2. CAESA R CIPHE R
7
S O L U T I O N .
Sinc e th e encipherin g shif t i s b 15, th e decipherin g shif t
is 2 6 15 = 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 11wheneve 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 - 18 2 4 5 2 3 2 0 7 conver t letter s t o number s
-+ 3 9 16 8 5 18 ad d 11o r subtrac t 15
^ 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 11an d b y subtractin g
15. W e wil l se e shortl y wh y bot h o f thes e method s ar e valid . Th e ciphertex t
tha t 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 hav e spen t s o muc h tim e convertin g fro m
letters t o numbers . I t ma y appea r tha t i t i s easie r 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 i t 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 th e 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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