Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
Determine the decoding function and find the plaintext message.

Determine the decoding function and find the plaintext message.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
See similar textbooks
icon
Related questions
Question

Help with this please

**Cryptography: Encoding and Decoding Messages using Linear Transformations** In this lesson, we will explore how to encode and decode messages using linear transformations. Specifically, we will work with the function \( f(p) = Ap + b \), which is used to encode a plaintext message. The corresponding decoding process allows us to recover the original message. **Encoding Function:** The encoding function used here is \( f(p) = Ap + b \), where: \[ A = \begin{pmatrix} 3 & 4 \\ 2 & 3 \end{pmatrix} \quad \text{and} \quad b = \begin{pmatrix} 2 \\ 5 \end{pmatrix} \] **Given Ciphertext:** The encoding function has been applied to a message (plaintext), resulting in the following ciphertext: **IJNWAIMUMUCAWTOWQYFDKO.** **Objective:** Our goal is to determine the decoding function and use it to retrieve the plaintext message. ### Steps to Decode the Message: 1. **Inverse the Matrix \( A \):** - Calculate the inverse of matrix \( A \), denoted as \( A^{-1} \), to reverse the transformation applied by \( A \). 2. **Formulate the Decoding Function:** - Using the inverse matrix \( A^{-1} \), formulate the decoding function. Given that the original encoding function was \( f(p) = Ap + b \), the decoding function \( g(c) \) can be derived to retrieve the plaintext \( p \): \[ p = A^{-1}(c - b) \] 3. **Apply the Decoding Function:** - Apply the decoding function to each pair of characters in the ciphertext to map them back to their plaintext equivalents. By understanding and applying these concepts, we can transform encoded messages back to their original form, thereby deciphering the important information they contain. Please proceed to solve the decoding function and find the plaintext message, using the tools and formulas provided above.
Transcribed Image Text:**Cryptography: Encoding and Decoding Messages using Linear Transformations** In this lesson, we will explore how to encode and decode messages using linear transformations. Specifically, we will work with the function \( f(p) = Ap + b \), which is used to encode a plaintext message. The corresponding decoding process allows us to recover the original message. **Encoding Function:** The encoding function used here is \( f(p) = Ap + b \), where: \[ A = \begin{pmatrix} 3 & 4 \\ 2 & 3 \end{pmatrix} \quad \text{and} \quad b = \begin{pmatrix} 2 \\ 5 \end{pmatrix} \] **Given Ciphertext:** The encoding function has been applied to a message (plaintext), resulting in the following ciphertext: **IJNWAIMUMUCAWTOWQYFDKO.** **Objective:** Our goal is to determine the decoding function and use it to retrieve the plaintext message. ### Steps to Decode the Message: 1. **Inverse the Matrix \( A \):** - Calculate the inverse of matrix \( A \), denoted as \( A^{-1} \), to reverse the transformation applied by \( A \). 2. **Formulate the Decoding Function:** - Using the inverse matrix \( A^{-1} \), formulate the decoding function. Given that the original encoding function was \( f(p) = Ap + b \), the decoding function \( g(c) \) can be derived to retrieve the plaintext \( p \): \[ p = A^{-1}(c - b) \] 3. **Apply the Decoding Function:** - Apply the decoding function to each pair of characters in the ciphertext to map them back to their plaintext equivalents. By understanding and applying these concepts, we can transform encoded messages back to their original form, thereby deciphering the important information they contain. Please proceed to solve the decoding function and find the plaintext message, using the tools and formulas provided above.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Encryption and decryption
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS