CY-302 Fundamental of Cryptography - Dec 2024 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
   aWhat is meant by perfect secrecy? Give characterization of perfect secrecy.
   How to answer

   • Definition of perfect secrecy: $P(M=m | C=c) = P(M=m)$
   • Characterization via Shannon's Theorem
   • Key size requirement: $|K| \ge |M|$
   • Implications for practical cryptosystems
2. 7 Marks
   bWhat do you mean by encryption? Discuss onetime pad encryption technique.
   How to answer

   • Definition of encryption (transforming plaintext to ciphertext)
   • Description of One-Time Pad (OTP) / Vernam cipher
   • Mathematical formulation ($C = M \oplus K$, $M = C \oplus K$)
   • Conditions for absolute secrecy and practical limitations
3. 7 Marks
   aDiscuss the applications of Pseudorandom Generators (PRGs) in cryptography.
   How to answer

   • Concept of Pseudorandom Generator (seed expansion, unpredictability)
   • Application in stream ciphers
   • Use in generating session keys, nonces, and initialization vectors (IVs)
   • Applications in zero-knowledge proofs and randomized algorithms
4. 7 Marks
   bWith the help of a suitable figure discuss symmetric encryption technique.
   How to answer

   • Definition of symmetric/secret key encryption
   • Block diagram showing Plaintext, Secret Key, Encryption, Ciphertext, Decryption
   • Explanation of components and role of shared key
   • Pros and cons (speed vs. key distribution challenge)
5. 7 Marks
   aWhat do you know about the term block ciphers? Discuss modes of operations of block ciphers.
   How to answer

   • Definition of block cipher (fixed-size block transformation)
   • Explanation of standard modes of operation: ECB, CBC, CFB, OFB, CTR
   • Diagrammatic or algorithmic summary of at least two modes (e.g., CBC and CTR)
   • Comparison of error propagation and security
6. 7 Marks
   bWhat is the need for message authentication? List various techniques used for message authentication. Explain any one.
   How to answer

   • Need for message authentication (protection against tampering, masquerade, replay)
   • List of techniques: Message Encryption, Message Authentication Code (MAC), Hash Functions / HMAC, Digital Signatures
   • Detailed explanation of one selected technique (e.g., MAC or HMAC) with structure/formula
7. 7 Marks
   aWrite about different types of security attacks on computer network. Give a classification of attacks.
   How to answer

   • Broad classification: Passive vs. Active attacks
   • Examples and details of passive attacks (snooping, traffic analysis)
   • Examples and details of active attacks (masquerade, modification, replay, denial of service)
   • Impact and detection/prevention differences
8. 7 Marks
   bWhat are the applications of Hash function in cryptography?
   How to answer

   • Brief overview of cryptographic hash function properties (one-way, collision resistance)
   • Application in Digital Signatures (signing digest)
   • Application in Message Integrity / HMAC
   • Password storage and verification
   • Blockchain and Merkle trees
9. 14 Marks
   Discuss following terms in detail. i) Birthday attack ii) Key exchange problem iii) One way trapdoor
   How to answer

   • Birthday Attack: Basis on birthday paradox, probability formulation, collision search complexity $O(2^{n/2})$
   • Key Exchange Problem: The challenge of securely distributing symmetric keys across insecure channels
   • One-way Trapdoor: Function easy to compute in one direction, computationally infeasible to invert unless specific trapdoor information is known; significance in asymmetric cryptography
10. 7 Marks
    aWhat do you mean by Secret Key Cryptography and Public Key Cryptography? How they are different from one another.
    How to answer

    • Definitions of Secret Key (symmetric) and Public Key (asymmetric) cryptography
    • Comparison table based on parameters: number of keys, key distribution, algorithm speed, key size, applications
    • Examples of each (DES/AES vs. RSA/ECC)
11. 7 Marks
    bWith the help of a suitable example write and explain Diffie-Hellman Key Exchange algorithm.
    How to answer

    • Core steps of Diffie-Hellman Key Exchange
    • Selection of public parameters prime $q$ and primitive root $\alpha$
    • Private key choices ($X_A, X_B$) and public key computations ($Y_A, Y_B$)
    • Computation of the shared symmetric key $K$
    • Step-by-step numerical example with small numbers demonstrating identical shared secret
12. 7 Marks
    aExplain RSA algorithm. Perform encryption and decryption using RSA algorithm for $p = 3$, $q = 11$ and $e = 7$, $M = 5$.
    How to answer

    • Outline RSA algorithm steps (Key Generation, Encryption, Decryption)
    • Compute $n = 3 \times 11 = 33$ and $\phi(n) = 2 \times 10 = 20$
    • Find private key $d$: $7d \equiv 1 \pmod{20} \implies d = 3$
    • Encryption: $C = 5^7 \pmod{33} = 14$
    • Decryption: $M = 14^3 \pmod{33} = 2744 \pmod{33} = 5$
13. 7 Marks
    bWhat is Digital Signature? Explain digital signature standard.
    How to answer

    • Definition of Digital Signature and services provided (authenticity, integrity, non-repudiation)
    • Overview of Digital Signature Standard (DSS) and Digital Signature Algorithm (DSA)
    • Key generation, signing, and verification process in DSS
    • Comparison between RSA approach and DSS approach
14. 14 Marks
    Write short notes on any two of the followings: a) Brute Force Attack b) Elliptic curve cryptography c) Cryptanalysis
    How to answer

    • Brute Force Attack: Concept of exhaustive key search, dependency on key length ($2^k$), defense methods
    • Elliptic Curve Cryptography: Basis on algebraic structure of elliptic curves over finite fields, offering equivalent security with much smaller key sizes compared to RSA
    • Cryptanalysis: Science and techniques of analyzing and breaking cryptographic systems without knowing the secret key (ciphertext-only, known-plaintext, chosen-plaintext attacks)