CHAPTER 2 Caesar Ciphe r Most of the cryptographic system s that w e will study ar e replacement o r substitution ciphers, whic h means that eac h letter of the alphabet i s replaced by another . Ther e ar e man y differen t way s to 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 usually d o this i n the 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 alphabets listed in (1) , we locate each letter 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, corresponding t o the plaintext wor d EXAMPLE is the ciphertex t wor d TBQDHST . To decipher, w e reverse th e process . Tha t is, we locate eac h ciphertex t lette r i n the 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 not difficul t t o reproduc e th e correc t sequence . We now turn ou r attentio n t o replacement system s that ar e more math - ematical than th e one 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 select a numbe r 6 , called th e enciphering shift. Th e ciphe r alphabet i s obtained 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 , we 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 get (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 up a ciphertex t lette r i n the botto m ro w and find it s correspondin g 3 http://dx.doi.org/10.1090/mawrld/025/02
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