6
2. CAESA R CIPHE R
plaintext:
AOLVYF - 1 15 12 2 2 2 5 6 conver t letter s t o number s
- 2 0 3 4 3 1 4 1 4 4 2 5 ad d 19
20 8 5 15 18 2 5 adjus t downwar d
^ T H E O R Y conver t number s t o letter s
In the exampl e above , we knew that th e ciphertex t wa s enciphered usin g
an encipherin g shif t o f b = 7 . W e deciphere d b y usin g a decipherin g shif t o f
b = 19; that is , w e adde d 19. Ther e i s a n alternat e approac h tha t w e coul d
have taken . Instea d o f addin g 19, we could hav e subtracte d 7 :
. AOLVY F - ^ 1 15 12 2 2 2 5 6 conver t letter s t o number s
(13)x
- - 6 8 5 15 18 - 1 subtrac t 7
There ar e tw o negativ e number s i n (13). Sinc e subtractin g i s lik e shiftin g
backwards,
1-»A, O ^ Z , -1-»Y, -2*-X , . . . .
In othe r words ,
(14) 0 = 26 , - 1 = 25 , - 2 = 24 , . . . .
For th e number s i n (13), we need t o continu e th e lis t i n (14) unti l w e reac h
—6. Alternately , not e that th e association s i n (14) ar e made in the followin g
way. Whe n a numbe r k i s les s tha n 0 , w e associat e i t wit h th e numbe r
—k + 26. Wit h thi s observatio n i t i s eas y t o rewrit e (13) an d recove r th e
plaintext:
AOLVYF— 1 1 5 1 2 2 2 2 5 6 conver t letter s t o number s
—•-6 8 5 15 18 - 1 subtrac t 7
^ 2 0 8 5 15 18 2 5 adjus t upwar d
* T H E 0 R Y conver t number s t o letter s
EXAMPLE
2.1. Us e a Caesa r Ciphe r wit h a n encipherin g shif t o f b = 16
to enciphe r SHIFT .
SOLUTION.
W e conver t fro m letter s t o numbers , ad d 16, make th e nec -
essary adjustments , an d conver t bac k t o letters :
SHIFT— 19 8 9 6 2 0 conver t letter s t o number s
- 3 5 2 4 2 5 2 2 3 6 ad d 16
9 2 4 2 5 2 2 10 adjus t downwar d
I X Y V J conver t number s t o letter s
The ciphertex t i s IXYVJ .
EXAMPLE
2.2 . Deciphe r th e ciphertex t RXEWT G that wa s enciphered us -
ing a Caesa r Ciphe r wit h a n encipherin g shif t o f b = 15.
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