Bsc CSIT Semester 5 – Cryptography – Unit 3. Asymmetric Ciphers

Given p = 61, q = 53. Calculate the public key, private key, and encrypt the message “42”. Then, decrypt the ciphertext to retrieve the original message.

Find the value of 7^2019 MOD 13 using Fermat’s Little theorem. Define Euler totient function with an example.

Show that Z 5is a field. John publishes the ElGamal public key (q, α, YA) =(101, 2, 14). Jane desired to send the secret message CSIT to John. Using the equivalence A = 0, B=1, … , Z=25, encrypt the message using John’s public key. Use a random number k = 4.

Define discrete logarithms. How key generation, encryption and decryption is done in RSA. In a RSA cryptosystem, given p=13 and q=7, determine private key, public key and perform encryption and decryption for the text M=”hi” using 0 to 25 for letters from a to z.

How Miller Rabin test is used for primality testing? Show whether the number 561 passes the test.

How does meet in middle attack work in Diffie Helman key exchange protocol? Explain.

Why do we need discrete logarithm? Illustrate with an example. Consider a Diffie-Hellman scheme with a common prime p = 13 between user A and user B. Suppose public key of A is 10 and public key of B is 8. Now determine their private keys and shared secret key. Select any valid primitive root of 13.

Find the multiplicative inverse of polynomial {95} using extended euclidean Algorithm.

Illustrate the man in middle attack in Diffie - Hellman key exchange protocol. Assume the prime number be 19 and 10 as its primitive root. Select 5 as private key and 4 as random integer. Find the cipher text of M = 2 using Elgamal crypto system.

State Fermat’s theorem with example. What is the implication of discrete logarithm?

What is the condition for two integers, x and y, to be relatively prime? Find whether 61 is prime or not using Miller-Rabin algorithm.

Why do we need discrete logarithm over normal logarithm? Find out whether 3 is primitive root of 7 or not.