Question: (3) Let the elliptic curve & bey' =a +r + 6 (mod 11). (a) Given the point o = (2, 7) on the elliptic curve

(3) Let the elliptic curve & bey' =a +r + 6 (mod 11). (a) Given the point o = (2, 7) on the elliptic curve &, calculate 20 and 30. 2 marks (b) Consider the elliptic curve ElGamal cryptosystem. Let the private key be s = 7. (i) What is the public key? (Hint: You don't need to include the known information &, p, a in the public key, but have to calculate B = so. ) 2 marks (ii) Encoding: Suppose the text has been converted to a point = (10,9) on E. Choose the random number k = 3. What are the points (or numbers) to be transmitted? 2 marks (iii) Decoding: When receiving information from (ii), how to recover the original text? 1 mark

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