Question 1) In ElGamal , given the prime p=31:

a) Choose an appropriate e₁ and d, then calculate e₂.

b) Encrypt the message “HELLO”, use 00 to 25 for encoding. Use different blocks to make P<p.

c) Decrypt the ciphertext to obtain the plaintext.

Question 2)

i

In the Elliptic curve E(1,2) over the GF(11) field:

a) Find the equation of the curve.

b)Find all the points on the curve and make a figure similar to Figure 10.14.(In the Text book cryptography and network security Page 334 )

c) Generate public and private keys for Bob.

d)Choose a point on the curve as a plaintext for Alice.

e) Create cipher text corresponding to the plaintext in part d for Alice.

f) Decrypt the Ciphertext for Bob to find the plaintext sent by Alice