We give an example of the EIGamal Cryptosystem implemented in F33. The poly- nomial a +...

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We give an example of the EIGamal Cryptosystem implemented in F33. The poly- nomial a + 2? + 1 is irreducible over Z3[r] and hence Z3[r]/( +2x2 +1) is the field F3. We can associate the 26 letters of the alphabet with the 26 nonzero field elements, and thus encrypt ordinary text in a convenient way. We will use a lexicographic ordering of the (nonzero) polynomials to set up the correspondence. ТABLE 6.3 EIGamal Ciphertext (31552, 3930) (19936, 721) (31590, 26470) (3781, 14409) (301, 17252) (30555, 24611) (20501, 2922) (4294, 2307) (14130, 22010) (25910, 19663) (26004, 25056) (5400, 31486) (3149, 7400) (27214, 15442) (5809, 30274) (27765, 29284) (29820, 7710) (15898, 30844) (19048, 12914) (28856, 15720) (5740, 31233) (3036, 20132) (19557, 10145) (18899, 27609) (12962, 15189) (27149, 20535) (25302, 10248) (346, 31194) (25038, 12483) (11685, 133) (16081, 16414) (28580, 20845) (2016, 18131) (19886, 22344) (21600, 25505) (27119, 19921) (23312, 16906) (3781, 14409) (5400, 31486) (16160, 3129) (24689, 7776) (13659, 5015) (2320, 29174) (1616, 14170) (9526, 3019) (9396, 3058) (29538, 5408) (1777, 8737) (23258, 3468) (8836, 25898) (10422, 5552) (26117, 14251) (7129, 18195) (26052, 20545) (8794, 17358) (1777, 8737) (25115, 10840) (14130, 22010) (23418, 22058) (24139, 9580) (21958, 5713) (1777, 8737) (3780, 16360) (173, 17075) (21563, 7891) (24271, 8480) (26592, 25457) (30499, 14423) (5839, 24179) (24875, 17641) (1777, 8737) (28250, 21321) (28327, 19237) (15313, 28649) (9660, 7939) (12846, 6598) (10267, 20623) (9284, 27858) (18825, 19671) (31306, 11929) (26664, 27572) (27011, 29164) (22763, 8992) (2059, 3977) (10536, 6941) (10422, 5552) (4328, 8635) (3576, 4630) (3149, 7400) (8951, 29435) (21541, 19004) (5865, 29526) (17561, 11884) (2209, 6107) (14884, 14280) (28327, 19237) (15313, 28649) (16258, 30341) (1777, 8737) (19371, 21005) (28250, 21321) (26521, 5803) This correspondence is as follows: A 1 В C æ +1 2x +1 x +1 x2 + x +1 x2 + 2x +1 2x +1 2x2 + r +1 2x2 + 2x +1 D E x + 2 F G H 2x + 2 I x + x 2 + 2x 2x2 J x + 2 x2 + a +2 x2 + 2x + 2 2x + 2 2x2 + x + 2 22 + 2x + 2 K M N Q # 2x2 + r + 2.x2 + 2x S U V W Y 11 in an EIGamal Cryptosystem; then 3 = x+2. Suppose Bob uses a = x and a Show how Bob will decrypt the following string of ciphertext: (K,H)(P,X)(N,K)(H,R)(T,F) (V,Y) (E,H) (F,A) (T,W) (J,D)(U,J) 分分付付 艹 We give an example of the EIGamal Cryptosystem implemented in F33. The poly- nomial a + 2? + 1 is irreducible over Z3[r] and hence Z3[r]/( +2x2 +1) is the field F3. We can associate the 26 letters of the alphabet with the 26 nonzero field elements, and thus encrypt ordinary text in a convenient way. We will use a lexicographic ordering of the (nonzero) polynomials to set up the correspondence. ТABLE 6.3 EIGamal Ciphertext (31552, 3930) (19936, 721) (31590, 26470) (3781, 14409) (301, 17252) (30555, 24611) (20501, 2922) (4294, 2307) (14130, 22010) (25910, 19663) (26004, 25056) (5400, 31486) (3149, 7400) (27214, 15442) (5809, 30274) (27765, 29284) (29820, 7710) (15898, 30844) (19048, 12914) (28856, 15720) (5740, 31233) (3036, 20132) (19557, 10145) (18899, 27609) (12962, 15189) (27149, 20535) (25302, 10248) (346, 31194) (25038, 12483) (11685, 133) (16081, 16414) (28580, 20845) (2016, 18131) (19886, 22344) (21600, 25505) (27119, 19921) (23312, 16906) (3781, 14409) (5400, 31486) (16160, 3129) (24689, 7776) (13659, 5015) (2320, 29174) (1616, 14170) (9526, 3019) (9396, 3058) (29538, 5408) (1777, 8737) (23258, 3468) (8836, 25898) (10422, 5552) (26117, 14251) (7129, 18195) (26052, 20545) (8794, 17358) (1777, 8737) (25115, 10840) (14130, 22010) (23418, 22058) (24139, 9580) (21958, 5713) (1777, 8737) (3780, 16360) (173, 17075) (21563, 7891) (24271, 8480) (26592, 25457) (30499, 14423) (5839, 24179) (24875, 17641) (1777, 8737) (28250, 21321) (28327, 19237) (15313, 28649) (9660, 7939) (12846, 6598) (10267, 20623) (9284, 27858) (18825, 19671) (31306, 11929) (26664, 27572) (27011, 29164) (22763, 8992) (2059, 3977) (10536, 6941) (10422, 5552) (4328, 8635) (3576, 4630) (3149, 7400) (8951, 29435) (21541, 19004) (5865, 29526) (17561, 11884) (2209, 6107) (14884, 14280) (28327, 19237) (15313, 28649) (16258, 30341) (1777, 8737) (19371, 21005) (28250, 21321) (26521, 5803) This correspondence is as follows: A 1 В C æ +1 2x +1 x +1 x2 + x +1 x2 + 2x +1 2x +1 2x2 + r +1 2x2 + 2x +1 D E x + 2 F G H 2x + 2 I x + x 2 + 2x 2x2 J x + 2 x2 + a +2 x2 + 2x + 2 2x + 2 2x2 + x + 2 22 + 2x + 2 K M N Q # 2x2 + r + 2.x2 + 2x S U V W Y 11 in an EIGamal Cryptosystem; then 3 = x+2. Suppose Bob uses a = x and a Show how Bob will decrypt the following string of ciphertext: (K,H)(P,X)(N,K)(H,R)(T,F) (V,Y) (E,H) (F,A) (T,W) (J,D)(U,J) 分分付付 艹

Answer rating: 100% (QA)

Here we just need to show that 1 r 2x 1 is irreducible over L3 Zar 0 r 2x... View the full answer