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Quiz 8 Solution

# Quiz 8 Solution - ECE-C490 Security in Computing Winter...

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ECE-C490 Security in Computing Winter Term 2005 Quiz #8 Solutions Numbers, J 16 + = {0, 1, 2, … 15} are encoded in the table so that they constitute a group < J 16 + , > where the group operation is defined as follows: x, y J 16 + , x y = (x 1 + 2 y 1 , x 2 + 2 y 2 , x 3 + 4 y 3 ). 0 0 0 0 1 0 1 0 2 0 0 1 3 0 1 1 4 0 0 2 5 0 1 2 6 0 0 3 7 0 1 3 8 1 0 0 9 1 1 0 10 1 0 1 11 1 1 1 12 1 0 2 13 1 1 2 14 1 0 3 15 1 1 3 For example, 1 5 would be [(0 + 2 0), (1 + 2 1), (0 + 4 2)] = [0,0,2] = 4. Given a subgroup H = {0, 2, 4, 6} Find ALL cosets of H. ( Hint: there are four .) Write your final answers below . Use the whitespace above or the back of the page for your work. We find cosets by performing the group operation between each member of the group and the members of the coset, one at a time. When attempting to generate a coset yields a
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