# exam1g - MATH 470 Exam 1 Section 503 You may use a...

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MATH 470 Exam 1: Section 503 You may use a calculator provided it only has the ability to add, multiply, subtract and divide. Some facts you might find useful [This test features the primes 17 , 211 and 431 ] ( mod 211) congruences 71457 139 , 17 53 48 , 17 17 92 139 53 136 , 53 139 56 , 139 139 9 ( mod 431) congruences 71457 342 , 342 50 30 , 342 108 90 , 108 342 16 , 139 211 319 , 17 211 241 , 139 17 294 , 17 17 74 ( mod 90941) congruences 51 2 2601 , 51 4 55841 , 10 6 90590 , 10 8 35567 , 55841 . 35567 36348 , 2601 . 90590 87400 , 2601 . 35567 22770 90 . 211 . 96 4220 , 47 . 136 . 431 26722 , 47 . 90 . 139 29634 Q1: Q2: Q3: Q4: Q5: Q6: Q7: Q8: Q9: Q10: Total:
[1] Alice is using an affine cipher and a 27 character alphabet that sets the space =0 and a =1 , b = 2 , . . . , z =26 to send a message to Bob. You intercept the ciphertext QAQGREEZGUDW LXGWYOTZ. The "QAQ" could very well be "bob". If you make this assumption can you recover the key?
[2] Alice and Bob agree to use a Hill cipher with a 4 × 4 encryption matrix M but they want M to be easy to remember and also invertible. They come up with M = 1 2 3 4 0 5 6 7 0 0 9 8 0 0 0 x . What restrictions should they place on the value of x to make this possible assuming they use the normal 26 letter alphabet. An explanation is required. (5 P OINTS )