6 2. CAESA R CIPHE R plaintext: AOLVYF - 1 1 5 1 2 2 2 2 5 6 conver t letter s t o number s - 2 0 3 4 3 1 4 1 4 4 2 5 ad d 1 9 20 8 5 1 5 1 8 2 5 adjus t downwar d ^ T H E O R Y conver t number s t o letter s In the example above, we knew that th e ciphertext wa s enciphered usin g an encipherin g shif t o f b = 7 . W e deciphered b y usin g a deciphering shif t o f b = 19 that is , we added 19 . Ther e i s an alternat e approac h tha t w e coul d have taken. Instea d o f adding 19 , we could hav e subtracte d 7 : . AOLVY F - ^ 1 1 5 1 2 2 2 2 5 6 conver t letter s t o number s (13)x - - 6 8 5 1 5 1 8 - 1 subtrac t 7 There ar e tw o negativ e number s i n (13) . Sinc e subtractin g i s lik e shiftin g backwards, 1-»A, O ^ Z , -1-»Y , -2*-X , ... . In othe r words , (14) 0 = 26 , - 1 = 25 , - 2 = 24 , ... . For th e number s i n (13) , we need t o continu e th e lis t i n (14 ) unti l we reac h —6. Alternately , not e that th e associations in (14 ) are made in the followin g way. Whe n a numbe r k i s les s tha n 0 , w e associat e i t wit h th e numbe r —k + 26. Wit h thi s observatio n i t i s eas y t o rewrit e (13 ) an d recove r th e plaintext: AOLVYF— 1 151 2 2 2 2 5 6 conver t letter s t o number s —•-6 8 5 1 5 1 8 - 1 subtrac t 7 ^ 2 0 8 5 1 5 1 8 2 5 adjus t upwar d * T H E 0 R Y conver t number s t o letter s EXAMPLE 2.1 . Us e a Caesa r Ciphe r wit h a n encipherin g shif t o f b = 16 to enciphe r SHIFT . SOLUTION. W e conver t fro m letter s t o numbers , ad d 16 , make th e nec - essary adjustments , an d conver t bac k t o letters : SHIFT— 19 8 9 6 2 0 conver t letter s t o number s - 3 5 2 4 2 5 2 2 3 6 ad d 1 6 9 2 4 2 5 2 2 1 0 adjus t downwar d I X Y V J conver t number s t o letter s The ciphertex t i s IXYVJ . EXAMPLE 2.2 . Deciphe r th e ciphertex t RXEWT G that wa s enciphered us - ing a Caesa r Ciphe r wit h a n encipherin g shif t o f b = 15 .
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