# FEReviewQs - CIS 3362 Final Exam Review Questions 1...

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CIS 3362 Final Exam Review Questions 1) Consider an affine cipher with an alphabet size of 45. Let the encryption function be f(x) = (16x + 7) mod 45. What is the corresponding decryption function? Note: To be valid, your answer must be of the form f -1 (x) = (ax + b) mod 45 with a and b in between 0 and 44, inclusive. x = (16y + 7) mod 45 45 = 2 x 16 + 13 13 – 4 x 3 = 1 (x – 7) = 16y mod 45 16 = 1 x 13 + 3 13 – 4(16 – 13) = 1 16y = (x – 7) mod 45 13 = 4 x 3 + 1 5 x 13 – 4 x 16 = 1 31(16y) = 31(x – 7) mod 45 5(45 – 2 x 16) – 4 x 16 = 1 y = (31x – 217) mod 45 5 x 45 – 14 x 16 = 1 y = (31x + 8) mod 45 Thus, 16 -1 = -14 mod 45 = 31 mod 45 2) Encrypt the phrase “PROGRAMS” using the Hill cipher with the encryption matrix . Answer = XJMOGZEE

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represented as 8 HEX characters? Answer = D9CE3DCB (read the bottom right entry in each S-box!) 4) Consider the field GF(2 3 ) mod x 3 + x + 1. What is the value of (x 2 + x + 1)(x 2 + 1) mod x 3 + x + 1? (x 2 + x + 1)(x 2 + 1) = (x 4 + x 2 + x 3 + x + x 2 + 1) mod x 3 + x + 1. = (x 4 + x 3 + x + 1) mod x 3 + x + 1. = x 4 mod x 3 + x + 1. = x
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FEReviewQs - CIS 3362 Final Exam Review Questions 1...

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