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(2) Cryptography is the process of coding and decoding messages. One type of code that is extremely difficult to break involves using a large invertible matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. The first matrix is called the encoding matrix and its inverse is called the decoding matrix. The following example uses a 2 × 2 to illustrate the method. First we start by identifying the symbols A, B, C,..., Z with the numbers 1, ..., 26. Let a space between the words be denoted by the number 27. For example, the message "HELLO ." will be coded as 8 5 12 12 15. The basic idea is to write the message as a matrix. For example, we may write "HELLO" as the 2 × 3 matrix 8 12 15 M = 5 12 27 If we now take a 2 × 2 invertible matrix A, we may encrypt the message as AM. For example, if 3 2 A = 2) the message "HELLO." becomes "34 45, 60 72, 99 102". This message can be decoded by reversing the encoding process. PROBLEM TO BE TURNED IN: Use the following encoding matrix -3 1 E = 0 1 2 2 4 to decipher the code from William Stein, codeveloper of SageMath. Show all of your work. 18 33 85-64 53 110 -34 28 71 3 43 113 24 55 124

(2) Cryptography is the process of coding and decoding messages. One type of code that is extremely difficult to break involves using a large invertible matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. The first matrix is called the encoding matrix and its inverse is called the decoding matrix. The following example uses a 2 × 2 to illustrate the method. First we start by identifying the symbols A, B, C,..., Z with the numbers 1, ..., 26. Let a space between the words be denoted by the number 27. For example, the message "HELLO ." will be coded as 8 5 12 12 15. The basic idea is to write the message as a matrix. For example, we may write "HELLO" as the 2 × 3 matrix 8 12 15 M = 5 12 27 If we now take a 2 × 2 invertible matrix A, we may encrypt the message as AM. For example, if 3 2 A = 2) the message "HELLO." becomes "34 45, 60 72, 99 102". This message can be decoded by reversing the encoding process. PROBLEM TO BE TURNED IN: Use the following encoding matrix -3 1 E = 0 1 2 2 4 to decipher the code from William Stein, codeveloper of SageMath. Show all of your work. 18 33 85-64 53 110 -34 28 71 3 43 113 24 55 124

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(2) Cryptography is the process of coding and decoding messages. One type of code that is extremely difficult to break involves using a large invertible matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. The first matrix is called the encoding matrix and its inverse is called the decoding matrix. The following example uses a 2 × 2 to illustrate the method. First we start by identifying the symbols A, B, C,..., Z with the numbers 1, ..., 26. Let a space between the words be denoted by the number 27. For example, the message "HELLO ." will be coded as 8 5 12 12 15. The basic idea is to write the message as a matrix. For example, we may write "HELLO" as the 2 × 3 matrix 8 12 15 M = 5 12 27 If we now take a 2 × 2 invertible matrix A, we may encrypt the message as AM. For example, if 3 2 A = 2) the message "HELLO." becomes "34 45, 60 72, 99 102". This message can be decoded by reversing the encoding process. PROBLEM TO BE TURNED IN: Use the following encoding matrix -3 1 E = 0 1 2 2 4 to decipher the code from William Stein, codeveloper of SageMath. Show all of your work. 18 33 85-64 53 110 -34 28 71 3 43 113 24 55 124
Transcribed Image Text:(2) Cryptography is the process of coding and decoding messages. One type of code that is extremely difficult to break involves using a large invertible matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. The first matrix is called the encoding matrix and its inverse is called the decoding matrix. The following example uses a 2 × 2 to illustrate the method. First we start by identifying the symbols A, B, C,..., Z with the numbers 1, ..., 26. Let a space between the words be denoted by the number 27. For example, the message "HELLO ." will be coded as 8 5 12 12 15. The basic idea is to write the message as a matrix. For example, we may write "HELLO" as the 2 × 3 matrix 8 12 15 M = 5 12 27 If we now take a 2 × 2 invertible matrix A, we may encrypt the message as AM. For example, if 3 2 A = 2) the message "HELLO." becomes "34 45, 60 72, 99 102". This message can be decoded by reversing the encoding process. PROBLEM TO BE TURNED IN: Use the following encoding matrix -3 1 E = 0 1 2 2 4 to decipher the code from William Stein, codeveloper of SageMath. Show all of your work. 18 33 85-64 53 110 -34 28 71 3 43 113 24 55 124
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