668 BELL SYSTEM TECHNICAL JOURNAL 



The matrix a,7 is the key, and deciphering is performed with the inverse 

 matrix. The inverse matrix will exist if and only if the determinant | 0,7 | 

 has an inverse element in the ring. 



7. The Playfair Cipher. 



This is a particular type of digram substitution governed by a mixed 25 

 letter alphabet written in a 5 x 5 square. (The letter / is often droj)ped in 

 cryptographic work — it is very infrequent, and when it occurs can be re- 

 placed by /.) Suppose the key square is as shown below: 



L Z Q C P 



A G N U 



R D MI F 



K Y H V S 



X B T E W 



The substitute for a digram AC, for example, is the pair of letters at the 

 other corners of the rectangle defined by .1 and C, i.e., LO, the L taken first 

 since it is above .1 . If the digram letters are on a horizontal line as RI, one 

 uses the letters to their right DF; RF becomes DR. If the letters are on a 

 vertical line, the letters below them are used. Thus PS becomes UW. If 

 the letters are the same nulls may be used to separate them or one may be 

 omitted, etc. 



8. Multiple Mi.xed Alphabet Substitution. 



In this cipher there are a set of d simple substitutions which are used 

 in sequence. If the period d is four 



mi m-i niz mi W5 m^ • • • 



becomes 



fi(mi) /2(m2) fsinis) fi{nh) fi{m^) /.(we) • • • 



9. Autokey Cipher. 



A Vigenere type system in which either the message itself or the resulting 

 cryptogram is used for the "key" is called an autokey cipher. The encipher- 

 ment is started with a "priming key" (which is the entire key in our sense) 

 and continued with the message or cryptogram displaced by the length of 

 the priming key as indicated below, where the priming key is COMET. 

 The message used as "key": 



Message 5 ENDS U P P L I E S ••• 



Key COMETS ENDS UP •■■ 



Cryptogram USZHLMTCOA Y H 



