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COT 5937 Quick Test Review Questions
1)
Assuming you want no fixed points, (these are letters that encrypt to themselves) how
different valid keys are there for the affine cipher?
When a=1, only key that gives rise to a fixed point is b=0. So there are 25 keys to
count.
When a>1, if b is even, we can find a fixed point, but when b is odd, we can not. We
determine this by examining the equation x = ax + b mod 26. Doing some algebra we
get x(a1) = b mod 26. Since we know a is odd, a1 is even. When this is the case, if b
is odd, there is no solution, but when b is even, there is a solution. Thus, we have 11
possible values for a and 13 for b, yielding another 11x13 = 143 keys to count.
Total = 25 + 143 = 168
2)
Here is a message encrypted using the shift cipher: YCMABQWVBEW. What is the
decrypted message. (Hint: The encrypting key, which is in between 0 and 25 has exactly
4 integer factors. Thus, for example, 25 is not the key because it has 3 factors: 1, 5 and
25.)
Shift = 8, factors are 1,2,4 and 8.
Message: QUESTIONTWO
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 Summer '09

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