Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question 5
![**Elementary Number Theory: Cryptography Exercises**
---
### 4. Linear Cipher Analysis
In a ciphertext using a linear cipher \( C \equiv aP + b \pmod{26} \), the most frequent letter is Q, followed by J.
- **(a)** Determine \( a \) and \( b \) by using the frequency of letters (E and T are frequent in English).
- **(b)** Decrypt the message "WCPQ JZQO MX".
### 5. Vigenère Cipher
- **(a)** Encrypt "HAVE A NICE TRIP" with the keyword "MATH".
- **(b)** Decrypt "BS FMX KFSGR JAPWL" assuming it uses the keyword "YES".
### 6. Autokey Cipher
- **(a)** Encrypt "HAPPY DAYS ARE HERE" with seed Q.
- **(b)** Decrypt "BBOT XWBZ AWUVGK" using seed RX.
### 7. Hill Cipher
- **(a)** Use the Hill cipher to encrypt "GIVE THEM TIME" with:
\[ C_1 \equiv 5P_1 + 2P_2 \pmod{26} \]
\[ C_2 \equiv 3P_1 + 4P_2 \pmod{26} \]
- **(b)** Decrypt "ALXWU VADCOJO" which uses:
\[ C_1 \equiv 4P_1 + 11P_2 \pmod{26} \]
\[ C_2 \equiv 3P_1 + 8P_2 \pmod{26} \]
### 8. Hill Cipher Analysis
A Hill cipher produces ciphertext with frequent two-letter blocks "HO" and "PP".
- **(a)** Calculate \( a, b, c, \) and \( d \) using:
\[ C_1 \equiv aP_1 + bP_2 \pmod{26} \]
\[ C_2 \equiv cP_1 + dP_2 \pmod{26} \]
Use common English bigrams (such as TH) for reference.
- **(b)** Decrypt the intercepted text.
---
The tasks guide you through deciphering different classical ciphers by determining](https://content.bartleby.com/qna-images/question/66c7b497-dac7-4855-b923-2e60bbc73063/51aad466-ac75-4ba8-bfbe-3c51cfae9c20/ymyu2p.jpeg)
Transcribed Image Text:**Elementary Number Theory: Cryptography Exercises**
---
### 4. Linear Cipher Analysis
In a ciphertext using a linear cipher \( C \equiv aP + b \pmod{26} \), the most frequent letter is Q, followed by J.
- **(a)** Determine \( a \) and \( b \) by using the frequency of letters (E and T are frequent in English).
- **(b)** Decrypt the message "WCPQ JZQO MX".
### 5. Vigenère Cipher
- **(a)** Encrypt "HAVE A NICE TRIP" with the keyword "MATH".
- **(b)** Decrypt "BS FMX KFSGR JAPWL" assuming it uses the keyword "YES".
### 6. Autokey Cipher
- **(a)** Encrypt "HAPPY DAYS ARE HERE" with seed Q.
- **(b)** Decrypt "BBOT XWBZ AWUVGK" using seed RX.
### 7. Hill Cipher
- **(a)** Use the Hill cipher to encrypt "GIVE THEM TIME" with:
\[ C_1 \equiv 5P_1 + 2P_2 \pmod{26} \]
\[ C_2 \equiv 3P_1 + 4P_2 \pmod{26} \]
- **(b)** Decrypt "ALXWU VADCOJO" which uses:
\[ C_1 \equiv 4P_1 + 11P_2 \pmod{26} \]
\[ C_2 \equiv 3P_1 + 8P_2 \pmod{26} \]
### 8. Hill Cipher Analysis
A Hill cipher produces ciphertext with frequent two-letter blocks "HO" and "PP".
- **(a)** Calculate \( a, b, c, \) and \( d \) using:
\[ C_1 \equiv aP_1 + bP_2 \pmod{26} \]
\[ C_2 \equiv cP_1 + dP_2 \pmod{26} \]
Use common English bigrams (such as TH) for reference.
- **(b)** Decrypt the intercepted text.
---
The tasks guide you through deciphering different classical ciphers by determining
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