Define Euler's Phi function and find

Find 5^24(mod using the repeated squaring algorithm.

Describe the Merkle-Damgard method and the Davies-Meyer method. Also explain how these methods can be used to construct cryptographic hash functions.

Explain the key expansion process in AES-128.

Encrypt the plain text

"INDIANEEDSWOMENLIKEYOUTOWINYYY",

using the permutation cipher with 53124 as the key.

Compute the discrete logarithm and the discrete antilogarithm to the base 3 in Z^*17.

Explain the key-scheduling algorithm of the RC4 cipher along with its pseudocode.

Use the Miller-Rabin test to check whether 1889 is composite or not.

Decrypt the ciphertext C which is obtained by the RSA system with public key 33).

Find the inverse of(l in R 1 x x Also, is 1 x x^4 invertible in R Give reasons for your answer.

Find the result of multiplying

x x^2 x x with

x x^4

mod x x^3 x^4 x^8 in F2[x].

Solve the equation 1O^X 52(mod 59) using the Baby-Step Giant-Step algorithm.

6. Which of the following statements are True, and which are False? Give reasons for your answers.

The symmetric key cryptosystems have no drawbacks.

There is no field with characteristic 9.

Diffusion is achieved by using an S-box in DES.

257 is a strong prime.

Given a sequence of bits, the frequency test suffices to check the randomness of the sequence.