Math Problem Statement

Extract all the text from this file and write in a order

Encipher the message MISSION IMPOSSIBLE by using a shift cipher with k = 7. Decipher the cryptogram, WSCCSYX MYWZVODON, assuming it was enciphered by using a shift cipher with k = 10.

Solution

Here's the extracted text from the uploaded image:


Name: Waleed Khalid
Roll No: F24610019

Table for shift cipher:
A B C D E F G H I J K L M\text{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\text{N O P Q R S T U V W X Y Z}


Q-1:
Encipher the message MISSION IMPOSSIBLE by using a shift cipher with k=7k = 7.

Solution:
Here k=7k = 7, so we need a shift of 7 letters to encipher the message.

MISSIONIMPOSSIBLE\text{MISSIONIMPOSSIBLE}
TPZZPVUPTWZZPISL\text{TPZZPVUPTWZZPISL}

Now, MISSION IMPOSSIBLE is converted to TPZZPVUPTWZZPISL by using a shift cipher with k=7k = 7.


Q-2:
Decipher the cryptogram, WSCCSYX MYWZVODON, assuming it was enciphered by using a shift cipher with k=10k = 10.


Would you like further details on solving this cipher problem?

Further Questions:

  1. How does the shift cipher encryption work in general?
  2. What happens if you use a negative value for kk in a shift cipher?
  3. Can you explain how to decrypt a message if you only know part of the text?
  4. What other types of substitution ciphers are similar to shift ciphers?
  5. How can shift ciphers be broken if the shift key is unknown?

Tip:

When decrypting a shift cipher, try shifting backwards by kk places to retrieve the original text.

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Math Problem Analysis

Mathematical Concepts

Cryptography
Shift Cipher
Caesar Cipher

Formulas

Shift cipher formula: E(x) = (x + k) mod 26 for encryption, D(x) = (x - k) mod 26 for decryption

Theorems

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Suitable Grade Level

Grades 9-12