B.TECH - Semester 7 cryptography Question Paper 2008 (dec)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Prove that $(a+b) \bmod n=(a \bmod n+b \bmod n) \bmod n$.
- Let $Z_{n}$ denotes set of non-negative integers less than $n\left(Z_{n}=\{0,1, \ldots, n-1\}\right)$. Prove that $Z_{8}$ does not have multiplicative inverse for all elements.
- Define Congruence class modulo $m$.
- Define discrete logarithm (DL) problem. What is the role of DL problem in cryptography?
- Discuss the advantages and disadvantages of stream cipher.
- Give an interactive zero knowledge proof between prover and verifier to prove the knowledge of discrete logarithm.
- Define pseudo prime. Prove 91 is pseudo prime to base 3.
- What are the properties and requirements of digital signature system?
- What are the various stages performed in a single round of AES algorithm except the first and last round?
- Define P, NP, NP Complete class of problems. Answer any two questions from each module. Each question carries 10 marks.
- Define ring and field. Prove that the set $Z_{9}=\{0,1, \ldots, 8\}$ under addition modulo 9 and multiplication modulo 9 is a ring but not field.
- State Fermat's little theorem and Euler's theorem. Find $5^{103} \bmod 103$ and $5^{102} \bmod 103$. Also find $\phi(35)$ and $\phi(37)$.
- Discuss the principle behind secret key cryptography and public key cryptography.
- Explain RSA algorithm. Perform encryption and decryption with public key $\mathrm{e}=7$ and $\mathrm{n}=187$ for $\mathrm{M}=88$. And $\phi(\mathrm{n})=160$.
- Explain the signing and verification of a digital signature scheme using a block diagram.
- Explain the principle behind Hill cipher. Encipher the message 17175 PAYMOREMONEY using the key $K$, the encoding matrix $K=211821$. 2219 Also find $K^{-1}$.
- Explain DES algorithm with neat diagram.
- On elliptic curve $y^{2}=x^{3}-36 x$ let $P(-3,9)$ and $Q(-2,8)$ be two points Find $P+Q$ and $2 P$.
- Explain Pollard's Rho method for factorization with an example. ( $6 \times 10=60$ Marks)