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Unformatted text preview: a 4 1 mod 10. (b) (10 points) What are the last three digits of 377 400 ? Explain your work carefully! 4. Given the permutation = p 1 2 3 4 5 6 7 8 9 2 5 8 4 6 1 3 9 7 P , (a) (10 points) calculate 3 and 1 (Use matrix or cycle notation, as you prefer). (b) (10 points) Write as a product of disjoint cycles. 5. (10 points) Here is the mathematical center of the RSA algorithm: You know that N = pq is the product of 2 large primes. A number x , which is smaller than p and smaller than q , has been encoded as y = x a mod N . You know ( N ) , and that ( a, ( N )) = 1. Explain carefully how you get x mod N back from y . Explain why the competition, even knowing N and a , cannot decode y . END OF EXAMINATION 2...
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 Summer '08
 BESCHER
 Algebra

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