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1.3. For this exercise, use the simple substitution table given in Table 1.11. (a) Encrypt the plaintext message The gold is hidden in the garden. (b) Make a decryption table, that is, make a table in which the ciphertext alphabet is in order from A to Z and the plaintext alphabet is mixed up. (c) Use your decryption table from (b) to decrypt the following message. IBXLX JVXIZ SLLDE VAQLL DEVAU QLB

1.3. For this exercise, use the simple substitution table given in Table 1.11. (a) Encrypt the plaintext message The gold is hidden in the garden. (b) Make a decryption table, that is, make a table in which the ciphertext alphabet is in order from A to Z and the plaintext alphabet is mixed up. (c) Use your decryption table from (b) to decrypt the following message. IBXLX JVXIZ SLLDE VAQLL DEVAU QLB

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Cipher Wheels: An Introduction **Figure 1.1: A Cipher Wheel with an Offset of Five Letters** A cipher wheel is a tool used to implement various cryptographic systems, most notably those based on simple substitution ciphers. It consists of two concentric circles, one with the letters of the alphabet arranged regularly, and the other with these letters shifted by a certain offset. In Figure 1.1, the offset is five letters. To understand how this particular cipher wheel functions, follow these steps: 1. **Inner Circle**: The inner circle of the wheel has letters of the alphabet arranged in their regular order: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z. 2. **Outer Circle**: The outer circle's letters are shifted five places forwards relative to the inner circle. Therefore, the pairings would be: - `A` -> `F` - `B` -> `G` - `C` -> `H` - `D` -> `I` - `E` -> `J` - And so on, until `Z` -> `E`. 3. **Using the Cipher Wheel**: To encrypt a letter from a plaintext message, you locate the plaintext letter on the inner circle and substitute it with the corresponding letter from the outer circle. For instance: - Encrypting `A` would result in `F` - Encrypting `B` would result in `G` Conversely, to decrypt a letter, you do the reverse: find the letter on the outer circle and replace it with the corresponding letter on the inner circle. This specific cipher wheel system is an example of a Caesar cipher, precisely Caesar Cipher with a shift of 5. This simple encryption technique offers insights into basic cryptographic principles and is an essential concept in cryptographic history. **Applications**: Such cipher wheels are primarily educational tools today, helpful in understanding the foundations of cryptographic methods and the importance of secure communication.
Transcribed Image Text:### Cipher Wheels: An Introduction **Figure 1.1: A Cipher Wheel with an Offset of Five Letters** A cipher wheel is a tool used to implement various cryptographic systems, most notably those based on simple substitution ciphers. It consists of two concentric circles, one with the letters of the alphabet arranged regularly, and the other with these letters shifted by a certain offset. In Figure 1.1, the offset is five letters. To understand how this particular cipher wheel functions, follow these steps: 1. **Inner Circle**: The inner circle of the wheel has letters of the alphabet arranged in their regular order: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z. 2. **Outer Circle**: The outer circle's letters are shifted five places forwards relative to the inner circle. Therefore, the pairings would be: - `A` -> `F` - `B` -> `G` - `C` -> `H` - `D` -> `I` - `E` -> `J` - And so on, until `Z` -> `E`. 3. **Using the Cipher Wheel**: To encrypt a letter from a plaintext message, you locate the plaintext letter on the inner circle and substitute it with the corresponding letter from the outer circle. For instance: - Encrypting `A` would result in `F` - Encrypting `B` would result in `G` Conversely, to decrypt a letter, you do the reverse: find the letter on the outer circle and replace it with the corresponding letter on the inner circle. This specific cipher wheel system is an example of a Caesar cipher, precisely Caesar Cipher with a shift of 5. This simple encryption technique offers insights into basic cryptographic principles and is an essential concept in cryptographic history. **Applications**: Such cipher wheels are primarily educational tools today, helpful in understanding the foundations of cryptographic methods and the importance of secure communication.
### Exercise 1.3: Simple Substitution Cipher #### Objective: Use the simple substitution table provided in Table 1.11 for encryption and decryption tasks. #### Instructions: 1. **Encryption Task:** - **(a)** Encrypt the following plaintext message using the simple substitution table: ``` The gold is hidden in the garden. ``` 2. **Decryption Task:** - **(b)** Create a decryption table. This table should have the ciphertext alphabet in order from A to Z and a randomized order for the plaintext alphabet. - **(c)** Utilize the decryption table created in step (b) to decrypt the following message: ``` IBXLX JVXIZ SLLDE VAQLL DEVAU QLB ``` #### Decryption Table Creation: In creating the decryption table, you align each letter in the ciphertext alphabet (A-Z) with a mixed-up version of the plaintext alphabet. The precise ordering will depend on the specific simple substitution table given in Table 1.11 (which you'll refer to from your course materials). #### Example: Assuming the given substitution is: ``` A -> X B -> Y C -> Z ... ``` (Continue the pattern with a specific substitution given by Table 1.11.) Then, to decrypt: 1. Locate each letter from the ciphertext in the decryption table. 2. Replace it with the corresponding plaintext letter. #### Practical Example Steps: 1. Encrypt the example plaintext message. 2. Create the decryption table. 3. Decrypt the provided ciphertext message using your table. #### Additional Notes: Ensure to refer back to Table 1.11 for the exact substitution mappings necessary for this exercise. Working through encryption and decryption using ciphers enhances understanding of cryptographic principles. Feel free to reach out if you have further questions or require additional guidance on this task.
Transcribed Image Text:### Exercise 1.3: Simple Substitution Cipher #### Objective: Use the simple substitution table provided in Table 1.11 for encryption and decryption tasks. #### Instructions: 1. **Encryption Task:** - **(a)** Encrypt the following plaintext message using the simple substitution table: ``` The gold is hidden in the garden. ``` 2. **Decryption Task:** - **(b)** Create a decryption table. This table should have the ciphertext alphabet in order from A to Z and a randomized order for the plaintext alphabet. - **(c)** Utilize the decryption table created in step (b) to decrypt the following message: ``` IBXLX JVXIZ SLLDE VAQLL DEVAU QLB ``` #### Decryption Table Creation: In creating the decryption table, you align each letter in the ciphertext alphabet (A-Z) with a mixed-up version of the plaintext alphabet. The precise ordering will depend on the specific simple substitution table given in Table 1.11 (which you'll refer to from your course materials). #### Example: Assuming the given substitution is: ``` A -> X B -> Y C -> Z ... ``` (Continue the pattern with a specific substitution given by Table 1.11.) Then, to decrypt: 1. Locate each letter from the ciphertext in the decryption table. 2. Replace it with the corresponding plaintext letter. #### Practical Example Steps: 1. Encrypt the example plaintext message. 2. Create the decryption table. 3. Decrypt the provided ciphertext message using your table. #### Additional Notes: Ensure to refer back to Table 1.11 for the exact substitution mappings necessary for this exercise. Working through encryption and decryption using ciphers enhances understanding of cryptographic principles. Feel free to reach out if you have further questions or require additional guidance on this task.
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