Problem: P36
Networking, Security & Dependability
Student Code
Answer all five questions below:
1. Does non-linearity make a cipher resistant to cryptanalysis or brute force attacks? Justify your answer.
2. Does computational security describe resistance to brute force or cryptanalytic attacks? Justify your answer.
3. The affine Caesar cipher replaces each plaintext character, p, with the ciphertext character, C, determined by the following equation: C = E([a, b], p) = ap + b mod N.
a and b are a pair of integers that act as the key. N is the size of the alphabet.
The fundamental requirement for any cipher is reversibility, i.e., that it creates a one-to-one mapping between each plaintext character and the ciphertext character to which it is encrypted. Mathematically, this implies that p = q if and only if E(p) = E(q). Does this requirement place any restrictions on the value of a for the affine Caesar cipher? What about b? Justify your answers.
4. Describe the brute force approach to breaking this cipher. In this approach, every possible key is tried until the decryption yields an intelligible message. Assume that the adversary knows the 32-character alphabet used and is capable of recognizing an intelligible message, and the only challenge is arriving at the correct key. Your answer should include the maximum number of guesses required for determining the key, with an explanation for how you determined this number.
5. Consider a cryptanalytic approach to breaking the affine Caesar cipher. Specifically, assume that an adversary can mount a finite number of successful chosen plaintext attacks, where they have the ability to determine the ciphertext character corresponding to a plaintext character of their choice.
Explain how these attacks can be used to break the cipher. Your answer should include the number of attacks necessary for breaking the cipher, with an explanation for how you determined this number.
