4
2. CAESA R CIPHE R
plaintext equivalen t i n th e 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 us e (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 A B C ,
while th e plai n alphabe t belo w i t begin s wit h X Y Z:
/r
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
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 tha t 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 letter s i n th e 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; t o 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, th e 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 associat e a number :
A B C D E F G H I J K L M
1 2 3 4 5 6 7 8 9 10 1112 13
(6)
N O P Q R S T U V W X Y Z
14 15 16 17 18 19 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 th e letter s i n
the alphabet . Sinc e A i s the firs t letter , i t i s assigne d th e numbe r 1, an d s o
on. Fo r th e wor d EXAMPLE , we mak e th e followin g associations :
(7)EXAMPL E ^ 5 2 4 1 13 16 12 5 .
When w e associat e th e number s
(8) 5 2 4 1 13 16 12 5
with th e plaintex t wor d EXAMPLE , we call the strin g i n (8 ) th e numeri c code
associated wit h th e plaintext . Th e proces s o f changin g fro m letter s t o 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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