MAT 350 Module Seven Application Project Guidelines and Rubric: Hill Substitution Ciphers This project introduces students to an encryption scheme called the Hill substitution cipher. This encryption technique encodes information via a matrix multiplication and decodes data by multiplying by the inverse matrix. The encoding matrix is typically kept private to keep the original information secure. Without this decoding \"key,\" the encrypted data is difficult to decode. This encoding and decoding process can be thought of as a coordinate transformation. Original English words/letters are mapped to a new set of scrambled \"coordinates\" in the encoded data. Multiplying encoded data by the inverse change-ofcoordinates matrix returns the scrambled data back to the original coordinates/words. Hill Substitution Cipher provides general background theory on this encoding scheme and also works similar examples to those you are asked to work below. Problems 1. Compute the following matrix product modulo 26. [ [ 1 2 4 17 5 18 2 1 9 11 2 2 22 20 1 4 6 13 5 4 9 2. Consider the key matrix 3. Compute A 1 [ 15 18 2 A= 1 2 3 5 7 17 . Use this key matrix to encode the phrase \"LINEAR ALGEBRA IS SO EASY\". mod 26 4. Decode the message KRTZLKKIUQAVTXFGTBGSK which was encoded using the key matrix A . Rubric Instructor Feedback: This activity uses an integrated rubric in Blackboard. Students can view instructor feedback in the Grade Center. For more information, review these instructions. Critical Elements Main Elements Computational Result (Correct Answers) Computational Analysis (Shows Work) Applies Course Content Quantitative Literacy Exemplary (100%) Completes all of the requirements, including finding the determinant and the inverse of both matrices, and codes and decodes the given messages All parts of the assignment are computed correctly (all answers correct) Substantially shows work in a meaningful sequence to support answers Proficient (85%) Completes most of requirements, such as finding the determinant and the inverse of one or both matrices, and codes or decodes the given messages Most parts of the assignment are computed correctly Needs Improvement (55%) Includes some of the requirements, such as finding the inverse, but not coding and encoding both messages Not Evident (0%) Includes less than half of the requirements Some parts of the assignment are computed correctly There are many computational errors 20 Shows work in an ordered sequence to support answers There is some work shown, but it is neither comprehensive nor in an ordered sequence 30 All of the relevant course content is correctly applied to the assignment Effectively works with matrices and solves the quantitative problem in the authentic context of cryptology Most of the relevant course content is correctly applied to the assignment Works with matrices and solves the quantitative problem in the authentic context of cryptology, but with moderate effectiveness Some of the relevant course content is correctly applied to this assignment Works with matrices and solves the quantitative problem with minimal effectiveness Little or no work shown to support answers, or it is unclear how computations link to correct answers Does not correctly apply any of the course content Is not able to work with matrices given and solve quantitative problem in the given context 10 Earned Total Value 25 15 100%