2. CAESA R CIPHE R 7 SOLUTION. Sinc e th e encipherin g shif t i s b 15 , th e decipherin g shif t is 2 6 1 5 = 11 . T o deciphe r w e ad d 11 alternately , w e ca n subtrac t 15 . Whether w e ad d o r subtract , w e wan t th e resultin g numbe r t o b e betwee n 1 an d 26 . Thus , w e ad d 1 1 wheneve r th e resul t i s les s tha n o r equa l t o 26 . Otherwise, w e subtrac t 15 : RXEWTG - 1 8 2 4 5 2 3 2 0 7 conver t letter s t o number s -+ 3 9 1 6 8 5 1 8 ad d 1 1 or subtrac t 1 5 ^ C I P H E R conver t number s t o letter s The plaintex t i s CIPHER . In Exampl e 2.2 , w e deciphere d bot h b y addin g 1 1 an d b y subtractin g 15. W e wil l see shortl y wh y bot h o f these method s ar e valid . Th e ciphertex t that appear s a t th e en d o f Chapte r 1 was enciphere d usin g a Caesa r Ciphe r with a n encipherin g shif t o f b = 17 . Befor e continuing , yo u shoul d deciphe r it. You ma y b e wonderin g wh y w e have spen t s o much tim e convertin g fro m letters t o numbers . I t ma y appea r tha t i t i s easier t o simpl y writ e dow n th e plain an d ciphe r alphabet s an d procee d withou t convertin g t o numbers . While tha t approac h ma y b e easie r fo r th e Caesa r Cipher , late r w e wil l encounter cryptographi c system s wher e workin g wit h number s i s essential . Thus, yo u shoul d vie w th e conversio n proces s a s practic e fo r futur e schemes . After decipherin g th e ciphertex t a t th e en d o f Chapte r 1 , yo u ma y hav e several concerns . First , translatin g fro m letter s t o number s an d vic e vers a i s tedious an d tim e consuming . I t woul d tak e minute s o r hour s t o enciphe r o r decipher a lengthy message . Fortunately , w e do not hav e to d o it b y hand w e can us e compute r program s t o d o thi s tim e consumin g wor k fo r us . Second , you ma y no t b e absolutel y certai n abou t ho w t o manipulat e al l the differen t numbers. Eve n i f yo u wer e abl e t o deciphe r th e introductor y message , yo u may b e unclea r abou t wh y yo u di d wha t yo u did . Mathematics , an d i n particular numbe r theory , wil l provid e th e answer . W e wil l leav e cryptolog y for a bi t i n orde r t o lear n abou t numbe r theory . Thi s wil l allo w u s t o pu t the discussio n o f th e Caesa r Ciphe r o n a mor e secur e footing . Exercises. 1. Writ e th e plai n an d ciphe r alphabet s fo r a n encipherin g shif t o f b = 7 . (a) Us e thes e alphabet s t o enciphe r th e plaintext : THI S I S EAS Y (b) Us e thes e alphabet s t o deciphe r th e ciphertext : OPKKL U (c) Us e thes e alphabet s t o verif y tha t th e decipherin g shif t i s b = 19 . 2. Fin d th e numeri c cod e fo r th e wor d COMPUTER . 3. Decod e 1 3 5 1 9 1 9 1 7 5 . Tha t is , determin e th e Englis h wor d represented b y th e numbers . 4. Us e a Caesa r Ciphe r wit h a n encipherin g shif t o f b = 5 t o enciphe r NUMBER.
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