hw08 - CS 70 Spring 2005 Discrete Mathematics for CS...

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CS 70 Discrete Mathematics for CS Spring 2005 Clancy/Wagner HW 8 Due Thursday, March 31 Coverage: This assignment involves topics from the lectures of March 1, 8, 10, 15, 17, and from Rosen section 2.6 and chapter 4. Administrative reminders: We will accept only unformatted text files or PDF files for homework sub- mission. Include your name, login name, section number, and partner list in your submission. Give the command submit hw8 to submit your solution to this assignment. Homework exercises: 1. (6 pts.) Repeated squaring The algorithm for computing a b mod c by repeated squaring does not necessarily lead to the minimum number of multiplications. Give an example of b ( b > 10) where the exponentiation can be performed using fewer multiplications, by some other method. 2. (10 pts.) RSA Let p and q be primes and let N = pq . Show how to determine p and q given N and ( p - 1 )( q - 1 ) . (In other words, given the public key ( e , N ) , e the encryption exponent and N the RSA modulus, and the

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hw08 - CS 70 Spring 2005 Discrete Mathematics for CS...

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