MIT6_042JF10_rec05

MIT6_042JF10_rec05 - 6.042/18.062J Mathematics for Computer...

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6.042/18.062J Mathematics for Computer Science September 24, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 5 1 RSA: Let’s try it out! You’ll probably need extra paper. Check your work carefully! 1. As a team, go through the beforehand steps. (a) Choose primes p and q to be relatively small, say in the range 5-15. In practice, p and q might contain several hundred digits, but small numbers are easier to handle with pencil and paper. (b) Calculate n = pq . This number will be used to encrypt and decrypt your messages. (c) Find an e > 1 such that gcd( e, ( p 1)( q 1)) = 1. The pair ( e,n ) will be your public key . This value will be broadcast to other groups, and they will use it to send you messages. (d) Now you will need to ±nd a d such that de 1 (mod ( p 1)( q 1)). Explain how this could be done using the Pulverizer. (Do not carry out the computations!) Find d using Euler’s Theorem given in yesterday’s lecture. The
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MIT6_042JF10_rec05 - 6.042/18.062J Mathematics for Computer...

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