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1.1. Build a cipher wheel as illustrated in Figure 1.1, but with an inner wheel that rotates, and use it to complete the following tasks. (For your convenience, there is a cipher wheel that you can print and cut out at www.math.brown.edu/~jhs/ MathCrypto/CipherWheel.pdf.) (a) Encrypt the following plaintext using a rotation of 11 clockwise. "A page of history is worth a volume of logic." (b) Decrypt the following message, which was encrypted with a rotation of 7 clock- wise. AOLYLHYLUVZLJYLAZILAALYAOHUAOLZLJYLALZAOHALCLYFIVKFNBLZZLZ (c) Decrypt the following message, which was encrypted by rotating 1 clockwise for the first letter, then 2 clockwise for the second letter, etc. XJHRFTNZHMZGAHIUETXZJNBWNUTRHEPOMDNBJMAUGORFAOIZOCC

1.1. Build a cipher wheel as illustrated in Figure 1.1, but with an inner wheel that rotates, and use it to complete the following tasks. (For your convenience, there is a cipher wheel that you can print and cut out at www.math.brown.edu/~jhs/ MathCrypto/CipherWheel.pdf.) (a) Encrypt the following plaintext using a rotation of 11 clockwise. "A page of history is worth a volume of logic." (b) Decrypt the following message, which was encrypted with a rotation of 7 clock- wise. AOLYLHYLUVZLJYLAZILAALYAOHUAOLZLJYLALZAOHALCLYFIVKFNBLZZLZ (c) Decrypt the following message, which was encrypted by rotating 1 clockwise for the first letter, then 2 clockwise for the second letter, etc. XJHRFTNZHMZGAHIUETXZJNBWNUTRHEPOMDNBJMAUGORFAOIZOCC

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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### Instructions for Developing and Using a Cipher Wheel **Step 1.1:** Construct a cipher wheel as depicted in Figure 1.1. This should consist of a rotating inner wheel and an outer fixed wheel. You can use this wheel to perform various cryptographic tasks. **Resource:** A printable cipher wheel template is available at [CipherWheel.pdf](https://www.math.brown.edu/~jhs/MathCrypto/CipherWheel.pdf). **Tasks:** **(a) Encrypt the following plaintext using a rotation of 11 positions clockwise:** ``` "A page of history is worth a volume of logic." ``` **(b) Decrypt the following message, which was encrypted using a 7-position clockwise rotation:** ``` AOLYLHYLUVZLJYLAZILAALYAOHUAOLZLJYLAZLAOHALCLYFIVKFNBLZZLZ ``` **(c) Decrypt the following message, which was encrypted by rotating 1 position clockwise for the first letter, 2 positions clockwise for the second letter, and so on:** ``` XJHRFTNZHMZGAHIUETXZJNBWNUTRHEPOMDNBJMAUGORFAOIZOCC ``` ### Notes on Graphs and Diagrams: The instructions refer to Figure 1.1, which would typically illustrate the construction and use of the cipher wheel. This figure is essential as it visually explains how the inner and outer wheels should be aligned and rotated to perform encryption and decryption tasks. Unfortunately, the specific figure is not provided in the text description. #### Detailed Explanation of the Cipher Wheel: 1. **Construction:** - The cipher wheel consists of two concentric circles, one smaller than the other. - The outer wheel is fixed and marked with the standard alphabet (A-Z). - The inner wheel is rotatable and also marked with the standard alphabet. 2. **Operation:** - To encrypt or decrypt, align the inner wheel to a specific starting letter according to the required rotation. - Each letter in the plaintext or ciphertext is then matched with its corresponding letter on the opposite wheel. By following these steps, you can use the cipher wheel effectively for basic cryptographic operations.
Transcribed Image Text:### Instructions for Developing and Using a Cipher Wheel **Step 1.1:** Construct a cipher wheel as depicted in Figure 1.1. This should consist of a rotating inner wheel and an outer fixed wheel. You can use this wheel to perform various cryptographic tasks. **Resource:** A printable cipher wheel template is available at [CipherWheel.pdf](https://www.math.brown.edu/~jhs/MathCrypto/CipherWheel.pdf). **Tasks:** **(a) Encrypt the following plaintext using a rotation of 11 positions clockwise:** ``` "A page of history is worth a volume of logic." ``` **(b) Decrypt the following message, which was encrypted using a 7-position clockwise rotation:** ``` AOLYLHYLUVZLJYLAZILAALYAOHUAOLZLJYLAZLAOHALCLYFIVKFNBLZZLZ ``` **(c) Decrypt the following message, which was encrypted by rotating 1 position clockwise for the first letter, 2 positions clockwise for the second letter, and so on:** ``` XJHRFTNZHMZGAHIUETXZJNBWNUTRHEPOMDNBJMAUGORFAOIZOCC ``` ### Notes on Graphs and Diagrams: The instructions refer to Figure 1.1, which would typically illustrate the construction and use of the cipher wheel. This figure is essential as it visually explains how the inner and outer wheels should be aligned and rotated to perform encryption and decryption tasks. Unfortunately, the specific figure is not provided in the text description. #### Detailed Explanation of the Cipher Wheel: 1. **Construction:** - The cipher wheel consists of two concentric circles, one smaller than the other. - The outer wheel is fixed and marked with the standard alphabet (A-Z). - The inner wheel is rotatable and also marked with the standard alphabet. 2. **Operation:** - To encrypt or decrypt, align the inner wheel to a specific starting letter according to the required rotation. - Each letter in the plaintext or ciphertext is then matched with its corresponding letter on the opposite wheel. By following these steps, you can use the cipher wheel effectively for basic cryptographic operations.
**Figure 1.1: A cipher wheel with an offset of five letters** **Description:** The diagram in Figure 1.1 showcases a cipher wheel, which is a common tool used in classical cryptography for encoding and decoding messages. The cipher wheel is structured as a circular arrangement of letters divided into two concentric circles. The outer circle contains the uppercase letters of the alphabet, starting from A and ending with Z in a clockwise direction. The inner circle contains the lowercase letters of the alphabet, similarly arranged. **Explanation:** Each letter on the outer circle is paired with a corresponding letter on the inner circle following a specific offset. In this instance, the offset is five letters. Therefore, each letter in the outer circle is connected to a letter in the inner circle that is five positions further along in the alphabet. For example: - A (outer circle) pairs with f (inner circle) - B pairs with g - C pairs with h - D pairs with i - E pairs with j - ... Continuing this pattern, the wheel circles back to the beginning of the alphabet. The arrowhead points to the starting pair (A and f), indicating the initial position that sets the five-letter offset. **Usage:** To encode a message using this cipher wheel, one would replace each letter of the original message with the corresponding letter from the inner circle. To decode, the reverse process is used, substituting each letter of the encoded message with its pair from the outer circle.
Transcribed Image Text:**Figure 1.1: A cipher wheel with an offset of five letters** **Description:** The diagram in Figure 1.1 showcases a cipher wheel, which is a common tool used in classical cryptography for encoding and decoding messages. The cipher wheel is structured as a circular arrangement of letters divided into two concentric circles. The outer circle contains the uppercase letters of the alphabet, starting from A and ending with Z in a clockwise direction. The inner circle contains the lowercase letters of the alphabet, similarly arranged. **Explanation:** Each letter on the outer circle is paired with a corresponding letter on the inner circle following a specific offset. In this instance, the offset is five letters. Therefore, each letter in the outer circle is connected to a letter in the inner circle that is five positions further along in the alphabet. For example: - A (outer circle) pairs with f (inner circle) - B pairs with g - C pairs with h - D pairs with i - E pairs with j - ... Continuing this pattern, the wheel circles back to the beginning of the alphabet. The arrowhead points to the starting pair (A and f), indicating the initial position that sets the five-letter offset. **Usage:** To encode a message using this cipher wheel, one would replace each letter of the original message with the corresponding letter from the inner circle. To decode, the reverse process is used, substituting each letter of the encoded message with its pair from the outer circle.
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