Assignment 2 – Encryption Scheme Sec Eng - Problems
Applied Cryptography and Security Engineering
1. Define a cryptosystem (answer is copied from the class slides)
A cryptosystem is defined by the following characteristics:
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A plaintext space M, the set of plaintext or clear-text messages.
A ciphertext space 𝒞, the set of ciphertext messages.
A key space 𝒦, the set of keys.
A randomized key generation algorithm Gen(1𝑛 ) the takes the security parameter n in unary
form as input and returns key k ∈ 𝒦.
An encryption algorithm ℰ = {ℰ𝑘 | 𝑘 ∈ 𝒦}, which is possible randomized. It takes a key and
plaintext message as input and returns the ciphertext or an error if the ciphertext is invalid.
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We write c = ℰ𝑘 (𝑚) or c ← ℰ𝑘 (𝑚), and c ← ℰ𝑘 (𝑚) if the algorithm is randomized. The error
output is denoted by ⊥.
A deterministic decryption algorithm 𝒟 = {𝒟𝑘 | 𝑘 ∈ 𝒦} takes a key and a ciphertext
message and input and returns the plaintext or an error symbol ⊥ if the ciphertext is invalid.
We write m = 𝒟𝑘 (𝑐) or m ← 𝒟𝑘 (𝑐).
2. Do a Vigenere Encryption where the plaintext m = theclassistough, and key k = apple. Then, using
the result (ciphertext from the encryption) to do Vigenere decryption using the same key. Hint: The
result shall be the same as the original plaintext m.
A=0, B=1,…,M=12,N=13,…,Y=24, Z=25.
Encryption: THECLASSISTOUGH
Decryption: TWTNPAHHTWTDJRL
+ APPLEAPPLEAPPLE
- APPLEAPPLEAPPLE
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TWTNPAHHTWTDJRL
THECLASSISTOUGH
3. Describe the difference between ‘Perfect Security” and ‘Computational Security”
A Perfect Security cryptosystem is unbreakable for any adversary, even if they have unlimited
computing power. On the contrary, Computational Security takes a more practical approach,
considering the attacker doesn’t have unlimited computing power. Accepting a small chance of
success, the computational approach estimates the probability of success in terms of time and
computing resources.
4. Define Indistinguishable Encryption Scheme and describe advantage of such scheme
Indistinguishability means that efficient adversaries are unable to find the correct plaintext out of
two possibilities if the ciphertext is given. The performance of the adversaries is not noticeably
better than random guessing. The advantage over random guesses is defined as the difference
between the probability of success and the probability of failure.
5. Describe pseudorandom number generator and its importance in encryption scheme
A pseudorandom generator is a deterministic algorithm that stretches a short truly random
sequence, or seed, and outputs to a long sequence that appears to be uniform random.
Pseudorandom number generators are important in practice for their speed in number generation
and their reproducibility.