1/16/2021 dhI
USN :
Adichunchanagiri Institute of Technology, Chikkamagaluru
DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING
III - INTERNAL ASSESSMENT
Semester: 7-CBCS 2017 Date: 16 Jan 2021
Subject: CRYPTOGRAPHY (17EC744) Time: 02:30 PM - 04:30 PM
Faculty: Dr Jagadeesh Chandra A P Max Marks: 30
PART A
Answer any1 question(s)
Q.No Marks CO BT/CL
1 a State and prove Fermat’s theorem. Find the value of 3
303
mod11 7 CO3 L2
b Write the Miller Rabin algorithm to test for primality. Using Miller Rabins 8 CO3 L2
algorithm test the given number n=29 for its primality
2 a State and prove Euler’s theorem. Find (i) Φ(41) (ii) Φ(231) 7 CO3 L2
b Explain the Chinese remainder theorem. Demonstrate the Chinese remainder 8 CO3 L2
theorem for n=341(11x31).
PART B
Answer any1 question(s)
Q.No Marks CO BT/CL
3 a What are the important characteristics of public key cryptosystems? In a 7 CO3 L2
public key system using RSA, intercept the cipher text C=10 with public key
e=5, n=35. What is the plain text.
b Consider a Diffie-Hellman scheme with a prime q=11 and a primitive root a=2, 8 CO3 L2
1. Show that 2 is a primitive root of 11
2. If user A has public key=9, what is A’s private key?
3. If user B has public key = 3, what is the secret key shared with A?
4 a What is digital signature? With a neat block diagram explain the concept of 8 CO3 L2
public key cryptosystem with authentication and Secrecy. Perform encryption
and decryption using RSA algorithm for p=11, q=13, e=17, M=7
b Users A and B use the Diffie-Hellman key exchange technique with a common 7 CO3 L2
prime q=19 and a primitive root a=10.
1. Show that 10 is a primitive root of 19
2. If user A has private key 5, what is A’s public key? If user B has private
key 5, what is B’s public key?
3. What is the shared secret key?
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