4 2. CAESA R CIPHE R plaintext equivalen t i n the to p row . Alternately , w e can switc h th e orde r o f the alphabet s i n (2) : cipher: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C plain: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z To use (4 ) mor e efficiently , w e rearrange th e orde r o f the letter s s o that th e top ro w begin s wit h A , not D . For eac h alphabe t i n (4 ) w e mov e th e fina l three letter s t o th e front . Thus , th e ciphe r alphabe t begin s wit h ABC , while the plai n alphabe t belo w i t begin s wit h X Y Z: cipher: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (5)N/r plain: X Y Z A B C D E F G H I J K L M N O P Q R S T U V W If yo u stud y (5 ) a bit , yo u wil l se e that th e botto m (plain ) alphabe t i s th e top (cipher ) alphabe t shifte d b y 2 3 places . Th e decipherin g schem e i s a Caesar Ciphe r wit h a shif t o f b = 23 . The las t sentenc e o f th e previou s paragrap h i s ver y important . Whe n we enciphe r usin g a Caesa r Ciphe r wit h a n encipherin g shif t o f b = 3 , w e decipher usin g a Caesa r Ciphe r wit h a decipherin g shif t o f b = 23 . Ther e is a n obviou s relationshi p betwee n th e encipherin g an d decipherin g shifts . Specifically, thei r su m i s 26, which i s the numbe r o f letters i n the alphabet . In general , w e describ e th e Caesa r Ciphe r a s follows . T o encipher , w e shift th e alphabe t b places to decipher , w e shift th e alphabe t 2 6 6 places. There ar e severa l advantage s o f thi s system . First , th e schem e i s easil y implemented th e use r onl y ha s t o remembe r th e shif t numbe r b. Mor e importantly, the processes of enciphering and deciphering are identical. And , in fact , th e decipherin g ke y i s related t o th e encipherin g key . Mathematically, w e carr y ou t th e Caesa r Ciphe r i n th e followin g way . With eac h lette r w e associate a number : A B C D E F G H I J K L M 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 (6) N O P Q R S T U V W X Y Z 14 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 Notice tha t th e number s i n (6 ) correspon d t o th e position s o f the letter s i n the alphabet . Sinc e A i s the firs t letter , i t i s assigned th e numbe r 1 , and s o on. Fo r th e wor d EXAMPLE , we make th e followin g associations : (7)EXAMPL E ^ 5 2 4 1 1 3 1 6 1 2 5 . When w e associate th e number s (8) 5 2 4 1 1 3 1 6 1 2 5 with the plaintex t wor d EXAMPLE , we call the strin g i n (8 ) the numeri c code associated wit h th e plaintext . Th e proces s of changing fro m letter s to num - bers i s calle d coding r similarly, th e proces s o f changin g fro m number s t o
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