CY-302 Fundamental of Cryptography - Dec 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aExplain transposition cipher and polyalphabetic cipher.
   How to answer

   • Define transposition cipher (rearranging character positions) with an example (e.g., Rail Fence).
   • Define polyalphabetic cipher (using multiple substitution alphabets) with an example (e.g., Vigenère cipher).
   • Discuss advantages and vulnerabilities of each.
2. 7 Marks
   bWrite differences between symmetric key ciphers and asymmetric key ciphers.
   How to answer

   • Tabulate comparisons between symmetric and asymmetric ciphers.
   • Number of keys: single shared secret vs. public/private key pair.
   • Speed and computational complexity: symmetric is faster.
   • Key exchange and management challenges.
   • Examples: AES/DES vs. RSA/ECC.
3. 7 Marks
   aExplain the encryption process in AES algorithm.
   How to answer

   • Overview of AES: block size (128 bits), key lengths (128, 192, 256 bits), and number of rounds.
   • Initial transformation: AddRoundKey.
   • Four round transformations: SubBytes (non-linear S-box substitution), ShiftRows (row-wise cyclic shifts), MixColumns (matrix multiplication over GF(2^8)), AddRoundKey (XOR with round key).
   • Final round differences (omits MixColumns).
   • Brief diagram/flow of rounds.
4. 7 Marks
   bDescribe ECB mode of block ciphers with a neat diagram.
   How to answer

   • Define Electronic Codebook (ECB) mode.
   • Explain independent encryption of plaintext blocks with the same key: $C_i = E_K(P_i)$.
   • Draw neat diagram of ECB encryption and decryption.
   • Highlight its primary weakness: identical plaintext blocks yield identical ciphertext blocks (reveals patterns).
5. 7 Marks
   aExplain Davies-Meyer construction of hash function.
   How to answer

   • Define the Davies-Meyer one-way compression function structure.
   • Provide formula: $H_i = E_{m_i}(H_{i-1}) \oplus H_{i-1}$, where $m_i$ acts as key and $H_{i-1}$ as input block.
   • Draw block diagram showing the feed-forward addition (XOR).
   • Explain security rationale (feedforward prevents finding inverses).
6. 7 Marks
   bIllustrate one-way trapdoor functions with an example.
   How to answer

   • Define one-way function: easy to compute $f(x)$ from $x$, computationally infeasible to compute $x$ from $f(x)$.
   • Define trapdoor one-way function: easy to invert given special secret information ("trapdoor").
   • Give a standard example, such as RSA / integer factorization: multiplying two large primes $p, q$ is easy, but factoring $n = p \cdot q$ is hard without trapdoor $p$ and $q$.
7. 7 Marks
   aDescribe how encryption and decryption is performed in Elliptic Curve cryptography.
   How to answer

   • Define elliptic curve equation (Weierstrass form: $y^2 = x^3 + ax + b \pmod p$).
   • Key generation: private key $d$, public key $Q = d \cdot G$, where $G$ is the base point.
   • Encryption: Map plaintext message $M$ to point $P_m$; pick random $k$; calculate ciphertext pair $C_1 = k \cdot G$, $C_2 = P_m + k \cdot Q$.
   • Decryption: Compute $P_m = C_2 - d \cdot C_1$ since $d \cdot C_1 = d(k \cdot G) = k(d \cdot G) = k \cdot Q$.
8. 7 Marks
   bExplain the steps of man in the middle attack.
   How to answer

   • Define Man-in-the-Middle attack concept.
   • Step-by-step procedure (e.g., against unauthenticated Diffie-Hellman): Alice sends public key to Bob, intercepted by Darth/Eve; Darth sends own key to Bob and Alice.
   • Darth establishes independent secret keys with Alice and Bob separately.
   • Interception, decryption, modification, and re-encryption of messages transparently.
   • Countermeasures (digital certificates, digital signatures).
9. 7 Marks
   aDescribe Euler's theorem for identifying prime numbers with an example of your own.
   How to answer

   • State Euler's totient function $\phi(n)$ and its formula.
   • State Euler's Theorem: If $\gcd(a, n) = 1$, then $a^{\phi(n)} \equiv 1 \pmod n$.
   • Explain its relationship to Fermat's Little Theorem when $n$ is prime ($\\phi(n) = n - 1$).
   • Provide a numerical example verifying the theorem (e.g., $a = 3, n = 10$, $\phi(10) = 4$, $3^4 = 81 \equiv 1 \pmod{10}$).
   • Discuss application in primality checking / RSA.
10. 7 Marks
    bIllustrate discrete logarithmic problem and how it is useful in cryptography?
    How to answer

    • Define the Discrete Logarithm Problem: Given $g, p$, and $y = g^x \pmod p$, find integer $x$.
    • Explain computational asymmetry: modular exponentiation is fast (polynomial time), but discrete log is hard for large primes.
    • Discuss its cryptographic usefulness: foundation for Diffie-Hellman key agreement, ElGamal encryption/signatures, and DSA.
11. 7 Marks
    aWrite differences between AES and DES algorithms.
    How to answer

    • Key size: DES (56 bits) vs. AES (128, 192, 256 bits).
    • Block size: DES (64 bits) vs. AES (128 bits).
    • Structure: DES uses Feistel Cipher; AES uses Substitution-Permutation Network.
    • Rounds: DES (16 rounds) vs. AES (10, 12, or 14 rounds).
    • Security status: DES is broken (vulnerable to brute force); AES is current secure standard.
12. 7 Marks
    bExplain how authentication can be done using digital signatures?
    How to answer

    • Define digital signatures and their security objectives (authentication, integrity, non-repudiation).
    • Signing process: Sender computes hash $H(M)$ of message and encrypts it with sender's private key: $S = E_{PR_A}(H(M))$.
    • Verification process: Receiver decrypts signature using sender's public key $D_{PU_A}(S)$ to recover hash, computes local hash $H(M)$, and compares them.
    • Explain how successful verification proves the sender's identity (authentication).
13. 7 Marks
    aExplain the disadvantages of RSA algorithm.
    How to answer

    • Slow speed: computationally expensive modular exponentiation compared to symmetric ciphers.
    • Large key size requirement (minimum 2048-4096 bits) for sufficient modern security.
    • Vulnerability to attacks if parameters are poorly chosen (e.g., small encryption exponent, common modulus).
    • Malleability of textbook RSA unless proper padding (e.g., OAEP) is applied.
    • Susceptible to quantum computing factoring algorithms (Shor's algorithm).
14. 7 Marks
    bPerform encryption and decryption using RSA algorithm for $p = 5$, $q = 11$, $e = 3$ and $M = 9$.
    How to answer

    • Compute modulus: $n = p \cdot q = 5 \times 11 = 55$.
    • Compute totient: $\phi(n) = (p - 1)(q - 1) = 4 \times 10 = 40$.
    • Find private exponent $d$: $3d \equiv 1 \pmod{40} \implies 3d = 81 \implies d = 27$.
    • Perform encryption: $C = M^e \pmod n = 9^3 \pmod{55} = 729 \pmod{55} = 14$.
    • Perform decryption: $M = C^d \pmod n = 14^{27} \pmod{55} = 9$.
15. 14 Marks
    Write short notes on: i) DES encryption ii) Play Fair Cipher iii) Diffie-Hellman Key Exchange Algorithm
    How to answer

    • i) DES encryption: Feistel structure, 64-bit block, 56-bit effective key, 16 rounds with permutation, expansion, S-boxes, XOR.
    • ii) Playfair Cipher: 5x5 matrix of characters using a keyword, rules for digraph encryption (same row, same column, rectangle).
    • iii) Diffie-Hellman Key Exchange: Mechanism for two parties to agree on a shared secret over an insecure channel using modular exponentiation and DLP.