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MIT6_042JS10_lec23_prob

MIT6_042JS10_lec23_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science April 2 Prof. Albert R. Meyer revised March 13, 2010, 108 minutes In-Class Problems Week 8, Fri. Problem 1. Let’s try out RSA! There is a complete description of the algorithm at the bottom of the page. You’ll probably need extra paper. Check your work carefully! (a) As a team, go through the beforehand steps. Choose primes p and q to be relatively small, say in the range 10-40. In practice, p and q might contain several hundred digits, but small numbers are easier to handle with pencil and paper. • Try e = 3 , 5 , 7 , . . . until you find something that works. Use Euclid’s algorithm to compute the gcd. • Find d (using the Pulverizer —see appendix for a reminder on how the Pulverizer works —or Euler’s Theorem). When you’re done, put your public key on the board. This lets another team send you a message. (b) Now send an encrypted message to another team using their public key. Select your message m from the codebook below: 2 = Greetings and salutations! 3 = Yo, wassup? 4 = You guys are slow! 5 = All your base are belong to us. 6 = Someone on our team thinks someone on your team is kinda cute. • 7 = You are the weakest link. Goodbye. (c) Decrypt the message sent to you and verify that you received what the other team sent!
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