. The Bell System technical journal . nce the only choice of indices is TiT~iTx = Ti. Thus the expansion of a general cipher into a sum of such simple trans-formations also exhibits it as a sum of pure ciphers. An examination of the example of a pure cipher shown in Fig. 4 discloses COMMUNICATION rilEORY OF SECRECY SYSTEMS 675 certain properties. The messages fall into certain subsets which we will callresidue classes, and the possible cryi)tograms are divided into correspondingresidue classes. There is at least one line from each message in a class toeach cryptogram in the corresponding class
. The Bell System technical journal . nce the only choice of indices is TiT~iTx = Ti. Thus the expansion of a general cipher into a sum of such simple trans-formations also exhibits it as a sum of pure ciphers. An examination of the example of a pure cipher shown in Fig. 4 discloses COMMUNICATION rilEORY OF SECRECY SYSTEMS 675 certain properties. The messages fall into certain subsets which we will callresidue classes, and the possible cryi)tograms are divided into correspondingresidue classes. There is at least one line from each message in a class toeach cryptogram in the corresponding class, and no line between classeswhich do not correspond. The number of messages in a class is a divisor ofthe total number of keys. The number of lines in parallel from a messageM to a cryptogram in the corresponding class is equal to the number ofkeys divided by the number of messages in the class containing the message(or cryptogram). It is shown in the appendix that these hold in general forpure ciphers. Summarized formally, we have:. CRYPTOGRAM RESIDUE CLASSES ] PURE SYSTEMFig. 4—Pure system. Theorem 3: In a pure system the messages can be divided into a set of residueclasses Ci , C2, ■ ■ ■, Cs and the cryptograms into a correspondingset of residue classes Ci , C2 , • ■ ■ ,Ca with the following properties: (1) The message residue classes are mutually exclusive and col-lectively contain all possible messages. Similarly for thecryptogram residue classes. (2) Enciphering any message in d with any key produces acryptogram in d . Deciphering any cryptogram in C,- zvithany key leads to a message in d . (3) The number of messages in d , say <fi , is equal to the numberof cryptograms in d and is a divisor of k the number of keys. 076 BELL SYSTEM TECHNICAL JOURNAL (4) Each message in d can be enciphered into each cryptogramin d by exactly k/(pi different keys. Similarly for importance of the concept of a pure cipher (and the reason for thename) lies in
Size: 1503px × 1663px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
