# Hmk4Sols - CIS 3362 Homework #4 Solutions Phi Function,...

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CIS 3362 Homework #4 Solutions Phi Function, Euler's Theorem, RSA Encryption 1) Determine the following values: a) Φ(170) = Φ((2)(5)(17)) = 1x4x16 = 64 b) Φ(3945) = Φ((3)(5)(263)) = 2x4x262 = 2096 c) Φ(5403265623) = Φ((3 8 )(7 7 )) = (3 8 – 3 7 )(7 7 – 7 6 ) = 3087580356 d) Φ(9834345) = Φ((3 3 )(5)(97)(751)) = (3 3 – 3 2 )(4)(96)(750) = 5184000 e) Φ(202500000) = Φ((2 5 )(3 4 )(5 7 )) = (2 5 – 2 4 )(3 4 – 3 3 )(5 7 – 5 6 ) = 54000000 2) Without the aid of any computing device, show how one can use Euler's Theorem to determine the remainder when 49 1058 is divided by 201. Φ(201) = Φ((3)(67)) = 2x66 = 132. It follows that 49 132 ≡ 1 mod 201. Then, we can show that: 49 1058 ≡ (49 132 ) 8 49 2 ≡ (1) 8 49 2 ≡ 49 2 ≡ 2401 ≡ 190 mod 201. Thus, the desired remainder is 190. 3) Create your own RSA keys given the following specifications: both p and q have to have 8 digits in their decimal representation and both e and d have to have at least 10 digits in their decimal representations. You may use Java's BigInteger methods, but

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## This note was uploaded on 07/13/2011 for the course CIS 3362 taught by Professor Staff during the Fall '08 term at University of Central Florida.

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Hmk4Sols - CIS 3362 Homework #4 Solutions Phi Function,...

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