Science:Math Exam Resources/Courses/MATH312/December 2009/Question 04 (a)
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Question 04 (a) 

Decrypt OAPB, which was encrypted by the affine transformation

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1  

It might help to refer to the following table
Note also that you are given the values of C and ask to compute P. 
Hint 2 

If needed, you can compute inverses modulo 26 via the Euclidean algorithm. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. First, we isolate for P in the given formula. To do this we need to compute the inverse of 7 modulo 26. We use the Euclidean algorithm to do this.
and back substituting
and so the inverse of 7 modulo 26 is (11) which is equal to 15 modulo 26. Hence
We plug in the four values of C given by and see that
Thus, the plaintext was the word TRIG. 