Math 480, Spring 2015, Assignment 3

Carefully define the following terms, then give one example and one non-example of each:

1. Primitive root (for $\mathbb{Z}_p$).
2. Symmetric cipher (this is defined as a $5$-tuple consisting of three sets and two mappings satisfying certain properties).
3. Ciphertext-only attack.
4. Known plaintext attack.
5. Chosen plaintext attack.
6. Chosen ciphertext attack.
7. Affine block cipher.

Carefully state the following theorems (you do not need to prove them):

1. Fermat's little theorem.

Solve the following problems:

1. Give a sample calculation to show how an affine block cipher can be defeated by a known plaintext attack. Make things easy on yourself by taking the blocksize to be $1$. In this case, how many known plaintexts are needed to recover the key with certainty?
2. Problems 1.26, 1.30(a), 1.32(a), and 1.45

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