Complete the following problems to strengthen your understanding of RSA encryption and the PKCS#1 v1.5 padding scheme.

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1. RSA Key Parameters

Given

$$p=17,\qquad q=11$$

calculate

$$N=pq$$

and

$$\phi(N)=(p-1)(q-1)$$

If

$$e=7$$

determine the corresponding private exponent

$$d$$

using the Extended Euclidean Algorithm.

Multiple Choice

A possible value of (d) is

• (a) 22
• (b) 23
• (c) 103
• (d) 183

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2. RSA Encryption

Using textbook RSA,

given

$$N=253,\qquad e=3$$

encrypt the message

$$m=57$$

using

$$c=m^e \bmod N$$

Multiple Choice

The ciphertext is

• (a) 240
• (b) 250
• (c) 196
• (d) 257

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3. Understanding PKCS#1 v1.5

Why is plaintext padding performed before RSA encryption in PKCS#1 v1.5?

Multiple Choice

• (a) To reduce the ciphertext size
• (b) To introduce randomness and improve security
• (c) To simplify modular exponentiation
• (d) To generate the private key

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4. Padding Structure

Which of the following best represents the structure of an encryption block in PKCS#1 v1.5?

• (a)

$$00\ ||\ 02\ ||\ PS\ ||\ 00\ ||\ M$$

• (b)

$$00\ ||\ 01\ ||\ FF\ ||\ M$$

• (c)

$$M\ ||\ PS\ ||\ 00$$

• (d)

$$02\ ||\ 00\ ||\ M$$

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5. Random Padding

Why must the padding string (PS) contain random non-zero bytes?

Your answer should explain

• why randomness is required,
• why zero bytes are avoided,
• how random padding improves security.

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6. Security Analysis

Explain why textbook RSA is deterministic and why this property makes it unsuitable for encrypting messages directly.

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7. Comparison

Compare textbook RSA and PKCS#1 v1.5 with respect to

• plaintext processing,
• randomness,
• security,
• practical deployment.

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8. Practical Observation

Use the simulation to encrypt the same plaintext multiple times.

Answer the following:

• Does the ciphertext remain the same every time?
• Explain your observation.
• What role does random padding play in producing this result?

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9. Modern Perspective

PKCS#1 v1.5 significantly improves the security of textbook RSA.

However, newer standards such as OAEP are recommended today.

State two reasons why OAEP provides stronger security than PKCS#1 v1.5.