In the problems below, “textbook” refers to Douglas R. Stinson, Cryptography: Theory and Practice, Third Edition, Chapman & Hall/CRC, 2006.

Problem 1: Feistel Network

Textbook, problem 3.2.

Problem 2: DES Complementation Property

Textbook, problem 3.3.

Problem 3: DES S-box S₄

Textbook, problem 3.11(a). [Omit part (b).]

Problem 4: Practice with mod

Read pages 3–4 of textbook and then work the following:

1. Textbook, problem 1.1.
2. Textbook, problem 1.2.
3. Textbook, problem 1.3.
4. Textbook, problem 1.4.

Problem 5: Extended Euclidean Algorithm

Textbook, problem 5.3. Show your work.

Problem 6: Linear Diophantine Equations

Textbook, problem 5.4. Show your work.

Problem 7: RSA Encryption

[This is problem 6.8.2 from Trapp & Washington, “Introduction to Cryptography with Coding Theory, Second Edition”, Pearson Prentice Hall, 2006.]

Suppose your RSA modulus is n = 55 = 5 × 11 and your encryption exponent is e = 3.

1. Find the decryption modulus d.
2. Assume that gcd(m,55) = 1. Show that if c ≡ m³ (mod 55) is the ciphertext, then the plaintext is m ≡ c^d (mod 55). Do not quote the fact that RSA decryption works. That is what you are showing in this specific case.