CIS3360_HW6_Solution-3-19-10

# CIS3360_HW6_Solution-3-19-10 - Page 1 of 7 CIS 3360...

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Page 1 of 7 CIS 3360 – Security in Computing Spring 2010 Solution for Homework 6 1) [10] Show steps to compute the four-bit checksum for the message 1110 1010 0110 1010 1001. Remember to take the 1’s and 2’s complement at the end. Write out the message that is transmitted with the checksum. Solution: 1110 + 1010 1000 + 0110 1110 + 1010 1000 + 1001 0001 1’s complement: 1110 2’s complement: 1111 Appending the 4-bit checksum to the message, we get: 1110 1010 0110 1010 1001 1111

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Page 2 of 7 2) [10] Show steps to compute four-bit CRC for the message 1011 1011 1101 1010 1111 using the polynomial x 4 + x 3 + x 2 + 1. Write out the message that is transmitted with the CRC bits. Solution: The polynomial gives us the divisor: x 4 + x 3 + x 2 + 1 11101 Performing XOR repeatedly using the divisor on the message gives us the CRC bits: 1011 1011 1101 1010 1111 XOR 1110 1 000 0000 0000 0000 0101 0011 1101 1010 1111 XOR 0 111 01 00 0000 0000 0000 00 10 0111 1101 1010 1111 XOR 00 11 101 0 0000 0000 0000 000 1 1101 1101 1010 1111 XOR 000 1 1101 0000 0000 0000 0000 0000 1101 1010 1111 XOR 0000 0000 1110 1 000 0000 0000 0000 00 11 0010 1111 XOR 0000 0000 00 11 101 0 0000 0000 0000 0000 1000 1111 XOR 0000 0000 0000 1110 1 000 0000 0000 0000 0 110 0111 XOR 0000 0000 0000 0 111 01 00 0000 0000 0000 000 1 0011 XOR 0000 0000 0000 000 1 1101 0000 0000 0000 0000 1110 Appending the four-bit CRC to the original message, we get: 1011 1011 1101 1010 1111 1110
Page 3 of 7 3) [10+10+10+10] Alice sends the following two messages to Bob: a. 1000 1011 1101 1011 0101 b. 1011 1111 0101 In each message, Alice has added either a four-bit checksum or four CRC bits using the polynomial x 4 + x 3 + x 2 + 1. This means the last four bits of the first message i.e. “0101” and the last four bits of the second message i.e. “0101” are either the checksum bits or the CRC bits. For each message, do the following:

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## This note was uploaded on 10/05/2010 for the course CIS CIS 3360 taught by Professor Guha during the Spring '10 term at University of Central Florida.

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CIS3360_HW6_Solution-3-19-10 - Page 1 of 7 CIS 3360...

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