(This is Problem 6.9, 2nd edition, or 7.9 4th edition) Decrypt the ElGamal ciphertext presented in Table 6.3 of page 270 (2nd edition) or Table 7.4 of page 305 (4th edition)

Cipher text-------------------------------

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

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The parameters of the system are p=31847, =5, a=7899 and = 18074. Each element of Zn represents three alphabetic characters encoded as in the following examples:

DOG 3262 +1426+6 = 2398 CAT 2262+026+19 = 1371 ZZZ 25262 +2526+25 = 17575

You will need to invert this process as the final step in your program.