Introduction to Cryptography Summer ’01 Homework #2 Assigned: Tuesday, 5/22/01 Due: Tuesday, 6/5/01 Do the following problems from the textbook: ppg. 39-43: 1.1, 1.4, 1.5, 1.11 Extra questions: For questions a and b, let a, b, c, d and n be arbitrary positive integers. a) Prove or disprove: if a ≡ b (mod n) and c ≡ d (mod n), then ad ≡ bc (mod n). b) Prove or disprove: if a ≡ b (mod n), then a/c ≡ b/c (mod n), provided that both a/c and b/c are integers. c) Find integers x and y that satisfy the equation 243x + 459y = -27. d) Here is a matrix to use for the Hill cipher: ( 2 3 5 ) ( 1 0 4 ) ( 8
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