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# exam1a - M ath 470/501 Spring 2011 Exam 1 H and work ONLY...

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> > Math 470/501 Spring 2011 Exam 1 Hand work ONLY Name: UIN: #1. A Linear Feedback Shift Register with initialization vector 00100 and recursion mod 2 is used to encrypt a binary string. The encrypted string is 011010001110. Find the plaintext. We compute the encryption string: 00100|1 01001|0 10010|0 00100|1 01001|0 10010|0 00100|1 The 12 digit encryption string is 001001001001, the initial vector and 7 more bits constructed down the right hand side. We XOR that with the crypttext 011010001110 001001001001 to get the plaintext: 010011000111. #2. When asked to raise 65535 to the 65536000007th power mod the prime 65537, Joe Ag grabs a copy of Maple and writes "65535^65536000007 mod 65537;" but Maple replies Error, numeric exception: overflow . a) What went wrong, and how should the command be modified to make it work? b) The correct answer is 65409. Compute that result by hand, justifying each step. Maple does, indeed, give that response. 65535^65536000007 mod 65537; Error, numeric exception: overflow The problem is that Maple cannot store in memory. It is too large.

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(2.1) > > > > (2.2) We modify the command using the inert operator & so that the mod is performed
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exam1a - M ath 470/501 Spring 2011 Exam 1 H and work ONLY...

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