CHAPTER 2
Caesar Ciphe r
Most o f the cryptographi c system s that w e will study ar e replacement o r
substitution ciphers, whic h means that eac h letter o f the alphabe t i s replaced
by another . Ther e ar e man y differen t way s t o desig n a replacemen t cipher .
One wa y t o describ e suc h a syste m i s t o lis t th e correspondence s betwee n
the plai n an d ciphe r alphabets . W e usuall y d o thi s i n th e followin g way :
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
cipher: Q W E R T Y U I O P A S D F G H J K L Z X C V B N M
To encipher a message using the alphabet s liste d i n (1), we locate each lette r
of th e plaintex t i n th e to p ro w an d fin d it s replacemen t lette r i n th e ro w
below. Fo r example , eac h occurrenc e o f the plaintex t lette r E is replaced b y
the ciphertex t lette r T . Hence, correspondin g t o th e plaintex t wor d EXAMPLE
is th e ciphertex t wor d TBQDHST . To decipher , w e revers e th e process . Tha t
is, w e locate eac h ciphertex t lette r i n th e botto m ro w an d find it s plaintex t
equivalent i n th e to p row . Applyin g thi s procedur e t o th e ciphertex t wor d
KQFRGD, we determine tha t th e plaintex t wor d i s RANDOM.
The arrangemen t o f th e letter s i n (1) i s no t a s rando m a s i t ma y first
appear. Th e letter s i n th e ciphe r alphabe t ar e i n th e orde r i n whic h the y
occur o n a standar d compute r keyboard . A s lon g a s on e ha s acces s t o a
keyboard, i t i s no t difficul t t o reproduc e th e correc t sequence .
We now turn ou r attentio n t o replacemen t system s tha t ar e mor e math -
ematical tha n th e on e in (1). On e of the oldes t suc h schemes was reportedl y
used b y Juliu s Caesar ; i t i s calle d th e Caesar Cipher i n hi s honor . T o us e
this method , w e selec t a numbe r 6 , called th e enciphering shift. Th e ciphe r
alphabet i s obtaine d b y shiftin g th e plai n alphabe t b places. W e first illus -
trate th e Caesa r Ciphe r fo r b 3, whic h wa s th e shif t tha t Juliu s Caesa r
selected. Sinc e th e encipherin g shif t i s b = 3 , w e begin th e ciphe r alphabe t
with D . When w e reach Z , we start ove r wit h A . Thus, w e have:
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
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
Observe tha t whe n w e use (2 ) t o enciphe r EXAMPLE , we ge t
(3) HADPSOH .
Just a s i n (1), t o deciphe r a tex t tha t ha s bee n enciphere d usin g (2) ,
we look u p a ciphertex t lette r i n the botto m ro w an d find it s correspondin g
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http://dx.doi.org/10.1090/mawrld/025/02
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