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Unformatted text preview: MATH 135 Fall 2007 Assignment #8 Due: Thursday 22 November 2007, 8:20 a.m. Notes : In problems 3 and 4, please do your work by hand and show this work. (Of course, using MAPLE to check your answers is probably a good idea.) The last page of this document contains some handy MAPLE commands. The text file Problem 6 Values contains the values of the large numbers in Problem 6 in text format. There will be a TA in the Tutorial Centre from 11:30 to 12:30 and 1:30 to 3:30 on Thursday 15 November and in MC 5077 to help with Maple issues from 4:30 to 6:00 on Wednesday 21 November. Hand-In Problems 1. Determine the complete solution to the congruence x 31 + 17 x 43 (mod 55). 2. Prove that n 21 n 3 (mod 21) for every integer n . 3. If p = 251, q = 281 and e = 73, find the associated RSA public and private keys. 4. (a) In an RSA scheme, the public key ( e, n ) = (23 , 19837) and the private key is ( d, n ) = (17819 , 19837). Using the Square and Multiply algorithm, encrypt the message M = 1975 using the appropriate key. (b) In an RSA scheme, the the public key is ( e, n ) = (801 , 1189), the private key is ( d, n ) = (481 , 1189). Note that 41 is a factor of 1189. Using the Chinese Remainder Theorem, decrypt the ciphertext...
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