Decrypt the ElGamal ciphertext presented in Table 7.4. The parameters of the system are p= 31847 , = 5, = 18074. Each element of Zn represents three alphabetic characters as in Exercise 6.12

The plaintext was taken from "The English Patient", by Michael Ondaatje, Alfred A. Knopf, Inc., New York, 1992.

Table 7.4

(3781, 14409) (31552, 3930) (27214, 15442) (5809, 30274)

(5400, 31486) (19936, 721) (27765, 29284) (29820, 7710)

(31590, 26470) (3781, 14409) (15898, 30844) (19048, 12914)

(16160, 3129) (301, 17252) (24689, 7776) (28856, 15720)

(30555, 24611) (20501, 2922) (13659, 5015) (5740, 31233)

(1616, 14170) (4294, 2307) (2320, 29174) (3036, 20132)

(14130, 22010) (25910, 19663) (19557, 10145) (18899, 27609)

(26004, 25056) (5400, 31486) (9526, 3019) (12962, 15189)

(29538, 5408) (3149, 7400) (9396, 3058) (27149, 20535)

(1777, 8737) (26117, 14251) (7129, 18195) (25302, 10248)

(23258, 3468) (26052, 20545) (21958, 5713) (346, 31194)

(8836, 25898) (8794, 17358) (1777, 8737) (25038, 12483)

(10422, 5552) (1777, 8737) (3780, 16360) (11685, 133)

(25115, 10840) (14130, 22010) (16081, 16414) (28580, 20845)

(23418, 22058) (24139, 9580) (173, 17075) (2016, 18131)

(19886, 22344) (21600, 25505) (27119, 19921) (23312, 16906)

(21563, 7891) (28250, 21321) (28327, 19237) (15313, 28649)

(24271, 8480) (26592, 25457) (9660, 7939) (10267, 20623)

(30499, 14423) (5839, 24179) (12846, 6598) (9284, 27858)

(24875, 17641) (1777, 8737) (18825, 19671) (31306, 11929)

(3576, 4630) (26664, 27572) (27011, 29164) (22763, 8992)

(3149, 7400) (8951, 29435) (2059, 3977) (16258, 30341)

(21541, 19004) (5865, 29526) (10536, 6941) (1777, 8737)

(17561, 11884) (2209, 6107) (10422, 5552) (19371, 21005)

(26521, 5803) (14884, 14280) (4328, 8635) (28250, 21321)

(28327, 19237) (15313, 28649)