Math 343 Fall 12 Day 5 PDF

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Math 343 Fall 12 Day 5 Code Breaking:

An Application of Matrix Multiplication and Inverses You have been hired by a top secret organization to encode messages. They wish to encode messages into strings of integers to transfer. The message you are to encode is: WELCOME TO THE MATRIX Task 1: Initially, you consider assigning each letter of the alphabet to an integer value. Create a system that works in this manner. Encode your message. (Don’t forget to encode spaces!) Task 2: Explain why this type of code system would be easy to break. Task 3: We want to leverage matrices to encode better. We will need an encoding and decoding matrix. Using your code from Task 1, convert the following matrix into numbers 

 W C E O H M R  E O E A I  L M T T T X Task 4: Now, we want to create a 3 × 3 encoding matrix A which we will multiply by on the left. This way, we can multiply an encoded message by A−1 to decode. Create such a matrix and discuss a general process for creating invertible encoding matrices. Task 5: Use your matrix A from the previous task to encode your message. Task 6: Why is this encoded message harder to break than the naive attempt in task 1? Task 7: Verify that you encoded your message correctly by decoding with the inverse. Task 8: Create an original original message (10-15 words) and encode it using your matrix. Task 9: Swap your encoded message with a neighbor and see if you can crack their message without knowledge of their matrix. Task 10: After 5 minutes, if you are unsuccessful cracking the message without their encoding matrix, request his/her encoding matrix (and only his/her encoding matrix) and attempt to crack the code. 1...