In the elliptic curve E(1, 2) over the GF(11) field: a. Find the equation of the curve. b. Find all points on the curve and make a figure similar to Figure 10.14. c. Generate public and private keys for Bob. d. Choose a point on the curve as a plaintext for Alice. e. Create ciphertext corresponding to the plaintext in part d for Alice

Example 10.14 Define an elliptic curve E 3(1.1). The equation is 22 - 2 + x + 1 and the calculation is done modulo 13. Points on the curve can be found as shown in Figure 10.14. Figure 10.14 Points on an elliptic curve ower GF(p) 12 11 8 (0, 1) (0,12) (1,4) (1,9) (4,2) (4.11) (5.1) (5.12) (7.0) (7,0) (8, 1) (8.12) (10,6) (10,7) (11.2) (11, 11) (12,5) (12,8) Points tom- 4 3 0 1 2 3 4 5 6 7 8 9 10 11 12 Graph Example 10.14 Define an elliptic curve E 3(1.1). The equation is 22 - 2 + x + 1 and the calculation is done modulo 13. Points on the curve can be found as shown in Figure 10.14. Figure 10.14 Points on an elliptic curve ower GF(p) 12 11 8 (0, 1) (0,12) (1,4) (1,9) (4,2) (4.11) (5.1) (5.12) (7.0) (7,0) (8, 1) (8.12) (10,6) (10,7) (11.2) (11, 11) (12,5) (12,8) Points tom- 4 3 0 1 2 3 4 5 6 7 8 9 10 11 12 Graph