CY-302 Fundamental of Cryptography - Jun 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. 9 Marks
   aWhat is Perfect Secrecy in Crypto System? Explain.
   How to answer

   • Define Shannon's notion of perfect secrecy: P(M = m | C = c) = P(M = m)
   • Condition on key space: |K| >= |M|
   • Explanation of theoretical security versus computational security
   • Example of a perfectly secure system (One-Time Pad)
2. 5 Marks
   bExplain the purpose of One-Time Pad encryption?
   How to answer

   • Define One-Time Pad (OTP) / Vernam cipher
   • Purpose: achieving theoretical perfect secrecy / unconditional security
   • Key requirements: truly random key, key length equal to message, never reused
   • Practical limitations in key distribution and storage
3. 10 Marks
   aHow does the DES algorithm work in cryptography? Discuss with suitable example.
   How to answer

   • Overview of DES: 64-bit block size, 56-bit key, 16 rounds of Feistel structure
   • Key schedule generation: 16 subkeys of 48 bits each
   • Round operations: expansion (E-box), XOR with round key, S-box substitution, P-box permutation
   • Initial and final permutations
   • Illustrative example with sample data
4. 4 Marks
   bWhat is Message Authentication Code (MAC)? Discuss about secure MAC.
   How to answer

   • Definition of MAC and its role in ensuring integrity and authentication
   • Operation using a shared secret key and cryptographic function
   • Criteria for a secure MAC (resistance to existential forgery under chosen-message attacks)
   • Examples of secure MAC constructions (e.g., HMAC, CMAC)
5. 9 Marks
   aWhat is Random Oracle Model in cryptography? Explain.
   How to answer

   • Definition of a random oracle: theoretical black box responding to queries with uniformly random values
   • Consistency property: identical inputs return identical outputs
   • Role in provable security and security proofs of cryptographic schemes
   • Practical considerations: replacing the oracle with cryptographic hash functions (e.g., SHA-256)
6. 5 Marks
   bWhat do you mean by trapdoor attacks? Explain.
   How to answer

   • Definition of a trapdoor in cryptography (secret mechanism allowing easy inversion)
   • Explanation of trapdoor attacks: exploitation of hidden vulnerabilities or intentional backdoors
   • Examples in cryptographic algorithms/implementations
   • Countermeasures to prevent or mitigate trapdoors
7. 7 Marks
   aWrite the importance of Discrete Logarithms in Cryptography?
   How to answer

   • Mathematical formulation: finding $x$ in $g^x \equiv y \pmod p$
   • One-way property: modular exponentiation is easy, discrete logarithm is computationally hard
   • Foundational role in Diffie-Hellman key exchange and ElGamal encryption/signature
   • Application in Elliptic Curve Cryptography (ECDLP)
8. 7 Marks
   bExplain the following: i) Authenticate ii) Confidentiality iii) Authorization
   How to answer

   • Authentication: verifying the identity of a user or system entity
   • Confidentiality: preventing unauthorized disclosure of information (using encryption)
   • Authorization: determining access permissions and privileges for authenticated entities
   • Distinction between authentication and authorization
9. 9 Marks
   aWhat is a SSL protocol? How many protocols are there in SSL discuss in detail.
   How to answer

   • Definition and purpose of SSL (transport layer security protocol)
   • List the four core protocols: Handshake, Change Cipher Spec, Alert, and Record Protocol
   • Detailed explanation of SSL Record Protocol (framing, fragmentation, compression, MAC, encryption)
   • Detailed explanation of SSL Handshake Protocol steps and peer negotiation
10. 5 Marks
    bDiscuss the role of number theory used in Cryptography?
    How to answer

    • Overview of number theory as the foundation of modern public-key cryptography
    • Prime factorisation and its role in RSA
    • Modular arithmetic and congruent equations
    • Fermat's Little Theorem and Euler's Totient Theorem
    • Applications to key exchange and digital signature algorithms
11. 6 Marks
    aWhat is Symmetric vs. Asymmetric Encryption? Discuss.
    How to answer

    • Define symmetric encryption (single shared secret key) and asymmetric encryption (public-private key pair)
    • Tabular comparison based on key management, encryption speed, computational overhead, and key sizes
    • Examples of algorithms for each (AES, DES vs. RSA, ECC)
    • Hybrid approach combining both systems
12. 8 Marks
    bExplain about AES algorithm with suitable example.
    How to answer

    • Overview of AES: block size 128 bits, key lengths (128, 192, 256 bits), rounds (10, 12, 14)
    • State matrix representation ($4 \times 4$ array of bytes)
    • Four main transformations in each round: SubBytes (S-box), ShiftRows, MixColumns, AddRoundKey
    • Initial and final round differences
    • Key expansion algorithm and suitable numeric/byte level example
13. 8 Marks
    aGive an overview of Diffie-Hellman problem? Discuss about the main problem that Diffie-Hellman key exchange faces?
    How to answer

    • Overview of Diffie-Hellman key exchange protocol: public parameters $p$ and $g$, private/public key pairs, shared secret derivation
    • Computational Diffie-Hellman (CDH) and Decisional Diffie-Hellman (DDH) problems
    • Main vulnerability: lack of authentication leading to Man-in-the-Middle (MitM) attacks
    • Solutions to mitigate MitM: digital signatures, certificates, STS protocol
14. 6 Marks
    bWrite about One-way vs Two-way hash functions?
    How to answer

    • Explain one-way hash function properties: pre-image resistance, second pre-image resistance, collision resistance
    • Explain that genuine cryptographic hash functions are strictly one-way and cannot be inverted
    • Address the concept of 'two-way hash functions' (which refers to reversible mappings, encryption/decryption, or lookup tables)
    • Comparison of applications: integrity checking vs data storage and retrieval
15. 14 Marks
    Explain any two of the following: a) Transport Layer Security b) Interactive protocols in Cryptography c) Hybrid Cryptosystem d) Hill Cipher
    How to answer

    • Transport Layer Security (TLS): successor to SSL, architecture, record and handshake protocols, forward secrecy
    • Interactive protocols: communication between prover and verifier, challenge-response, zero-knowledge proofs
    • Hybrid Cryptosystem: combination of asymmetric key exchange (RSA/ECC) for symmetric session key and symmetric cipher (AES) for bulk data encryption
    • Hill Cipher: polygraphic substitution cipher based on linear algebra, matrix multiplication modulo 26, key matrix invertibility