MATH 456 Midterm: MATH456 ROSENBERG-J SPRING2013 0101 MID SOL

• School: University of Maryland
• Department: Mathematics
• Course: MATH 456
• Professor: All

Document Summary

Friday, march 1, 2013: (20 points total) a hill-style cipher works as follows. The plaintext, written as a sequence of bits, is broken into 3-bit blocks, each thought of as a length-3 vector with entries in z/2 (the integers mod 2). A block x is then encoded to another 3-bit block via the map x 7 xa, where a is an invertible 3 3 matrix with entries that are integers mod 2. Suppose the blocks (0, 1, 1), (1, 1, 1), and (1, 0, 1) encode to (1, 1, 0), (1, 0, 1), and (0, 0, 1), respectively. (a) (10 points) find the matrix a. 0 0 1 where a = a b c d e f g h i. And all numbers are taken mod 2. From the rst row, d + g = 1, e + h = 1 and f + i = 0.