1.Which of the following statements are true, and which are false? Justify your answers. IP in DES does not contribute to security. A block cipher in CTR mode of operation can be used as a stream cipher. An affine cipher is a special case of a simple substitution cipher. The probability of success in finding the second pre-image of a hash is higher than that of finding a collision for the hash. Any finite field is isomorphic to Zp, for some prime p.

2.(a) Generate the first 5 terms of the Blum-Blum-Shub sequence, given p 19, q 23 and initial seed 15.
Is x^2 a field? Why, or why not? Suppose Bano chooses p 109. Check. that 6 is a primitive root modulo 109. Bano chooses the secret value x 40 and public key 7). Bano receives the pair 45) from Asha. Find the message.

3.(a) Describe the pseudo-random generation algorithm of RC4.
Starting from state such that 255-i, run PRGA for 3 steps.
Decrypt the following affine cipher. You are given information that the message starts with the word GOOD

NBBYR BQWXW N.

4.(a) If x^3 x 1 and x^3 x^2 x 1
are polynomials in use the extended Euclidean algorithm to find and in such that where is the gcd of and Explain the Birthday Paradox. Calculate the probability of two persons from a group of 5 being born on the same day of the week.

5.(a) Describe the toy block cipher with a block diagram for 1 round.

(ii) Decrypt the first round toy cipher 010110110111 with the following parameters:

key =110110111

S-box <img src='./qimages/12513-5a.jpg'>
Compute 5^13 (mod 43) using the repeated squaring algorithm.

6.(a) Suppose Asha wants to send the message =25 to Bano. She wants to sign the message using the RSA signature scheme, with parameters n e d 37. Find the signature of the message.

(ii) What information should Bano receive to be able to verify the signature Further, give the procedure for verifying Asha's signature.


(b) Find the multiplicative inverse of x^7 x^3 1 inF2[x] x^8 x^4 x^3 x 1