math 311w homework9

# math 311w homework9 - n = 143 and a = 103 were used Decode...

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Homework 9. Due Monday, April 12,2010 Explain solutions of all problems. Problem 1. Calculate φ (390) , φ (300) , φ (768). Find at least two different numbers x, y 6 = 1 such that 1. 11 x 11 y = 11 mod 390 2. 11 x 11 y = 11 mod 300 3. 11 x 11 y = 11 mod 768 Problem 2. Assume you know that gcd ( m, 187) = 1. You’ve got a number M = m 27 . Find a number l such that M l = m . Problem 3. A public key code has n = 143 = 11 · 13 and a = 103. 1. Find φ ( n ). 2. Find b such that a · b 1 mod φ ( n ). 3. You received two encrypted messages 10 / 03. For encryption numbers

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Unformatted text preview: n = 143 and a = 103 were used. Decode them to numbers and then decode them to letters using the following agreement: J = 1 ,N = 2 ,R = 3 ,H = 4 ,D = 5 ,A = 6 ,S = 7 ,Y = 8 ,T = 9 ,O = 0 Problem 4. Find the inverse of ± 1 2 3 4 5 6 7 8 9 10 7 5 6 9 10 2 1 4 8 3 ² 1 Problem 5. Calculate πσ and σπ and check if they are equal π = ± 1 2 3 4 5 6 7 7 5 6 2 1 4 3 ² σ = ± 1 2 3 4 5 6 7 3 2 6 1 7 4 5 ² 2...
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