Use the PART III provided in the simulation page to solve the following problems. The tool includes a Shift Cipher calculator and a workspace for your analysis.

1. Encrypt the following plaintext using key k = 7.

Given:

• Plaintext: Lord Rama was a good king.
• Key: k = 7

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2. Given a plaintext and its corresponding ciphertext, determine the key used for encryption.

Given:

• Plaintext: abcdefghijklmnopqrstuvwxyz
• Ciphertext: tuvwxyzabcdefghijklmnopqrs

Hint: Compare the first few letters: a→t, b→u, c→v...

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3. How many different keys are possible with an n-letter alphabet?

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4. For the English alphabet (n = 26), how many distinct keys exist?

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5. Decrypt the following ciphertext using a brute-force attack.

Given: HAAHJR HA KHDU

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6. Why is the Shift Cipher vulnerable to brute-force attacks even though a secret key is used?

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7. Explain how frequency analysis can be used to recover the plaintext of a Shift Cipher. Under what conditions is frequency analysis more effective?

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8. Suppose the alphabet contains n symbols. Explain how increasing the alphabet size affects the key space. Is increasing the key space alone sufficient to make the Shift Cipher secure? Justify your answer.

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9. Compare brute-force attack and frequency analysis for breaking the Shift Cipher. Which technique guarantees recovery of the plaintext? Explain your reasoning.

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10. If an attacker knows one plaintext character and its corresponding ciphertext character, explain how the encryption key can be determined.

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11. Write an algorithm or program in a programming language of your choice to:

• Encrypt a plaintext using the Shift Cipher.
• Decrypt a ciphertext using a given key.
• Perform a brute-force attack by testing all possible keys.

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12. Modern encryption algorithms such as AES also use secret keys. State two reasons why AES is significantly more secure than the Shift Cipher.