proved that a message M...

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Introduction to Cryptography Summer ’01 Homework #4 Assigned: Tuesday, 6/26/01 Due: Thursday, 7/12/01 Do the following problems in the textbook(ppg. 157-161): 4.3, 4.4, 4.6(both), 4.7, 4.8 1) Given that gcd(m,n) = 1, prove that φ (mn) = φ (m) φ (n). 2) Using the result from part a, and employing a slightly different strategy than shown in class, prove the result stated on page 10 of the text concerning φ (n), when given n’s
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Unformatted text preview: prime factorization. 3) We proved that a message M correctly gets encrypted and decrypted using RSA encryption when gcd(M,n) = 1. Prove that the message M ALSO gets encrypted correctly when gcd(M,n) > 1. 4) Prove the following result stated on page 123 of the text: If α is a primitive element modulo p and β = α i , then the order of β modulo p is (p – 1)/gcd(p – 1, i)....
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