2. CAESA R CIPHE R 5 letters i s decoding. I n thi s context , th e wor d "code " doe s no t connot e some - thing secre t o r hidden . Whe n w e represent th e wor d EXAMPL E with th e strin g of number s i n (8) , w e ar e no t tryin g t o obscur e th e plaintext . Rather , w e use number s t o mak e th e encipherin g proces s easier . Frequently , th e word s "code" an d "cipher " ar e use d a s synonyms indeed , w e use d the m inter - changeably i n Chapte r 1 . Fro m no w on , w e wil l b e carefu l t o distinguis h between them . To enciphe r EXAMPL E usin g a shif t o f b = 3 , w e ad d 3 t o eac h o f th e numbers i n (7) . Afte r doin g thi s addition , w e us e (6 ) t o translat e fro m numbers t o letters : (9) 8 2 7 4 1 6 1 9 1 5 8 ^ H7DPS0H . Notice tha t (9 ) contain s a questio n mar k correspondin g t o th e numbe r 27 , which doe s no t represen t an y letter . Earlie r whe n w e created a ciphe r alpha - bet, onc e w e reache d Z we starte d ove r wit h A . Mathematically, thi s mean s that onc e w e reac h 26 , w e begi n agai n wit h 1 . Thus , 2 7 = 1 . Makin g thi s replacement i n (9 ) give s u s 8 1 4 1 6 1 9 1 5 8 ^ HADPSOH . In summar y then , EXAMPLE— 5 2 4 1 1 3 1 6 1 2 5 conver t letter s t o number s -^ 8 2 7 4 1 6 1 9 1 5 8 ad d 3 ^ 8 1 4 1 6 1 9 1 5 8 adjus t downwar d H A D P S O H conver t number s t o letter s The ciphertex t i s HADPSOH , which agree s wit h wha t w e foun d earlie r i n (3) . We us e exactl y th e sam e proces s t o decipher . Fo r example , suppos e w e know tha t th e ciphertex t AOLVY F was enciphere d usin g a n encipherin g shif t of 6 = 7 . W e begi n b y convertin g fro m letter s t o numbers : (10) AOLVY F ^ 1 1 5 1 2 2 2 2 5 6 . To deciphe r w e ad d 2 6 7 = 1 9 t o eac h o f th e number s i n (10) : (11) 2 0 3 4 3 1 4 1 4 4 25 . Unfortunately, fou r o f th e number s i n (11 ) ar e greate r tha n 26 . Befor e w e can recove r th e plaintext , w e have t o rewrit e (11 ) usin g number s i n the rang e from 1 to 26 . W e d o thi s b y makin g th e associations : (12) 2 7 = 1 , 2 8 = 2 , 2 9 = 3 , 3 0 = 4 , 3 1 = 5 , 3 2 = 6 , .. . For th e number s i n (11 ) w e nee d t o continu e th e lis t i n (12 ) unti l w e reac h 44. Alternately , not e tha t th e association s i n (12 ) ar e mad e i n th e followin g way. Whe n a numbe r k i s greate r tha n 26 , 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 (11 ) an d recove r th e
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